4 AO % LASTS oe P~ @ L Cg 2 "ili E 3 P = : : i NCHS 4 “© 72) < YJ k rd 5) n A Concurrent Validational Study of the NCHS General Well-Being Schedule U.S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE Public Health Service Health Resources Administration VITAL and HEALTH STATISTICS DATA EVALUATION AND METHODS RESEARCH Library of Congress Cataloging in Publication Data Fazio, Anthony F. A concurrent validational study of the NCHS’ general well-being schedule. (Vital and health statistics: Series 2, Data evaluation and methods research; no. 73) (DHEW publication; (HRA) 78-1347) Includes bibliographical references. Supt. of Doc. no.: HE20.6209:2/73 1. Depression, Mental—Testing. 2. General well-being schedule. I. Title. II. Series: United States. National Center for Health Statistics. Vital and health statistics: Series 2, Data evalu- ation and methods research; no. 73. III. Series: United States. Dept. of Health, Education, and Welfare. DHEW publication; no. (HRA) 78-1347. RA409.U45 no. 73 [RC537] 312°.07°23s [616.852] ISBN 0-8406-0105-0 77-608139 For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 Stock No. 017-022-00591-3 DATA EVALUATION AND METHODS RESEARCH Series 2 Number 73 A Concurrent Validational Study of the NCHS General Well-Being Schedule A comparative analysis of the concurrent validity of several self- report schedules in predicting interviewer’s assessment of depressed mood. DHEW Publication No. (HRA) 78-1347 U.S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE Public Health Service Health Resources Administration National Center for Health Statistics Hyattsville, Md. September 1977 NATIONAL CENTER FOR HEALTH STATISTICS DOROTHY P. RICE, Director ROBERT A. ISRAEL, Deputy Director JACOB J. FELDMAN, Ph.D., Associate Director for Analysis GAIL F. FISHER, Associate Director for the Cooperative Health Statistics System ELIJAH L. WHITE, Associate Director for Data Systems JAMES T. BAIRD, JR., Ph.D., Associate Director for International Statistics ROBERT C. HUBER, Associate Director for Management MONROE G. SIRKEN, Ph.D., Associate Director for Mathematical Statistics PETER L. HURLEY, Associate Director for Operations JAMES M. ROBEY, Ph.D., Associate Director for Program Development PAUL E. LEAVERTON, Ph.D., Associate Director for Research ALICE HAYWOOD, Information Officer DIVISION OF HEALTH EXAMINATION STATISTICS MICHAEL A. W. HATTWICK, M.D., Director HAROLD J. DUPUY, Ph.D., Psychological Adviser LINCOLN OLIVER, Chief, Psychological Statistics Branch ROBERT S. MURPHY, Chief, Survey Planning and Developing Branch Vital and Health Statistics-Series 2 No. 73 DHEW Publication No. (HRA) 78-1347 Library of Congress Catalog Card Number 77-608139 FOREWORD The National Health Survey Act of 1956 provided for the establishment and continuation of National Health Surveys to obtain informa- tion about the health status of the population in the United States. Subsequent legislative author- ity to collect and make available health statistics including data on the determinants of health is contained in Public Law 93-353, Section 306 (par. (b); item (1)). The responsibility for the development and conduct of that program is placed with the National Center for Health Statistics, a research-oriented statistical organiza- tion within the Health Resources Administration of the Public Health Service. The Health Exami- nation Survey is one of several different pro- grams employed by the National Center for Health Statistics (NCHS) to accomplish the objectives of the National Health Survey. It is used to collect data by drawing samples of the civilian noninstitutionalized population of the United States and undertakes to characterize the population under study by means of medical, dental, psychological, and nutritional examina- tions and various tests and measurements. In addition to the data collected by the examining, measuring, and testing procedures, a wide range of other data are collected concern- ing each of the sample persons examined. Therefore, it is possible to study a variety of potential relationships among the examination findings. Psychological components are included in Health Examination Surveys to provide a more complete assessment of the health and well- being of the U.S. population. They are em- bedded in an interdisciplinary approach in the study of mental health, psychological relation- ships with medical and nutritional conditions, growth, development, aging, and other aspects of health. Examination conditions and competing re- quirements for examination time dictate that each examination component must be specifi- cally designed to fit within these constraints. A long-range effort is underway to develop specific psychological examination procedures within an overall plan of psychological assessments that can be employed in the Health Examination Surveys. The General Well-Being (GWB) sched- ule was developed in the NCHS and, after pretesting' on 373 adults, was administered to over 6,900 adults as part of the national study of the Health and Nutrition Examination Sur- vey, which had begun in April 1971 and was completed in October 1975. The GWB schedule is a self-report instru- ment designed to assess selected aspects of self-representations of subjective well-being and distress. Questions and response options were formulated to provide indications of the presence, severity, or frequency of some symptoms that are generally considered impor- tant in clinical assessments of subjective well- being and distress. A report is being prepared on the rationale and some properties of the GWB schedule. This report presents some findings obtained from a research investigation conducted inde- pendently of the NCHS in terms of funding and of direct participation of its personnel. The major import of the findings from the analyses contained in this report are as follows: The GWB was slightly better than the other assessments used in this study in terms of concurrent validity in predicting inter- viewers’ ratings of depression among 195 college students. The GWB served as well in assessing depres- sive mood and anxiety states as did the other instruments which had been specifically and rigorously designed to measure these psycho- logical conditions. The extensive comparative analyses of the GWB depression and tension-anxiety sub- scales with other scales included in this study indicated that these subscales seem to measure the relevant properties of the psychological states or conditions for which they were designed, thus supporting the content meaning of these subscales. Harold J. Dupuy, Ph.D. Psychological Adviser Division of Health Examination Statistics National Center for Health Statistics CONTENTS Foreword Introduction Purpose of the Study Design of the Study Sources of the Major Data Elements The Minnesota Multiphasic Personality Inventory (MMPI) Psychiatric Symptoms Scale (PSS) The General Well-Being Schedule (GWB) Personal Interview Data Preparation Procedures we Demographic Characteristics General Population From Which the Sample Was Drawn The Study Sample Descriptive Psychological Characteristics of Study Sample General Well-Being Data Personal Interview Data MMPI Data or Zung Self-Rating Depression Scale Data .......... rispecieenind College Health Questionnaire Data Psychiatric Symptoms Scale Data rererets Personal Feelings INVENIONY DIAL uirpsisiruiisisissmermosssmismtssssssisssatssssrrt stss ses siosss feassnis st dts ssssssansqhive Comparative Validity of the Major Data Elements With Interviewer Ratings of Depression ....cc.eeeeersnneee bot Item-Level Correlations of the GWB and Zung With Interviewer Ratings......ccecseeesecsssensersssrneassesssssensns Scale Correlations With the Interviewer Ratings Intercorrelations Among the Depression, Anxiety, and GWB Scales.....cccccrennne ev teRe ast rs re RRO TETT Ere vivisers Some Content Properties of the GWB Reliability. The Meaningfulness of the GWB “Person Types” —Cluster and Discriminant Analyses Overall Evaluation of the GWB.......... sPrvateees References List of Detailed Tables APPERUIX caverirsireprssmssssisrsrmmenssssisssessssrorsaress TEXT FIGURE 1. Mean MMPI profiles for males and for females.......ccceussrerenns LITRE set yas TER Te tS Sa AR SA Sara A ae TR ET ii ov BOB 00 Lo Ot Ov Ov NNN OY O00 00 12 14 15 30 vi LIST OF TEXT TABLES A. Product-moment correlations of scales and subscales (in rank order) with interviewer depression ratings, BY SEX .uciesiesiserssasnioes B. Multiple correlations of Depression and Anxiety scales with six General Well-Being (GWB) subscales, zero-order correlations with total GWB scale, and mean correlations, by SeX succoceseecssnsssesssssssnsosaecsss 10 C. Internal consistency coefficients of reliability by sex for GWB and Zung SCales ....cccereeressaesrarsessnserasras 11 SYMBOLS Data not available-----------moomoemmm eee oo Category not applicable-------------secummmemeeecnenenn Quantity zero - Quantity more than 0 but less than 0.05--—-- 0.0 Figure does not meet standards of reliability or precision---------s=sesesemeeemmeieeaas * “A CONCURRENT VALIDATIONAL STUDY OF THE NCHS GENERAL WELL-BEING SCHEDULE Anthony F. Fazio, Ph.D.,2 The University of Wisconsin-Milwaukee INTRODUCTION The General Well-Being (GWB) schedule was an initial effort directed toward the use of a highly structured instrument for assessing self- representations of subjective well-being and dis- tress. This instrument was developed in 1970 for the National Center for Health Statistics by Dr. Harold Dupuy,! Psychology Adviser, Division of Health Examination Statistics. It was used as part of a national health examination of 6,931 adults aged 25-74 years conducted from April 1971 through October 1975. Since then, the GWB schedule has been and is being used in several fairly large-scale studies. However, its most important clinical use has been made in the Sacramento, California, Divi- sion of Mental Health by Dr. Daniel W. Edwards. The GWB was initially administered to patients upon admission to variotis mental health pro- grams, weekly thereafter until treatment was terminated, and again at a 3-month post- treatment followup. About 600 patients partici- pated in the initial phase. This report presents some findings and evalu- ations of the GWB compared with several other self-report scales in terms of their concurrent validity against interviewer ratings of current depression and the intercorrelations among these several scales. These findings were derived from 2 Associate Professor of Psychology and Director of Clinical Psychology of the Department of Psychology at the University of Wisconsin-Milwaukee. a study of a sample of 195 college students who participated in a major investigation into ways of assessing depression among college students. PURPOSE OF THE STUDY A simple two-process model of effective psychotherapy, interpreted from a problem- solving framework, has been developed along the lines of Andrews’ suggestions? for treatment by Fazio.3,4 According to this model, patients must develop a positive rapport with the thera- pist in such a way that patients are motivated to engage in therapeutic exercises. For example, with respect to phobias, these exercises would involve the gradual exposure to anxiety- producing stimuli. The exercises are judged to be therapeutic if they effect changes in the under- lying hypothetical psychopathological condition (e.g., extinguish anxiety) and its symptoms (e.g., avoidance behavior or loss of composure). In order to test the generality of the model from which specific treatments for specific problems are derived, a variety of disorders other than phobias have to be studied. Phobic reactions have been studied extensively, however, because of the ease with which one can operationally measure and quantify the extent of the hypo- thetical underlying construct (i.e., fear) and its observable operationally defined symptoms (e.g., avoidance behavior). The Behavioral Avoidance Test (BAT), or one of its many variations, has been used extensively in this regard.5,6 Gen- erally, the construct validities of an experimental measure are estimated by the concurrent admin- istration of a variety of other more traditional assessment devices such as self-report scales of fear.?” However, when attempts are made to in- vestigate other less explicit and more global psychological states such as depression, readily agreed upon operational definitions are not available. The purpose of the major investigation was to study the interrelationships of a variety of approaches and techniques for assessing psycho- logical depression to determine the best set for use in therapy evaluation studies. In an effort to locate a variety of assessment devices for de- pression, library searches were undertaken by several assistants. Computerized indexes were searched using a variety of keywords (e.g., suicide), and researchers known to be interested in research on depression were contacted. A literature search as part of a doctoral disserta- tion by Ray Shipley in this laboratory found very few published therapy experiments on depression in psychology journals. Shipley and Fazio® used the Depression scale (D) of the Minnesota Multiphasic Personality Inventory (MMPI) and a rater-judged estimate of voice in- tensity suggested by Hargreaves and Stark- weather? in a small-scale study. Although the Zung Self-Rating Depression Scale! 0 was used initially, retest scores were judged to be too unstable for our purposes of evaluating changes associated with short-term psychotherapy. The rater-judged estimates of voice intensity were not associated with any changes in pretherapy to posttherapy or in treatment versus control groups. Only the MMPI D scale revealed any statistically significant changes in pretherapy to posttherapy depression scores. During the summer of 1972, 39 college students recruited from summer-session classes were interviewed in a second attempt to esti- mate the diagnostic utility of voice indicators of depression. Again, no statistically significant, meaningful diagnostic indexes were found with this sample for these behavioral indicators. For example, vocal response latency to five neutral and to five stressful interview questions for subjects who were considered to be depressed and not depressed on the basis of MMPI D scale T scores. The next attempt based on two larger samples of college students from the University of Wisconsin-Milwaukee was directed in a different manner. During the fall of 1972, the first sample was given a battery of tests in two sessions approximately 1 week apart. Subse- quently, the second sample was examined in the spring of 1973. The battery of tests employed in those assessments contained several well-known measures of depression, anxiety, and other aspects of mental health. One instrument of particular interest to the principal investigator Anthony F. Fazio was the General Well-Being (GWB) schedule developed by Dupuy of the National Center for Health Statistics (NCHS) of the Department of Health, Education, and Wel- fare.l1 The GWB promised to be of research value because of its psychometric properties (e.g., item response scores of 0-5 as opposed to 0-1), its rational content structure, its brevity, the possibility of accumulating a large data base from which norms could be generated for comparison, and its use as part of a comprehen- sive Health and Nutrition Examination Survey (HANES) being conducted by NCHS. Since the entire battery of tests and the interview used in this research were administered within 1 week for most subjects, and since no known system- atic or planned form of intervention occurred during this brief interim period, the concurrent validities of the GWB and its various subscales were analyzed using the variety of other assess- ment devices also employed. Another report concerned with the con- current validity and content relevance of the GWB to other tests presently exists. Celeste Simpkins and Frank Burkell present, among other items, phi coefficients between a sample of mental health patients and a sample of community residents drawn from the same catchment area for all of the GWB items in addition to several other scales. This study replicates part of their work and extends the nomological network of the GWB into new areas. DESIGN OF THE STUDY During the fall of 1972, all college students enrolled in introductory psychology classes were approached with an Interest Inquiry form letter (see the appendix). All participants who re- ported for testing were informed that the questionnaires had to do with mental health testing, that their responses would be kept strictly confidential, and that an elaborate code had been devised to keep their answers anony- mous. They were requested to sign an Assurance of Confidentiality Statement and an Authoriza- tion for Release of Academic Records (see the appendix). Later the students were divided into smaller groups and were asked to complete the battery of tests as will be described below. The battery was administered in two parts, each about 1-1% hours in duration and approximately 1 week apart. Different tests were given first because of the differences in schedule times for many students. The interview always occurred at the end of the second session. Of the more than 170 students initially responding, 127 of them completed all phases of all tests and were identified as group 1. During the spring of 1973, the identical - procedure was followed. Of the more than 100 students who responded, 68 completed all tests and were identified as group 2. Some of the tests administered_in the fall were not administered in the spring and vice versa. SOURCES OF THE MAJOR DATA ELEMENTS The appendix presents some of the tests used and their appropriate scoring keys for both groups 1 and 2. Tests administered to both groups are as follows: The Minnesota Multiphasic Personality In- ventory (MMPI). The Psychiatric Symptoms Scale (PSS). The General Well-Being schedule (GWB). Personal interview. The Minnesota Multiphasic Personality Inventory (MMPI) Devised by Hathaway and McKinley! 2 this is a bH66-item true-false inventory with 10 clinical scales and 3 validating scales.13 For each subject, 13 scale scores were tabulated from this particular inventory which was chosen because it is a “standard” in the field. A brief description of the MMPI scales follows. Number of items Validity scales 15 (L) Lie—A high score indicates re- sponses that places one in the most acceptable light socially. 64 (F) Validity—a low score indicates rational and relatively pertinent re- sponses. 30 (K) Correction—a high score indicates defensiveness that verges upon deliber- ate distortion in making a more ‘“nor- mal” appearance. Clinical scales 33 (Hs) Hypochondriasis—a high score indicates abnormal concern about bodily functions. (K-corrected) 60 (D) Depression—a high score indicates a symptom complex of depression. 60 (Hy) Hysteria—a high score indicates conversion-type hysteria symptoms such as paralyses. (K-corrected) 50 (Pd) Psychopathic Deviate—a high score indicates absence of deep emo- tional response, inability to profit from experience, and disregard of social mores. (K-corrected) 60 (Mf) Masculinity-Femininity Inter- ests—a high score indicates a deviation of basic interest pattern in the direc- tion of the opposite sex. 40 (Pa) Paranoia—a high score indicates suspiciousness, oversensitivity and de- lusions of persecution, with or with- out expansive egoism. 48 (Pt) Psychasthenia—a high score indi- cates phobic and compulsive behavior. (K-corrected) 78 (Sc) Schizophrenia—a high score indi- cates bizarre and unusual thoughts or behavior. (K-corrected) 46 (Ma) Hypomania—a high score indi- cates overproductivity in thought and action. (K-corrected) 70 (Si) Social Introversion-Extraversion— a high score indicates a tendency to withdraw from social contact with others. Psychiatric Symptoms Scale (PSS) This 45-item true-false scale, constructed by Dohrenwend and Crandel,!3 was derived from the Langner Scale used in the Stirling County and Midtown Manhattan studies.!4 Additional items were suggested by psychiatric personnel associated with a research project. This scale was selected for its updated revision of other “stand- ard” tests in the field. For these analyses two subscales were constructed using the criterion that 6 out of 8 judges agreed that the item was relevant a priori to either anxiety or depression but not to both. These two subscales contain 10 and 7 items, respectively. The items for each subscale are shown separately in the appendix. General Well-Being Schedule (GWB) This schedule contains 33 items—the first 14 items are 6 response option items, the next 4 items are 0-10 rating bars, and the last 15 items are criterion-type behavioral and self-evaluation items.1 1-16 Six subscales measure health worry, energy level, satisfying interesting life, de- pressed-cheerful mood, emotional-behavioral control, and relaxed versus tense-anxious. These ratings can be obtained as well as an overall total scale score. The GWB was included in this investigation to “test” the robustness of its short, direct, and rational approach to assessing self-representations of depression and tension- anxiety compared with the more generalized approaches used in the other assessment instru- ments. (See the appendix for a copy of the GWB and its case record summary sheet for item response scoring.) The GWB is scored in a positive direction in that a high score reflects a self-representation of well-being. Personal Interview A personal interview was conducted with each subject. This half-hour, face-to-face inter- view took place at the end of the second half of the second testing session, 1 week after the first testing session. Because of the number of sub- jects and questionnaires involved, many assist- ants participated in the data collection phases and also conducted the interviews. Demographic data were requested along with statements of satisfaction about progress toward goals and other pertinent information. In all, 39 items were recorded. After the subject had left, the interviewer rated the degree of depression, if any, which was manifested by the subject during the interview. The three items used in these analyses were age, sex, and the interviewer’s rating of depression. A copy of the interview schedule for group 2 is shown in the appendix. For group 1, the following additional ques- tionnaires were administered: The Zung Self-Rating Depression Scale (SDS).—This is a 20-item scale, with 4 choice response options for each item, specific to psychological depression.10 For each subject a converted raw score for each of the 20 items was tabulated and later converted to a total depres- sion score with a possible range of 25-100. This questionnaire was chosen because it was easy to administer, short, and contains many items of clinical interest for the assessment of depression (see the appendix). The College Health Questionnaire (CHQ).— This is an 82-item multiple-choice test with 16 subscales and 2 validating scales.!7 For these analyses 3 subscale scores were tabu- lated—current depression, 19 items; past depres- sion, 14 items; and anxiety, 6 items (see the appendix). This questionnaire was chosen be- cause of its apparent relevance to college student populations. For group 2, the following questionnaire was substituted for the SDS and the CHQ: The Personal Feelings Inventory (PFI).—This questionnaire consists of 2 subscales—anxiety, 21 true-false items; and depression, 45 true-false items. These 66 items were obtained from Zubin and Fleiss18 and were factor analyzed from nearly 700 items from the combined Present State Examination of Wing et al. (1967)19 and the Psychiatric Status Schedule of Spitzer et al. (1970).20 These subscales were used because they were reported to be able to discriminate anxiety from depression. Thus, in all, approximately 800 elements of information were obtained from each subject which were reduced to 91 data elements taken from the tests as just described. Because a variety of scales was administered, scale scores rather than individual items (many of which are scored only as true-false) are the main bases for comparison. DATA PREPARATION PROCEDURES Each subject was assigned an identification number by drawing without replacement from a set of numbers prepared earlier. A code sheet was kept by the principal investigator in case subjects had to be recalled at a later time. After all testing was completed, the code sheet was destroyed, making it impossible to identify any subject’s responses to the questions. All tests were scored at least twice by independent assistants, after which all scores were transferred to coding sheets for keypunching. Each coding sheet was doublechecked for errors, missing entries, etc. All keypunching was verified and off-line lists were again checked for errors. Finally, the data were checked using a computer program for field limits, number of cases, and other specifications. The principal investigator personally supervised and/or checked every one of the 91 data elements for each of the 195 subjects in the data base. The data were arranged by group and sex of the subject in two-card records. A machine- readable data file, containing a complete case record summary listing of the data set, was prepared. A coding manual containing the data element sources and their scoring, their location in the data set, etc., also was prepared. All data analyses were computed by use of a UNIVAC 1106 or 1110, as well as programs from the Basic Statistical Package (BSP), which was developed by the Social Science Research Facil- ity of the University of Wisconsin-Milwaukee. For the purpose of this report, the 91 data elements were reduced to 74. This reduction reflects the use of sex as a control variable and the exclusion of the 9 items of question 24 of the GWB and 7 interview items. The major statistical measure used in this report to show the degree of association or relationship between any two data elements is the product-moment correlation coefficient. The degree of associa- tion between any two data elements varies positively with the numerical value of this coefficient. DEMOGRAPHIC CHARACTERISTICS General Population From Which the Sample Was Drawn During the fall and the spring semesters of 1972-73, the student population at the Univer- sity of Wisconsin-Milwaukee was approximately 23,000, mostly young white adults aged 18-25 years, of which approximately 57 percent were male. The subpopulation of students in intro- ductory psychology classes consisted of approxi- mately 60 percent females. The Study Sample The sample of 79 males from both semesters may be characterized by the following data: age in years, X = 19.6, SD = 2.4; freshman; holding a part-time job; and not on medications. The sample of 116 females may be charac- terized as: age in years, X = 18.9; SD = 2.5; freshman; holding a part-time job; and not on medications. Consistent with the data for the introduc- tory psychology classes, 59.5 percent of the sample was female. While the sex-age characteristics of the study sample appeared to reasonably approximate the subpopulation, the statistical findings reported herein, however, are not to be taken as charac- terizing this subpopulation. Furthermore, the purpose of this report is not to make population estimates but rather to make comparative analy- ses of the relationships among several measures of depression. This report thus limits its scope to these comparative analyses and evaluation of these relationships. DESCRIPTIVE PSYCHOLOGICAL CHARACTERISTICS OF STUDY SAMPLE Table 1 contains the summarized data for males, females, and both sexes for each item in the case record summary listing. General Well-Being Data Remembering that the GWB is scored in a positive direction, the average scores for both sexes indicated that they were: 1. In good spirits. 2. Only a little bothered by nervousness. 3. Generally in firm control of behavior and feelings. 4. Only alittle sad at times but not bothered by it. 5. Under some pressure or stress, but about the usual amount. 6. Fairly happy with their personal life. 7. Virtually not at all worried about losing control of their mind. 8. Anxious enough to be bothered by it. 9. Often sleeping fairly well. 10. Only a little bothered by illness and pain. 11. Interested in life a good bit of the time. 12. Feeling downhearted and blue only a lit- tle of the time. 13. Feeling emotionally stable a good bit of the time. 14. Feeling worn out only a little of the time. 15. Generally not concerned about their health. 16. Feeling more relaxed than tense. 17. Feeling more energetic than listless. 18. Feeling more cheerful than depressed. Although the students reported occasional personal problems, they tended neither to have sought help nor to have been concerned about their problems. Very few reported having had a nervous breakdown or having had feelings tend- ing toward a breakdown. Even fewer had been clinical patients or had seen professionals for psychological problems. Average scores for the six GWB subscales and for the total scale were generally lower than those for the sample of community resi- dents in Nashville, Tennessee, as reported by Simpkins and Burke.!1 Personal Interview Data In general, the subjects were young adults graduated from public schools, satisfied with their living arrangements, and not interested in psychological therapy. They reported being satis- fied with their girlfriend/boyfriend arrangements and with the progress they were making toward their goals. The interviewers did not find them to be manifestly depressed. Tables 2 and 3 present a basis for comparing data from the GWB with the unweighted national sample in terms of Dupuy’s tentative descriptive attribu- tion of well-being and distress and the joint distribution of GWB scores and interviewer ratings in the study sample. The GWB mean and median scores indicate that the study sample was at a level of marginal positive well-being and slightly above mild problem-indicative distress. The interviewer ratings placed 36.9 percent, or 72 out of 195, of the study sample as showing at least some concern about their problems or being slightly depressed, compared with 40.5 percent, or 79 out of 195, who scored at the problem-indicative or clinically significant dis- tress levels on the GWB. MMPI Data The average profiles for males and for females are presented in figure 1. For this sample of interviewees, the average MMPI profile might be interpreted to reflect a little greater impulsivity than would be expected normally and a tendency toward unconventionality in both thought and behavior.21 Whether these scores characterize college students on this campus or only students interested in being part of a psychological experiment was not explored in this report. The D scale (Depression) has a mean of 59.0, which is 0.9 of a standard deviation above ‘normal’ which indicates a slightly depressive affect. There were also 42.6 80 70 50 40 MMPI SCORES 30 0 1 1 1 1 1 1 1 1 1 Late 1 1 L F K Hs D Hy Pd Mf Pa Pt Sc Ma Si MMPI SCALE NOTE: See section “Sources of the Major Data Elements” for definition of MMPI scale. Figure 1. Mean MMPI profiles for males and for females. percent who made a score of 60 or higher and 21.5 percent who made a score of 70 or higher, which is 1 and 2 standard deviations above 50.0, respectively. Zung Self-Rating Depression Scale Data Consistent with the scores on the other scales, the interviewees reported only a little distress, concern, or depression. The average total converted scores for both sexes (45.0) was somewhat higher than that reported by Zung for his “100 normal controls” (33.0) but not as high as for his patient population groups (63-90 before treatment). Simpkins and Burke reported mean scores for their community subjects of 40.5 for males and 44.4 for females,!! com- pared with 42.3 and 46.7 in this sample, respectively. Thus the sample showed a slightly more depressive affect than these comparison groups. College Health Questionnaire Data Because of several discrepancies in details described by the authors of this scale in separate publications, it is impossible to compare our findings with otherwise similar studies. 7? These data are presented in table 1 for future compari- sons by other researchers. Psychiatric Symptoms Scale Data Published norms do not exist for the unique subscales of Depression and Anxiety developed for this study. No comparisons can be made. Future researchers can score their findings ac- cording to our codes for comparisons. Personal Feelings Inventory Data Again no published norms are available for comparisons using the two subscales for Depres- sion and Anxiety. Future researchers can use these findings for their own comparisons. In summary, the findings from the inter- viewer ratings, the GWB, MMPI, and Zung scales indicate that about one-third of the study sample reflected some degree of mild or greater depressive affect which was slightly greater than expected when compared with other investiga- tors’ “normative” findings. However, it is clear that the study sample distribution of scores on the depression measures provides a range of scores sufficiently great enough to allow a statistical determination of association to emerge among the different measures of depres- sion, if there is in fact a definite relationship among these measures. COMPARATIVE VALIDITY OF THE MAJOR DATA ELEMENTS WITH INTERVIEWER RATINGS OF DEPRESSION The interviewer’s rating of depression is viewed here as an independent criterion against which to assess the concurrent validity of the various measures of depression and other self- reported data elements. The interviewer used a structured questionnaire as a stimulus to elicit structured, semistructured, and open-field re- sponses. The questionnaire did not include any specific or explicit questions about depression or anxiety. After each interview, the interviewer then made his or her rating of depression on a partially structured scale of 0-10 and possibly higher. A copy of the interview form is shown in the appendix. Table 3 shows the distribution of the ratings for the 195 students in the study. The high skewness of these ratings is apparent in that 63 percent of the ratings were 0 or 1, which reflect a positive or neutral affect, respectively. This skewness will tend to restrict the numerical values of the correlation coefficients for the scales which allow for more positive expressions of well-being such as the GWB and, to some extent, the Zung scale. Table 4 presents the product-moment corre- lation coefficients and significance levels of 73 major data elements with the interviewer ratings for males, females, and both sexes separately. Note that negative signs are" not shown in the correlations except where the relationship was opposite from expected and for the three validity scales of the MMPI and age which are needed for interpretation. All GWB data ele- ments, since they are scored as positive, would have negative signs; they are not shown since it would complicate the description of findings. The .01 level or better of statistical significance is used to describe a significant relationship in the presentation of findings. Item-Level Correlations of the GWB and Zung With Interviewer Ratings All 18 items of the GWB total scale were significantly correlated with the criterion for the total sample; however, only 10 items among the males but 17 items among the females had significant correlations. For the 6 criterial items, all were significant for the total sample, none were for males separately while 5 were for females separately. It is surprising that the correlations among the females were as high as they were considering the low frequency of response to having had or having felt near a nervous breakdown, or having been a clinical patient, or having had professional help (4 items). The responses to the question reflecting psychologic problems over the past year were moderately correlated with the criterion for both sexes. The social-emotional support item had a rather low relationship with the criterion and thus its content may not reflect a dis- tressing aspect in students’ lives in that only 12 students reported a lack of such support (op- tions 3, 4, and 5 of the original code). Among the 20 items in the Zung scale only 4 items for the total sample, none for males, and only 8 for females had a significant correlation with the criterion. Surprisingly, 13 items for the males and 2 items for the females had correla- tions in a negative direction with the criterion, which is opposite to what would be expected. The highest item correlations with the cri- terion for each sex on the GWB scale were .44 for males (nervousness) and .46 for females (sad, discouraged, hopeless). For the Zung scale the highest item correlations were .34 for males (losing weight) and .36 females (still enjoy sex). In general, item-criterion correlations were higher among females compared with males for both scales, and notably higher for the GWB items compared to the Zung items for both sexes. Age was not significantly correlated with the criterion for either sex although there was a slight tendency for more depressed ratings with higher age in this college sample. Scale Correlations With the Interviewer Ratings Of the 28 scales and subscales (SS) used in this study, 24 correlated with the criterion at the ..01 level or better of significance for the total sample. However, only 8 scales among males compared with 20 scales among females were correlated at the .01 level or better (table A). While the Personal Feelings Inventory (PFI) 45-item Depression scale had the highest correla- tions with the criterion for both the total group and males, these data were obtained for only 68 students—30 males and 38 females. The GWB 18-item total scale and its 2 subscales of cheerful versus depressed mood (4 items) and emotional- behavioral control (3 items) had the next highest correlations for all of the 195 students and generally for males and females separately. Of the remaining scales, only the 10-item Anxiety subscale of the Psychiatric Symptoms Scale (PSS) and the 4-item GWB subscale of relaxed versus tense-anxious correlated at the .01 level or better for both males and females separately. Thus, the three very short subscales of the GWB correlated with the criterion about as well as or better than the many other scales that had many more items. The 18-item GWB total scale had the highest correlations with the criterion when responses from the total sample (n = 195) are considered. The MMPI Depression scale and the Zung Depression scale worked very poorly for males (essentially zero correlations) but moder- ately well for females. Table A. Product-moment correlations of scales and subscales (in rank order) with interviewer depression ratings, by sex Ban. Scale and subscale Total Male Ts 2 Criterion correlation 1 PFl—Depression ...... 1.50 157 142 2 GWB—-TOotal scale.......ocsirssrsssssssssessisasencivenes 147 145 148 3 GWB—(SS) Cheerful versus depressed mood... 144 136 1.48 4 GWB—(SS) Emotional-behavioral CONtrol .........c.cceevereeunseeruessanenns oe 1.43 136 1.48 5 PEL a ATTRIB ou sisvniss sivimmisass sissies a i Ys AA AER Sp Eh 0 a 1.41 42 1.42 6 PSS—Anxiety........ 1.40 136 1.42 7 PSS—DEpression wu. issseersssessesmesssnsassas v 1.39 .25 1.47 8 GWB—{S8) Relaxed VErSUS 1BNS8, BNXIOUS. uu sirsssassissresissisrasiinssnivsrseasssesnsdosnisininsissusmsinssmssnssinissss 138 135 1.40 9 CHO ~CUTIONT DODIEBRION sseusmmimarsncinssessprisssamibssonsnsssumsinsosdinsesisismresssot Inset sia Eas SAR ii 136 || -.01 1.48 10 CHQ—Past Depression .........eeeerenne 134 03° 145 1 GWB—(SS) Satisfying, interesting life... 134 23 139 12 GWB—(SS) Energy level 1.31 25 135 13 ZV = DIT BEER ONY sre inssinimmsintearvhriuristsnsstrshesnssnisin lope invsa ess iste ios ant bes sor Te Beep Ere TA ST 128 || -.01 139 14 GWB—(SS) Free from health worry... 127 135 21 15 MMPI—(Pd) PsychopathiC.............. 1.26 .08 1.37 16 MMPI1—(Sc) Schizophrenia. 125 A3 134 17 MMPI—(Hs) Hypochondriasis .. 124 133 19 18 MMPI —(D) Depression............. 121 .05 132 19 MMPI —(Pt) Psychasthenia . 2.21 .14 1.27 20 MMPI—(Hy) Hysteria..... 119 a7 20 21 MMPI—(Ma) Hypomania ol 118 14 21 22 MMPI —(Pa) Paranoia .......cruesreesresrsasrsesrsesrsens 118 .01 1.27 23 MMPI1—(Si) Social Introversion-Extraversion . 17 A2 19 24 CHO —ANXICRY 1ocvinrssrsrenssvmmicasaiassst sassessarsrsssions 10 .02 13 25 MMPI1—(Mf) Masculinity-Femininity INTErests .......cccsrsrvverersrsrssnnsssirrssssansssssessarssssssassnssssssessssasasans 08 .07 16 MMPI validity scales 1 CEN VBI, arnt iviva snp mit a RAR is HF ERE va re Svan nasa aves hare gr EH va Sgr ata sna doros 134 12 145 2 (K) Correction . I-21 -.01 1-30 3 HET ET I JT CE Se Se MM IL Ne Le) -.12 -.21 -.06 1Correlations significant at .01 level. An overview of these correlations suggests that the interviewer ratings of depression actu- ally correlated about as highly with Anxiety scales as with the Depression scales. Thus, either the scales or the interviewers or both failed to differentiate between these two psychological states. It is also of interest to note the significant correlations with the criterion among males of the two scales reflecting fear or concern about health and health complaints while these did not significantly correlate with the criterion among females. Intercorrelations Among the Depression, Anxiety, and GWB Scales Table 5 presents the intercorrelation matrix among the Depression, Anxiety, GWB scales, and interviewer ratings for males and females combined. The correlation between the College Health Questionnaire (CHQ) Current and Past Depression scales (.96) should be ignored since 12 of the 14 items in the Past Depression scale are also included in the Current Depression scale; subscale correlations of the GWB with the GWB total scale should also be ignored since each subscale forms a part of the total scale. In general the intercorrelations among the depres- sion scales, among the anxiety scales, and between the two sets of scales are quite high. No scale seems to be definitely more highly corre- lated with the other scales for either the depression or anxiety scales. The GWB subscale of cheerful versus depressed mood had an average correlation of .63 with the other six depression scales and of .54 with the four anxiety scales. The GWB subscale of relaxed versus tense-anxious had an average correlation of .59 with the seven scales of depression and of .63 with the other three scales of anxiety, while these two GWB subscales correlated .70. Thus, while these two GWB subscales are highly correlated, they were slightly more related to their respective psychological states as reflected by other measures of these states. The GWB subscale of emotional-behavioral control had high average correlations with the depression scales (.60) and with the anxiety scales (.57). The GWB total scale had a very high average correlation of .69 with the six independent depression scales and of .64 with the three independent anxiety scales. In general the seven depression and four anxiety scales seemed to have measured almost equally well the psychological states they had been constructed to measure; however, none of them clearly differentiated depression from anxiety. The total GWB scale measured depres- sion and anxiety better than the separate scales measured them. Multiple linear regression equations were computed using the six GWB subscales to predict each of the other depression and anxiety measures to determine the maximum amount of variance that could be accounted for in these measures. In table B the results are shown in terms of the multiple correlation coefficients and compared with the simple zero-order product-moment correlations with the GWB total scale. The mean multiple correlations (R) indicate that very little was gained by differen- tial weighting of the GWB subscales to predict a given measure above that of the GWB total scale scores. One thing of interest is that the mean multiple R’s for males and females are the same while there was a slight difference by sex for the total GWB scale. The conclusion drawn from this is that the GWB total scale is as predictive for these various measures as a group for both sexes as would be differential weighting of the six GWB subscales. SOME CONTENT PROPERTIES OF THE GWB Reliability The GWB was readministered to 41 students from the original sample about 3 months after the first test. The test-retest correlation was .851 for the total scale. The mean values of 74.6 for the first test and 73.0 for the second and standard deviations of 16.6 for the first test and 16.7 for the second were virtually identical. These data indicate that for each of these students the total GWB score was about the same at these two points in time. The internal consistency coefficients of reli- ability were computed for the 18-item GWB total scale and the 20-item Zung scale by use of Table B. Multiple correlations of Depression and Anxiety scales with six General Well-Being (GWB) subscales, zero-order correlations with total GWB scale, and mean correlations, by sex Depression and Anxiety scale Fe- Fe- Total || Male idle Total || Male rials IV LBIVIEWBT TBING ivi crrvssrrarrmssnsssssssinstaserersisessrassnsissssonssssessvssssnsssions MMPI—(D) Depression... Zung—Depression........... CHQ—Current Depression ..... CHQ~—Past Depression........... CHO = ANXIOIY .. i riarsssrsssssssinissassasesstovarssesisrssvosssssesse PEI DODrBSSION isos iisivisasessicssrsunnsrvasnnnisssesinsinmvs PFI—Anxiety........... PSS—Anxiety .......... PSS —Dopression ....ceisrssrrsrsines VIEEN COPTBIBTION vvivrserverssssiasrmsissrsniisctitsstrsmsssonssansiosesmisssssuanentvessns sve Multiple correlation Zero-order correla- tion 491 484 | 518 .468 445 .482 sr 574 .b64 .638 534 442 .631 eR .691 .739 .684 .661 618 .668 eidaey .810 732 1...836 .801 .726 .820 She .726 .684 | .755 .692 626 .707 dan 571 632 557 516 481 510 Tersane .803 932 .800 .780 || .840 .730 Ad 674 .794 .643 .630 .716 .538 aay 797 .758 817 .759 T37 774 JessRrrs vA Eason J36 { .722 | .758 .704 || .658 729 wrrsesiivsisnasrriiniune 687 .703 .701 .654 627 .659 10 Table C. Internal consistency coefficients of reliability by sex for GWB and Zung scales Num- Fe- Scale Cer Male idle Internal consistency coefficient OLA GWE .onserassssssinsnsesrinrasssaivonseisrpes 195 | 912 .945 UNI cv vnsssassvrasirnreiinssatasssssmnprensnisitssesss 127 | .830 .886 item to total scale score correlations for each sex and are shown in table C. The GWB total scale was somewhat more internally consistent than the Zung scale for both sexes while the differ- ences between males and females within scales were not very great. The high level of internal consistency of the 18 GWB total scale items indicated that it is a homogeneous scale basically measuring a singular dimension or general psychological state in this sample. Thus, the subscales of the GWB also measured some properties of this general state and were some- what highly intercorrelated as can be seen in table 6. Using a different approach, the six subscales of the GWB were submitted to a cluster analysis along with the total score and the interviewer rating. The analyses were performed separately for males, females, and both sexes. Although the total score was first combined with subscale 5 (emotional-behavioral control), the stress values for that subscale and every other combination suggested that all of the separate subscales were at least partially independent of each other. The Meaningfulness of the GWB Taking into consideration the designated titles of the various measures used in this study as reflecting expressions of psychological states of depression and anxiety or the absence there- of, the moderate-to-high correlations of the GWB with these measures indicates that its major measurement dimension is also reflecting these states. It seems reasonable to view each of these two states as constituting a dimensional- ized continuum of feelings of distress but not necessarily extending to a state of well-being. Since the GWB was the only measure in this study which purports to measure a sense of well-being and distress, its value in measuring well-being cannot be assessed herein. However, its capability to measure distress is clearly supported. The weakest meaningful property of the GWB seems to be in the differentiation of the total scale into the six subscales. However, this weakness does not lie in the rational effort to differentiate a more global concept into its component parts, but rather in the need to include more elements of assessment in each component part so that more reliable measures can be made of these parts. An intensive analyses of the GWB item intercorrelations and their correlations with other measures indicated that the items in each subscale are most mean- ingfully placed within the designated subscale if these six rational subscales are to be used. For example, the two items in the health worry or concern subscale correlated .49 with each other which was higher than either one of them correlated with any of the other 16 GWB items. The desideratum is to construct a large number of items for each subscale and empirically determine the most homogeneous set that would also be least correlated with other subscales. However, even though the GWB subscales inter- correlated fairly highly in this college student sample, they may well show a more differen- tiated pattern (lower intercorrelations) among more severely distressed samples with more clearly differentiated symptom patterns, such as clinical patients. The surprisingly high correlations of the GWB items with the other measures of depres- sion and anxiety indicate that the multiple response options of these items are properly ordered and form mini-scales in their own right (table 7). “PERSON TYPES""—-CLUSTER AND DISCRIMINANT ANALYSES A completely different approach was taken to explore the possibility that the study sample could be clustered into several “person types” with respect to the seven measures from the GWB (i.e., the six subscales plus the total) and the interviewer rating. Cluster analyses were run separately for males and females. Since there are no hard and fast rules regarding the optimum 1 number of groups to be obtained, the error factor associated with putting persons with grossly different scores in the same group must be weighed against the total number of groups that can be meaningfully identified. Five groups of males and five groups of females seemed to be the optimum number in this sample. These five groups were then submitted to a discriminant analysis which provided descriptive statistics on how the eight variables contributed to the differential group membership. The following interpretation is based on the statistics shown in table 8. For the males the five groups of interviewees appeared to differ with respect to overall adjust- ment, interviewer rating, and the energy level subscale. These five groups might be described as: high well-being (group 1); about average well- being (group 2); about average well-being but concerned about their health (group 3); below average well-being (group 4); and distressed, unhappy, and depressed but not severely lacking in energy (group 5). For the females the five groups of inter- viewees differed with respect to overall adjust- ment, interviewer rating, and subscale scores as had the males. These five groups might be described as: high well-being (group 1); about average well-being (group 2); below average well-being with somatic concern and low in energy (group, 3); below average well-being with little somatic concern (group 4); and generally distressed, unhappy and depressed (group 5). OVERALL EVALUATION OF THE GWB After a great many statistical analyses of several different kinds, what can be said about the utility and validity of the GWB for assessing general well-being? The ‘hard” reasons for including the GWB in this research investigation were stated earlier in the text (see ‘“Purpose”). In addition, the GWB was “‘pragmatically profes- sional” when compared with the 566-item true- false MMPI or the relatively new College Health Questionnaire with its multiple-choice format. The GWB is well designed, easy to comprehend, and its content coverage is apparent. Since no previous data existed when this investigation was started in 1972, it was truly an untried instru- 12 ment and was included because of its manifest properties. However, did the GWB differentiate the more depressed students in our sample from the less depressed ones? The answer, as reflected in several criterial measures, is affirmative. It was clearly better than most of the other measures for each sex in its strength of relationship with the interviewer rating of depression. The total GWB scale and the two short, 4-item subscales of depression and tension-anxiety intercorre- lated as highly with the other more extensive measures of these two states as these other measures did among themselves. None of the sample persons expressed any trouble either in understanding or in responding to the GWB items—unlike the true-false forced-choice format of the MMPI—and the GWB emerged as the single most useful instrument in measuring de- pression. This particular study did not provide a reliable way to evaluate the GWB criterial section items because the sample was too homo- geneous and markedly skewed on these behav- ioral manifestations of psychological distress. Evaluation of some of the GWB items and subscales was limited also because the criterial measures were selected basically to measure depression and anxiety and not some of the other rational content area built into the GWB. The major weakness of the GWB seems to be that the subscales have too few items to provide content homogeneous and reliable subscales for individual assessment on these aspects of well- being or distress. Where does the GWB stand in terms of current-day relevance? A recent article by Campbell22 indicates that statistics, national or otherwise, have too long involved monetary and tangible product manifestations of our lives, while if it is the quality of the life experience of the population that is of concern, then measures have to be developed to assess the individual’s sense of well-being. The General Well-Being schedule seems to have originated before its time but is now in the right place at the right time to present coherent and useful data about the subjective well-being of large cross sections of our citizenry. Because the GWB is brief, well designed, and relevant in content, it should be useful in a variety of research and applied settings, such as a quality-of-life index, a mental health status appraisal, a measure of psychotherapy outcome evaluation, and a social indicator for measuring population changes in sense of well-being over time. Accordingly, at a practical action level, it was recommended and included in a 1976 health needs study, involving a larger sample of college students (n = 419) attending the University of Wisconsin-Milwaukee. Data collected from this larger independent sample are very similar to the data reported here with respect to GWB scale score means, standard deviations, and other measurements. Because of the very large data base (n = 6,931) for the GWB from the NCHS’ National Health Examination Survey of Adults (1971-1975), meaningful norms can be estab- lished against which individual and special sam- ple comparisons can be made by researchers in many settings throughout the United States. O00 13 REFERENCES INational Center for Health Statistics: The psycho- logical section of the current health and nutrition exami- nation survey. Proceedings of the Public Health Confer- ence on Records and Statistics, Meeting Jointly With the National Conference on Mental Health Statistics, 14th National Meeting June 12-15, 1972. DHEW Pub. No. (HRA) 74-1214. Health Resources Administration. Washington. U.S. Government Printing Office, 1973. 2Andrews, J.: Psychotherapy of phobias. Psychol. Bull. 66:455-480, 1966. 3Fazio, A. F.: Treatment components in implosive therapy. J. Abnorm. Psychol. 76:211-219, 1970. 4Fazio, A. F.: Implosive therapy with semiclinical phobias. J. Abnorm. Psychol. 80:183-188, 1972. 5Bandura, A.: Principles of Behavior Modification. New York. Holt, Rinehart & Winston, Inc., 1969. 6Fazio, A. F.: Verbal and overt-behavioral assessment of specific fear. J. Consult. Clin. Psychol. 33:705-709, 1969. "Wolpe, J., and Lang, P. J.: A fear survey schedule for use in behaviour therapy. Behav. Res. Ther. 2:27-30, 1964. 8Shipley, C. R., and Fazio, A. F.: Pilot study of a treatment for psychological depression. J. Abnorm. Psychol. 82:372-376, 1973. 9Hargreaves, W., and Starkweather, J.: Vocal and verbal indicators of depression. Calif. Ment. Health Res. Digest 3:59-60, 1965. 10Zung, W. W.: A Self-Rating Depression Scale. Arch. Gen. Psychiatry 12:63-70, 1965. Hgimpkins, C., and Burke, F. E.: Comparative analy- ses of the NCHS’ General Well-Being schedule: Response distributions, community vs. patient status discrimina- tions, and content relationships. Unpublished document. 12Hathaway, S., and McKinley, C.: Minnesota Multi- phasic Personality Inventory, New York. The Psycho- logical Corporation, 1951. 14 13Dohrenwend, B. P., and Crandell, M.D.: Psychiatric symptoms in community, clinic, and mental hospital groups. Am. J. Psychiatry 126:87-97, 1970. 14gy0le, L., Langner, T. S., Michael, S. T., Opler, M. K., and Rennie, T. A. C.: Mental Health in the Metropolis: The Midtown Manhattan Study, Vol. 1. New York. McGraw-Hill Book Co., 1962. 151 eighton, D. C., Harding, J. S., Macklin, D. B., Macmillan, A. M., and Leighton, A. H.: The Character of Danger, New York. Basic Books, 1963. 16pupuy, H. J.: Developmental rationale, substantive, derivative, and conceptual relevance of the General Well-Being schedule. Unpublished working paper. 17Whitney, W., Cadoret, R. J., and McClure, J. N.: Depressive symptoms and academic performance in col- lege students. Am. J. Psychiatry 128:766-770, 1971. 187 ubin, J., and Fleiss, J.: Current biometric ap- proaches to depression, in R. R. Fieve, ed., Depression in the 70’s, Proceedings of the Symposium, New York, October, 1970. Excerpta Medica, The Hague, 1971, pp. 7-19. 19Wing, J. K., Birley, J. L. T., Cooper, J. E., Graham, P., and Isaacs, A. D.: Reliability of a procedure for measuring and classifying present psychiatric state. Br. J. Psychiatry 113:499, 1967. 20gpitzer, R. L., Endicott, J., Fleiss, J. L., and Cohen, J.: Psychiatric Status Schedule: A technique for evalua- ting psychopathology and impairment in role function- ing. Arch. Gen. Psychiatry 23:41, 1970. 21Gilberstadt, H., and Duker, J.: 4 Handbook for Clinical and Actuarial MMPI Interpretations, Philadel- phia, W. B. Saunders, Co., 1965. 22Campbell, A.: Subjective measures of well-being. Am. Psychol. 31:117-124, Feb. 1976. LIST OF DETAILED TABLES Means, standard deviations, and score ranges for the major data elements, DY SEX .......ccciirririiiiiimmmminiiiiiii esas. Evaluative assessment of unweighted national sample based on the General Well-Being (GWB) total scale Scores .............ccueueen. Number and percent distribution of study sample, by total General Well-Being (GWB) scale score and interviewer depression FEI YO ISR AI es prraresssnssspropsasrnnevarssssrsonsss npn ss sass ntme REPRE Ee LIHEAP HR RE RST Product-moment correlation coefficients of major data elements with interviewer depression rating, and significance levels, DIV BBN es criaprnnitmmnrcrssmmp nin ES EAS TEA RF ATR RARER AERA ER renee Intercorrelations among the Depression, Anxiety, and GWB scales for combined male and female sample........ccccvvcvreneeerreneennns Product-moment correlations of major data elements with General Well-Being (GWB) total scale, subscales, and subscale multi- ple correlations (R) fOr tO1al SAMPIR ..........ccccrccicccrsnrrererarsersrersrrrsressesessssnserenranes Product-moment correlations of the major data elements with other Depression and Anxiety scales for total sample ................. Person-type cluster analyses descriptive statistics, by group type, sex, and scale 16 18 19 20 22 23 26 28 15 Table 1. Means, standard deviations, and score ranges for the major data elements, by sex Score range | Mean value Standard deviation tony Potential Actual total num- Major data element ber Fe- Fe- J : Total || Male hale Total || Male ole Low | High | Low | High GENERAL WELL-BEING SCHEDULE (GWB) Scale items1,2 1 Good spirits 29 3.1 2.8 10 0.9 1.0 0 5 0 5 2 Nervousness 3.7 3.8 3.5 ; 5 i 11 0 5 0 5 3 Firm control of behavior, emotions. > 3:7 3.9 3.5 1:1 1.1 1.1 0 5 0 B 4 Sad, discouraged, hopeless...........cccuveennnnenns 4.0 4.2 3.8 1.2 11 1.2 0 5 0 5 5 Stross, Strain, PrESSUIS ..overrerisssssssssssssrsssore 2.7 2.8 2.7 1.2 1.3 1.2 0 5 0 5 6 Happy, satisfied with life 2.7 2.6 2.7 1.3 1.2 1.4 0 5 0 5 7 Afraid of losing mind, or losing control 4.3 4.4 4.2 1.2 1.2 1.2 0 5 0 5 8 Anxious, worried, upset ... 3.3 3.6 3.1 1.2 1.1 1.3 0 5 0 5 9 Waking fresh, rested ......cccvevenenes 2.8 2.8 2.8 1.4 1.2 1.3 0 5 0 5 10 Bothered by bodily disorders... 4.0 4.3 3.9 1:3 1.0 1.2 0 5 0 5 1 Interesting daily life 3.2 3.1 3.3 1.3 1.3 1.2 0 5 1 5 12 Downhearted; blue.......cccececunerenens 3.5 3.7 3.4 1.0 0.9 1.0 0 5 0 5 13 Emotionally stable, sure of self .... 35 3.8 33 1.2 1.1 1.2 0 5 0 5 14 Feeling tired, Worn OUt......ccceeeernrvennnns 3.2 3.4 3.1 1.1 1.1 1.2 0 5 0 5 15 Health concern, WOrrY.........euvsreseescnsinns 7.2 7:3 7.2 2.4 2.5 2.4 0 10 0 10 16 Relaxed-tense.......... 5.4 5.7 5.2 2.4 23 25 0 10 0 10 17 Energy level.......... 6.0 6.3 5.8 2.1 1.9 21 0 10 1 10 18 Depressed-cheerful ........ueuueneen. ‘ 6.2 6.2 6.2 2.3 2.0 2.2 0 10 0 10 Criterial items1,2 19 Psychologic problems .......csscierssressncisssnnss 3.5 3.7 3.4 1.1 1.0 1.2 1 5 1 5 20 Felt near nervous breakdown .... 2.6 2.7 2.6 0.7 0.7 0.7 1 3 1 3 21 Had nervous breakdown......... 29 2.9 29 0.3 0.2 0.3 1 3 1 3 22 Clinical patient........... 29 2.9 2.9 0.3 0.3 0.3 1 3 1 3 3 Psychologic attention.... 2.9 2.8 2.9 0.4 0.4 0.4 1 3 1 3 24 Social-emotional support......ccccuernniiiiiniennens 4.7 4.5 4.8 1.3 1.2 1.3 1 7 1 7 Subscales!:2 25 Freedom from health concern, worry, OF QISTBSS cinrussssssssrersissununessone eressrsnsnrsssenes 11.3 71.6. { 13.1 3.2 3.2 3.1 0 15 1 15 26 Energy level 11.9 12.5 11.6 3.6 3.3 3.8 0 20 3 19 27 Satisfying, interesting life .........oooveeriinnnnnnnnns 5.9 5.7 6.0 22 1.9 23 0 10 1 10 28 Cheerful versus depressed mood........cccueeees 16.71 172.2 § 16.3 4.5 4.2 4.7 0 25 4 25 29 Relaxed versus tense, anxious.... 15.1 15.9 14.5 5.0 4.8 5.0 0 25 4 25 30 Emotional-behavioral control..........cccecuneeeee 11.5 121 11.1 2.8 2.7 2.8 0 15 2 15 31 GWE 10tal SCAB? ..cviminminminimsinssisisirisns 72.414 75.1.1 70.5 16.7 || 14.8 | 17.8 0 110 27 108 32 BADD. Li rt ennnsriieimmmns side ans SS Bat SA SE EUR SAE 19.2|| 19.6 | 18.9 25 24 25 16 34 33 Interviewer depression rating......cccceeevininnns 1.4 13 1.4 15 1.3 15 0 10 0 8 PSYCHIATRIC SYMPTOMS SCALE (PSS) 1 34 INOIRIELY ov so innimmssimsmsnsssssontiom santa hsm as AAs TA mI: 29 24 3.2 2.7 25 2.8 0 10 0 10 35 DDB rBESION ou vussssssvmisimgaitons basis ious ipssvanss sins 1.7 1.5 1.8 1.8 28 1.9 0 7 0 7 16 See footnotes at end of table. Table 1. Means, standard deviations, and score ranges for the major data elements, by sex—Con. Score range Viorh Mean value Standard deviation ; Aor. Miior data element Potential Actual total ber Fe- Fe- . : Total || Male male Total || Male rivale Low | High | Low | High MINNESOTA MULTIPHASIC PER- SONALITY INVENTORY (MMPI) T SCORES1.3 Validity scales 36 {LY BGs inivinimmrssoniessommasiatansdevessersaistnnispns 47.0 || 48.4 | 46.0 6.6 7.6 5.6 36 86 36 73 37 (BY VBIOIY .oovicnnniininrmmsisiasinsssmstorinsimss 59.1 || 58.8 | 59.4 10.6 9.9 | 11.0 44 110 44 98 38 UIC) COMBOHION. ..osvumisavsseissmsnsinssnassssbemisnsesss 51.6 || 52.9 | 50.6 8.8 9.4 8.3 27 83 31 75 Clinical scales! 39 (Hs) Hypochondriasis.......ceeereeeeriveeerneeiianens 55.0 || 56.1 | 54.3 10.2 111.3 9.4 20 118 34 103 40 (D) Depression ............. 59.0 || 60.8 | 57.8 13.8 || 14.2 | 13.4 28 120 34 103 41 (Hy) Hysteria... 58.6 || 59.2 | 58.2 8.9 9.1 8.9 24 118 38 86 42 (Pa) PSYChODATNIC «.ivismssenssinensesunsinees 62.0 || 64.5 | 60.3 12.2 if 17.6: 1 12.3 20 119 29 97 43 (Mf) Masculinity-Femininity Interests 53.1 64.1 45.6 13.0 9.5 9.1 20 110 20 90 a4 APA) PATaNBia....rcrvsumprriviministrsssrasssss 68.7 {| 57.3 | 59.7 10.5 || 10.5 | 104 27 120 27 91 45 (Pt) Psychasthenia..... 61.7 || 62.7 | 61.0 11.3 || 12.4 | 105 20 120 26 93 46 (Sc) Schizophrenia... 65.0 || 65.3 | 64.7 143 || 159 | 13.2 21 119 25 115 47 (Ma) Hypomania .........ccocueeeivnesinennne 8 61.7 || 60.9 | 62.2 11.9 12.5 (“11.8 21 108 35 96 48 (Si) Social Introversion-Extraversion........... 56.5 || 54.8 | 57.7 11.7 1} 11.0. 12.0 25 97 36 87 ZUNG DEPRESSION ITEMS4 49 Downhearted, DIug........coemsivsissnss masessupsons 1.7 1.6 1.8 0.7 0.8 0.7 1 4 1 4 50 Morning, feel Bost... osssscisemironissismizns 3.1 3.3 3.0 0.9 0.8 0.9 1 4 1 4 51 Crying spells........... 1.4 1.3 1.7 0.7 0.3 0.7 1 4 1 4 52 Trouble sleeping 1.6 1.5 1.6 0.8 0.8 0.8 1 4 1 4 53 Eat as much as usu... mms ismmarestnn 1.8 1.3 2.0 1.4 0.8 1.2 1 4 1 4 54 Stl‘BAJOY SBR .rssrsrssssssrrinnisssssssssninranssnsstaspnss 1.6 1.6 1.6 1.0 1.0 1.0 1 4 1 4 55 Losing weight... 1.5 13 1.6 0.9 0.6 10 1 4 1 4 56 Constipated...... 1.3 1.2 1.3 0.6 0.4 0.7 1 4 1 4 57 Heart beats fast .... 1.4 1.4 1.4 0.6 0.7 0.5 1 4 1 4 58 Get tired for no reason. 17 1.3 1.9 0.9 0.6 1.0 1 4 1 4 59 Mind clear as usual ....... as 1.9 1.7 2.1 1.0 0.9 1.0 1 4 1 4 60 Easy 10 G0 thingsu....ccccssssssssrssarivsinissorssnsrrsns 2.1 2.0 2.1 1.1 1.0 14 1 4 1 4 61 Restless, can’t keep still........mumminsmsmens 21 2.1 2.2 1.0 1.2 1.0 1 4 1 4 62 Hopeful about SULUI ......commireessssnsassussnsinsses 1.8 1.6 2.0 1.0 0.8 1.1 1 4 1 4 63 More irritable than usual .......c.ceeveeeeeeerenennnns 1.7 1.6 1.8 0.8 0.8 0.8 1 4 1 4 64 Easy to make deciSions........cueevereereeeeesienennes 2.2 1.9 24 1.1 1.0 +3 1 4 1 4 65 Feel useful and needed.........ccceeeeeererererernnnne 2.2 22 22 “3 11 11 1 4 1 4 66 Life's pretty full ......coummirimesnsis reer 1.8 1.9 1.8 1.0 0.9 1.0 1 4 1 3 67 Others better off if | were dead..........c........ 1:3 1.2 1.1 0.5 0.6 0.4 1 4 1 4 68 StH ENJOY UNINGS ciiisscsesrissessnrisrmssssssmpnning 1.9 1.9 1.9 1.0 1.0 1.0 1 4 1 4 69 Zung total score (SDS) .....cccveevieerrnrerinnnnne 45.0 || 42.3 | 46.7 11.8 || 10.2 | 12.4 25 100 28 81 COLLEGE HEALTH QUESTIONNAIRE (CHQ)4 70 CUrrent DeOression cu. c.ussvomvsemsicmsspissonss 38.9 || 36.3 | 40.6 9.6 7.0 10.6 19 75 22 65 7" Past Depression 28.6 25.5 | 30.5 8.7 6.5 9.3 14 56 15 48 72 ANRIOLY . o.oo sis er seummsis ans himmss rad TE ass r i a 11.1 9.8 | 11.9 3.7 29 3.9 6 25 6 21 See footnotes at end of table. 17 Table 1. Means, standard deviations, and score ranges for the major data elements, by sex—Con. Score range | Mean value Standard deviation fern . Potential Actual total num- Major data element be Tout Lives § FF 1 rors [mae] FT) 4 High | L Hi ota ale | le ota ale | le ow ig ow igh PERSONAL FEELINGS INVEN- TORY (PFI)5 73 DRESS Oasis simmnitrmriisissiianisstesnssasrssnaisive 10.3 9.8 | 10.6 7.9 9.0 7.1 0 45 0 32 74 AIREY oi dinnisincernivaisassniossssssnnsinmssabionmmssoninin 4.8 3.8 B.5 3.8 3.8 3.6 0 2 0 18 1Total number of students = 195 (79 males, 116 females). 2A higher GWB score reflects higher positive well-being. 3Scored according to the revised 1967 manual. 4Total number of students = 127 (49 males, 78 females). 5Total number of students = 68 (30 males, 38 females). Table 2. Evaluative assessment of unweighted national sample based on the General Well-Being (GWB) total scale scores Percent Total distri- Descriptive attribution of evaluative assessment of general well-being or distress GWB |, bution score of sample POLE 1 niesisnsssvassvnrissessinivsammeersrsivensnssssssssssisunsntisnnnen iss RaE EEE FEA RISIE TT THES STI 449042 E AE TREE EF ER OR ER AFAI SISTA SR RRR ERE 100.0 POSTIVE WEBRING 1s crirerssimnessnpnhio ss sre Teas A TS A ET ATE Ar TAR pra A rr Tre RTL ARSE RA SEP 74.1 EUG HTIOON coaieisvssssntsnarsonenninssrsiovarsiasisssssans ives sansa sens nab REA AE SETAE REE EHH AY STATI THY STIR REPRO CREAR PHO SATA RR Re 101-110 10.4 Strong positive .... 91-100 22.7 Moderately high .. 81-90 22.4 Low positive.. A 76-80 + 95 NV LORI hi rsithencese netsesvsntsnsinnenson tosis ent nis tome erg RS AAR TE TA Sr eee rosie the wns vis essa sans ian sn sie SOAS sAs SH Fe TT er ton nn 71-75 oO. POD SI NT CAEIVE STrBS ii iitorsassssnssrnirnnnsssssinrsernansbnsanssssn ri isasasssssnbe bE EUaRsRER LALA RR ISTATA LIER E RRR REA ASIA TEA uk pURR RAL 16.3 66-70 6.9 61-65 5.4 56-60 4.0 9.6 51-565 3.1 41-50 35 26-40 23 00-25 0.7 NOTES: n = 6,931; X = 80.3; S.D. = 17.7. 18 Table 3. Number and percent distribution of study sample, by total General Well-Being (GWB) scale and interviewer depression rating scale Percent Depression rating scale GWB score distri- Total bution 0 1 2 3 4 5 6 7 8 10 Number All students........ccceerunenns 100.0 195 63 60 42 15 6 5 2 1 1 - Positive well-being................ 59.6 116 49 42 20 3 2 - - - - - FO Ed rr sires sannammissarainianshs 2.6 5 3 1 1 - - - - - - - 91-100.... 10.3 20 8 8 3 - 1 - - . - - 81-90...... 21.0 41 37 13 9 2 - - - - - - 76-80...... 15.4 30 11 13 5 1 - - - - - - ai Teta athens abbas aa swe 10.3 20 10 7 2 - 1 - - - - - Problem-indicative stress...... 22.5 44 11 1 13 3 2 3 1 - - - 9.7 19 3 4 7 3 1 1 - - - 7.7 15 5 5 4 - - 1 - - - - 5.1 10 3 2 2 - 1 1 1 - - - 17.9 35 4 6 9 9 2 2 1 1 1 - 8.7 17 4 4 4 4 1 - ’ - - 3 4.6 9 - 1 3 3 1 1 - - - - 4.6 9 - 1 2 2 - 1 1 1 1 - Mean GWB SCOrE ....cccicrcssismsmsersirnves 72.4 | 784 | 76.0 | 69.6 | 57.7 | 66.8 | 51.8 | 45.0 | 40.0 | 31.0 - Standard deviation .... 16.7 i 13.2 jy 13.81 15.3 | 17.0] 158 | 14.3 - | 12.0 - - 19 Table 4. Product-moment correlation coefficients of major data elements with interviewer depression rating, and significance levels, by sex Item Fe- Fe- num- Major data element Total {| Male halo Total || Male male ber GENERAL WELL-BEING SCHEDULE (GWB) Correlation coeffi- Significance level Scale items cient 1 DO OQSIIIIILS os vsuvaroassnsnssnsdorsssrsbeibiRenness ass sssssnsssnsesnsnneesnsssssssassssssanssssnsnamnesnbuss 34 28 38 .000 || .012 .000 2 INEIVOMSIIOSS cout i 0s ssrsanespastarsvesiesnntinas 35 44 30 .000 || .000 .001 3 Firm control of behavior, emotions.. i 38 31 43 .000 {| .006 .000 4 Sa, iSCOUIAGEU, NODBIBES. ove isiivmirismmssssismmsnstmmssssastrmssashasssiessasms sisainsnsan 39 27 46 .000 || .016 .000 5 STDS, SErAINY AD OISUNE crrvraceisisiosissssrenmmssmrssnsirasinsinnnisssssssensivsnsessssnsanshsoebonnnins 26 15 33 .000 | .197 .000 6 Happy, satisfied with life......cccccccuviinnnne. 28 25 30 .000 || .027 .001 7 Afraid of losing mind, or losing control.. 34 30 37 .000 || .007 .000 8 ANXIOUS, WOTTIOU, UDSEL s.verivissicssmarsnisimsissssssamnssssssisssssivnsassnsssssssssssiiiavinns 33 33 35 .000 || .005 .000 9 Waking Srasly, rOSIOO ..coscirsissscinsrissssrsmrssininssssssenssessntonmasnsssnssntbonsssssiisssostonins 28 24 30 .000 || .031 .001 10 Bothered by bodily disorders . 29 37 26 .000 || .001 .006 11 Interesting daily life.............. 29 13 39 .000 || .267 .000 12 DoWnheartad, DINE ji wimicirommariermtsoinssstissrssasseisssresserssessnss asses 39 31 44 .000 || .005 .000 13 Emotionally stable, SUre of Self ......arirerrsrrrssasssssssosssssnssnsnsinssnsins 33 24 39 .000 || .032 .000 14 Feeling tired, worn out.............. 24 07 33 .001 .540 .000 15 Health concern, worry .. 20 30 14 .005 || .008 A382 16 Relaxed-tense............ 32 29 33 .000 || .009 .001 17 Energy level............ i 27 22 30 .000 || .046 .001 18 DEprassEtl-CHBBITUN ..ivisscirerermmisissisissimmmssssissssssivisn me mmsrrsis assis csernsrrers sivas 38 35 40 .000 || .002 .000 Criterial items 19 P3YCHOIOQIC PrOBIBITIS iessisssrrrsrrrmmserrasersninnsinsssnisnssssrsssasnrionsinssrssssasssssssssnsasonys 30 26 32 .000 .021 .001 20 Felt near nervous breakdown . 25 01 39 .001 || .955 .000 21 Hac) NETVOUS DIORKUOWIN 2.0100 issersssassrsrssssarssssasasmsssnsiins sassasisnssaninssbnnninsssshnss vis 25 12 31 .001 .307 .001 22 CHR CaHRATIONT esis essnsassirsimrsisrir ssi sisss THES reir rT aoa esse amare reasy 28 21 32 .000 || .065 .001 23 Psychologic attention... ae 18 08 25 .010 || 474 .008 24 SOC Alem OL IONG) SUPPO TE vosrrrirrirrersssensrssasmsvssssssnsesnsinsinunnntinnibs ss stisnnpessions 19 15 22 .008 || .196 .016 Subscales 25 Freedom from health concern, Worry, diStress ...........ccovveireerieereeeernnenennnesenes 27 35 21 .000 || .002 .021 26 3s AE EO DR 31 25 35 .000 || .028 .000 27 Satisfying, interesting life. 34 23 39 .000 || .044 .000 28 Cheerful versus depressed mood.......... 44 36 48 .000 || .001 .000 29 Relaxed versus tense, anxious feeling .. ii 38 35 40 .000 || .002 .000 30 EMOHONBI-DENAVIOIA) COMIIOL 110s eissisvinsmmenmirrsississssssreritssssss mess savsnrvssansssiusin 43 36 48 .000 || .001 .000 31 GWE 1018) S010 ..0ii0misivnisismranio sisrssssssissvitarss mmbssns sos savmimsisestsessss ai snnsspesss pias 47 45 48 .000 || .000 .000 32 NGO isnt Be ARTE ER EYE FEE ANA EA A PEE aps TRA pee SATA RAS 15 22 12 .031 || .053 .184 33 Interviewer ABPresSSION FaTIND. cru cutenssienssmensimrnimsstisiisbotssinisssdorsitatbosnrvunis PSYCHIATRIC SYMPTOMS SCALE (PSS) 34 AATIXEORY vs inironssiuvss savin ston nin ei isss sas vrasas sinsssai in Sammi sins ns SHURE Eh ms aR RB re amr 40 36 42 .000 || .001 .000 35 ODT BSS ON 35. dens rrasrrerssnrrnsennisntnshona sada nas ties snas IEE FER A RAN ST rasa 39 25 47 .000 || .025 .000 MINNESOTA MULTIPHASIC PERSONALITY INVENTORY (MMPI) Validity scales 36 LY 00, is vss mmsensini ims rma teres sass ssa thos A AT A TE A nia Bons -12 -21 -06 .083 || .066 516 37 (F) Validity ...... 34 13 45 .000 || .251 .000 38 (K) Correction -21 -01 -30 .003 il .397 .002 20 Table 4. Product-moment correlation coefficients of major data elements with interviewer depression rating, and significance levels, by sex—Con. item : Fe- Fe- pun. Major data elements Total || Male tale Total || Male ole Clinical scales Correlation coeffi- Significance level cient 39 (Hs) A I A 24 33 19 .001 || .003 .045 40 (D) Depression .. 21 05 32 .003 || .683 .001 41 (Hy) Hysteria ....... 19 17 21 .008 .141 .027 42 (Pd) PoyChopathic 26 08 37 .000 || .489 .000 43 (Mf) Masculinity- Femininity Interests » 08 07 16 .290 || .544 .088 44 (Pa) Paranoia......... 18 01 27 .014 || .917 .003 45 (Pt) Psychasthenia.... 21 14 27 .003 || .210 .004 46 (Sc) Schizophrenia... 25 13 34 .001 .250 .000 47 (Ma) Hypomania ...........cocersssssnsonsieness 18 14 21 .010 || .203 .024 48 (Si) Social Introversion-Extraversion..... 17 12 19 .018 || .282 .037 ZUNG DEPRESSION ITEMS 49 DOWNNEEIIB, DIUB....init irrvriresrimvseensrssmimssivmmatsderssmsvisessnistissossessissiose 19 -13 34 | .033 | .381 .002 50 Morning, feel best..... 07 -08 15 404 || .560 .182 51 Crying spells.......... 7 -17 24 .062 237 .032 52 Trouble sleeping....... 05 -11 13 .603 || .465 337 53 Eat as much as usual. 13 -05 19 131 .754 .095 54 Still enjoy seX........... 18 -20 36 .043 || .158 .001 55 Losing weight... 05 34 -04 652 || .018 .720 56 Constipated........... 09 -10 15 .291 .506 .192 57 Heart beats fast ...... 03 14 -04 754 || .347 .726 58 Get tired for no reason. 16 -02 20 .081 902 .082 59 Mind clear as usual ....... 21 -07 33] .016 || .636 .003 60 Easy to do things.......... 07 -09 13 442 || .554 .245 61 Restless, can’t keep still... 26 19 31 .004 || .196 .006 62 Hopeful about future ...... 22 14 24 .014 || .346 .032 63 More irritable than usual . 25 05 33 .006 || .750 ,003 64 Easy to make decisions.... 10 01 13 .254 || .946 242 65 Feel useful and needed. 22 09 29 .012 || .652 .011 66 Life is pretty full.. 15 -07 24 102 || .641 .036 67 Others better off i V3 were deed ave 15 -06 30 .100 || .692 .009 68 SEH BOIOY TINGE 1vviiuiinrionsssrsmmimmaninmssesesens passekiTa seams ts bas sss ss de henss ass nnsnasin 17 -08 29 065 |i .579 .009 69 ZING E018) SCOTE ISDB) ..ivrisirisisimninsmiiaismssimsiismm stems rasssssnssss sons So rssas 28 || -01 39 .002 || .934 .001 COLLEGE HEALTH QUESTIONNAIRE (CHQ) 70 UPTON DOPIESSION rium inv si as Sasa sas sw Serer TESS se ds RES Eg 36 -01 48 .000 || .960 .000 7 Past Depression 34 03 45 | .000 || .812 .000 72 Anxiety 10 02 13 .243 || .877 .268 73 Depression 50 57 42 .000 || .001 .009 74 Anxiety 41 42 42 .001 || .019 .008 NOTE: Decimal omitted before correlation coefficients. 21 Table 5. Intercorrelations among the Depression, Anxiety, and GWB scales for combined male and female sample Scales and subscales (1) (2) (3) (4) (5) (6) (7) | (8) (9) (10) | (11) | (12) | (13) | (14) | (15) | (16) |(17) Depression 1. Interviewer depression rating. hed 2. GWB—Cheerful versus depresse: 44 vie 3. PSS—Depression..... 39 70 en 4, MMPI—Depression . 21 50 53 oo. 5. Zung—Depression... 28 62 63 72 ob 5 6. CHQ—Current Depression 36 n mn 50 66 wh 7. CHQ—Past Depression .. 34 58 65 40 59 96 Tr 8. PFl—Depression 50 67 78 65 | (1) (1) (1) Anxiety 9. GWB—Relaxed versus tense-anxious............ 38 70 59 39 51 69 61 66 ‘es 10. PSS—Anxiety .. 40 60 65 43 56 78 75 | 78 76 ge 11. CHQ—Anxiety 10 37 42 26 46 63 65 | (1) 51 72 vi. 12. PFI-Anxiety ... 41 51 65 45 (1) (1) (1) | 66 62 80 (1) Other GWB 13. Emotional-behavioral control...........ecuevennne 43 69 64 41 61 64 57 | 63 64 62 45 58 He 14. Satisfying, interesting life 34 72 52 50 55 47 33 54 52 43 24 37 55 7% 15. Energy level Po 31 64 52 42 52 67 59 | 70 58 54 44 46 53 48 16. Freedom from health concern, worry or distress... 27 25 29 28 26 44 44 | 46 48 49 34 38 33 16 41 or 17. Total scale.. 47 87 70 53 66 80 69 | 78 88 76 52 63 79 n 79 56 Number of items per scale or subscales . 1 4 7 60 20 19 14 | 45 4 10 6 21 3 2 3 2 18 Number in sample... 195 [195 | 195 {195 | 127 | 127 | 127 | 68 | 195 | 196 {| 1127 68] 195 | 195] 195] 195 | 195 22 1Scales not taken together by the same students. NOTE: Decimal omitted before correlation coefficients. Table 6. Product-moment correlations of major data elements with General Well-Being (GWB) total scale, subscales, and subscale multi- ple correlations (R) for total sample GWB subscale E Sub- Item Health Satis- =Mo- | scale num- Major data element Yor con- fying, | Cheer Re- | tional |i. ber scale Sern Brergy inter. ful Yor laxed boy. ple Hp eve esting sus o versus ioral R worly life presse tense con- trol GENERAL WELL-BEING SCHEDULE (GWB) Scale items 1 GOO SPIES: cvs 20 00rvrrassssinsmmmsninsissseunsniesitsn shimstis 73 14 59 64 83 58 57 84 2 Nervousness... es RATE 67 35 36 40 55 78 54 79 3 Firm control of behavior, emotions. LE 65 21 45 44 59 B52 82 82 4 Sad, discouraged, hopeless.... 72 29 41 50 79 62 69 84 5 STross, SIAN, PICSSUNE w.rsrisremssssssssssssasssnssssrminairk 68 38 51 38 53 75 49 76 6 Happy, satisfied With 11§8..1.......ccocmssrsibesnrmmsianerss 64 12 43 87 69 47 51 88 7 Afraid losing mind, or losing control. 52 30 28 35 41 40 77 80 8 Anxious, worried, UPSet .......coeeverens 75 37 45 47 67 81 62 83 9 Waking fresh, rested ............. 60 28 79 39 47 47 36 80 10 Bothered by bodily disorders 52 75 41 19 28 43 40 77 1 Interesting daily life ............. 57 16 42 85 55 41 42 86 12 Downbhearted, blue... 77 19 54 64 88 64 65 89 13 Emotionally stable, sure ¢ of Seif 76 29 55 54 68 64 83 85 14 Feeling tired, worn out............ 67 45 77 34 50 55 47 79 15 Health concern, worry... 48 94 33 12 19 43 24 95 16 Relaxed-tense.. 77 45 53 45 59 920 59 91 17 Energy level.. ot 69 31 88 47 60 46 47 89 18 Deprassedhcheeriul RRR SA ATALANTA EARS 78 21 62 68 92 60 53 93 Criterial items 19 Psychologie DrODICINIS ...ovmmserrnsssuissrssssinbevensassinsssns 49 37 43 22 40 38 45 55 20 Felt near nervous breakdown .........ccceeeviinciinnennnns 47 34 32 24 34 48 43 52 21 Had nervous breakdown ....... 12 20 05 02 10 07 1 125 22 Clinical patient............... 25 30 17 13 19 17 23 34 23 Psychologic attention........ 17 29 09 07 09 12 18 32 24 Social-emotional support 26 18 22 23 23 15 24 32 Subscales 25 Freedom from health concern, worry, or distress... 56 Pa 41 16 25 48 33 26 ENCrOY 18Vel...conivinsmsrrsimiriimsrinimssmrnsmisiaion 79 41 ae 48 64 58 53 27 Satisfying, interesting life.....cceeeeeeveninisisnenenenenenns 71 16 48 me 72 52 55 28 Cheerful versus depressed mood .. 87 25 64 72 Dek 70 69 29 Relaxed versus tense-anxious...... 88 48 58 52 70 a 64 30 Emotional-behavioral control ......ccceeveiiirrinninnnnnnns 79 33 53 55 69 64 31 GWE LOA $0815. criss ssrsrississtins srsssssnersimsssanseinisins 56 79 71 87 88 79 32 NG chro ei EA A AA -13 01 -10 -20 -16 -05 -13 123 33 Interviewer depression rating.........cc.oeeeerevevennnnnnes -47 -27 -31 -34 -44 -38 -43 -49 PSYCHIATRIC SYMPTOMS SCALE (PSS) 34 ANKIGY iicoivereissnminiisisesssss ass Rs SARS EEA ES 76 49 54 43 60 76 62 80 35 EDOPTBSE ON cules cus irumunssrsnsasurssmninsssgsaisnisasanesiensuns 70 29 52 52 70 59 64 74 INot significant at .01 level. 23 Table 6. Product-moment correlations of major data elements with General Well-Being (GWB) total scale, subscales, and subscale multi- ple correlation (R) for total sample—Con. GWB subscale Bio Sub- Item Health Satis- - | scale num- Major data element To con- z fying, Chaer- | Fe Yonal, multi- ber cern NOISY | mere | Tulver-iy laze bahay ple level . sus de- versus ioral R or esting worry life pressed tense con- trol MINNESOTA MULTIPHASIC PERSONALITY INVENTORY (MMPI) T SCORES Validity scales 36 YB, Lis ie tris innstEessssnri ima amisn ness unsnsnonsgins 24 21 23 09 17 25 "13 30 37 (F) Validity .... -56 -40 -45 -38 -46 -43 -53 -60 38 (K) Correction 49 33 43 25 40 a4 39 52 Clinical scales 39 (HS) HY POChONGRIASIS....c cv seis ss crsmssriresssasssanassns 40 33 32 25 31 33 32 42 40 DY DBD BEEION orien rtarinsissani vounmribnaresisnsostab it tuumnrsis 53 28 42 50 50 39 41 57 41 (HY) HYSIBEIN oviiinnnsiaiisssimssansmsrarssssisnssivenss 39 31 29 30 32 29 33 43 42 (PA) PSYCHODALINIG cvcorsnrevsirnseresssssmssissssnsmmsssssssitis 46 33 34 39 43 31 36 52 43 (Mf) Masculinity-Femininity Interests................. 01 00 03 -12 01 04 02 120 44 {PBS PAPEIIBIE ov iereiinsorsnrsvanrsssirsshsstnasriressansinnmnes 36 32 15 18 28 36 33 45 45 (Pt) Psychasthenia.... son 45 19 32 39 42 39 39 47 46 {S0) SCRIZOBNIBIIG toreissserrisrssssisvisrarissansssssstansanns 53 35 38 36 44 43 52 56 47 (Ma) Hypomania ........cceveeereirnvneaenn. 16 22 13 11 07 16 27 43 48 (Si) Social Introversion-Extraversion.. A 15 36 41 42 35 36 47 ZUNG DEPRESSION ITEMS 49 Downhearted, DIUS ...c.casimimmri simian 52 17 36 49 52 38 53 59 50 MIOTAING, TE0L DBE .vuiisssisiirsrrersuissremcnmeissinrivhesine 01 05 08 03 01 01 03 115 51 PY INGIBDBIS cress cmnniesssnnirerniasssssisgstinansrsrorassrmrnsans 39 23 29 22 37 33 33 41 52 TroUbIE SIGEDING .oscisriivrersivirsrsmismormvssmrssssssssessss 27 18 33 08 16 20 27 39 53 Eat as much 88 USUBl..cicerisrrm srrsss mas snsnmmssssssssasanes 32 18 14 25 30 27 34 38 54 SLi BION SEX. e ovis rrsinrsrmrssrssssasessesnassiosasasensetingsins 31 06 23 31 35 20 31 38 55 LOSING WBIBNT cooisssnsvsscmsissmsnusnsssimimasssnsnsssssnssansnn 1 08 01 09 09 1 13 119 56 CONSUPAIEt ..... cover sivssinrenrsnmersienmsivismmmersssrissssnents 25 08 18 30 19 29 12 40 57 Heart beats fast .............. siseirid snare 15 13 07 05 1 13 22 125 58 Get tired for no reason... stese 43 24 45 36 36 27 36 50 59 Mind cloar as USUB) ...csssmeermirsessisrss mining 46 13 24 41 45 44 45 53 60 EASY 10.00 thITO8. ..unerrmssrnssmirenmasestrnsssssssrsssns 42 14 41 35 41 33 34 46 61 Restless; can’t Keep StHll.....iccccisverreesmemssivasssassserres 36 28 25 16 28 35 28 39 62 Hopeful 3bout FUTUN wivisssmirrsianissssisrinsns 47 06 37 46 54 30 45 58 63 More irritable than usual .......cccceueeeereeieninneniniennnns 33 24 33 15 27 26 21 37 64 Edsy 10 NARS TBOISIONS...ommrrissnrrsssmsssersssssssesrinsenas 40 12 34 32 38 35 36 43 65 Feel useful and needed... He 56 19 50 48 53 42 45 59 66 Lifes profly SUM... vrssinmsensinmsscimsossnsinererssy 41 12 26 58 42 28 28 58 67 Others better off if | were dead... whit 25 02 17 24 29 14 34 39 68 Still enjoy thINGS wsseinsirisiinissnnsssssnnseivesvrnts 37 19 29 27 32 28 39 41 69 2ZUng toa) SEOTB SDS)... cere mrersvneersnreininmernnss 66 26 52 55 62 51 61 69 24 INot significant at .01 level. Table 6. Product-moment correlations of major data elements with General Well-Being (GWB) total scale, subscales, and subscale multi- ple correlations (R) for total sample—Con. GWB subscale Emo Sus. Item Health Satis- =O | scale num- Major data element Void con- | fying, Lh Be Yona multi- ber cern Nargy inter- u yor axe be 2 ple oF eve esting | e versus | iora R Worty life presse tense con- trol COLLEGE HEALTH QUESTIONNAIRE (CHQ) 70 Current Depression , 80 44 67 47 71 69 64 81 71 Past Depression... wk 69 44 59 33 58 61 57 73 72 ANKIBLY So cvcisisimmninisvnsnvssinmvrersssstassssssssssssasassunesson 52 34 44 24 37 51 45 57 PERSONAL FEELINGS INVENTORY (PFI) 73 Depression... etree REAR 78 46 70 54 67 66 63 80 74 INCIIBRY ov suivinsnsassmrirb hint saa RS A RRR ATF Urn tt nih 63 38 46 37 51 62 58 67 NOTE: Decimals omitted before correlation coefficients. 25 Table 7. Product-moment correlations of the major data elements with other Depression and Anxiety scales for total sample Pussies College Health Porson ymploms MMPI | Zung Questionnaire eelings Scale (CHQ) Inventory (PSS) (PF1) Item num- Major data element Cur- Posi ber Anx- | De De: De- fea dee | Amx-] P| An jety | O15 | Ores | pres © | pres- | iety | PTS | ety sion sion sion pres- | Gon sion sion GENERAL WELL-BEING SCHEDULE (GWB) Scale items 1 GOO SDITIIE co unriivsissssmomaisnsisnasmnssssiinransisstisrsssgs 50 53 39 49 60 49 36 56 44 2 INBIVOUSNIESS. cvuvesssssssssssssansnsnsnsasssrerse 67 52 37 43 58 52 36 57 52 3 Firm control of behavior, emotions... 45 50 21 46 52 47 38 45 40 a4 Sad, discouraged, hopeless............... 56 72 43 56 68 59 33 57 45 5 Stress, strain, pressure ......... . 51 46 21 32 50 44 40 42 41 6 Happy, satisfied with 11€.....ciusurercsssssrsaresusennnansen 41 47 41 47 39 28 23 41 31 7 Afraid losing mind, or losing control ............cce... 46 49 39 51 52 48 34 34 37 8 Anxious, worried, UPSet ......ceeerreerens 65 59 32 48 67 62 49 53 45 9 Waking fresh, rested ....cocecrsrissnssneerinsians 43 37 33 41 52 46 27 59 34 10 Bothered by bodily disorders .........c...... 48 37 28 36 47 49 34 46 46 1 Interesting daily life .......coceunennne 31 45 46 50 42 28 18 83 33 12 Downhearted, blue .......ccceeeeeriunenes 55 65 44 58 65 59 32 62 50 13 Emotionally stable, sure of self .... 61 55 41 B65 57 48 40 66 57 14 Feeling tired, worn out ...........c... 50 43 33 39 60 55 36 61 47 15 Health concern, worry... w 42 21 22 14 35 35 29 38 28 16 REIBXOAABNGG .ovsiessivasssesseininimsssserbivsssssnssrnsssssannnios 67 44 37 43 55 46 43 61 60 17 ENGIOY JBVEL...corscsnssvsssnnsarebisrirsomas verse seinsrsesssnsosnss 44 46 40 48 53 43 37 60 39 18 Depressed-chesrful .....ccusssimm sess rmrimesiesny 49 55 46 54 57 43 29 55 39 Criterial items 19 Psychologic problems... ...cc.cusmreereessrrrsrmnsirmsnrarare 48 38 19 34 49 51 41 47 59 20 Felt near nervous breakdown ......cceeeeeieieieiiiniennnnne 53 39 23 31 49 45 45 33 26 21 Had nervous breakdown ......ursmmnsnsssessisssise 18 18 15 07 12 15 09 06 09 22 Clinical patient.............. 23 19 17 21 21 22 17 04 09 23 Psychologic attention... 5, 23 18 16 21 16 18 12 10 12 24 SoCial-smotional SUDO .......vsrrissrssssssssssssssnsnsianss 23 31 31 31 26 22 05 27 26 Subscales 25 Freedom from health concern, worry, or distress... 49 29 28 26 44 44 34 46 38 26 ENEIOY 18VBL..i cs cimimnrristrmsrinmivisssisansyssmssisssine 54 52 42 52 67 59 44 70 46 27 Satisfying, interesting 8.......c.irerercessisssarsrrsnenesnes 43 52 50 55 47 33 24 54 37 28 Cheerful versus depressed mood......c.cceeevunnrennnnnnee 60 70 50 62 71 58 37 67 51 29 Relaxed versus tense, anxious 76 59 39 51 69 61 51 66 62 30 Emotional-behavioral control 62 64 41 61 64 57 45 63 58 31 GWE O10) SCALE SCOT wives erssisivsivismiaisursssssirinssss 76 70 53 66 80 69 52 78 63 32 IE Drs tear a EE TE LNs SAA Ania TARE ss ER Rte -02 10 04 -05 02 01 -02 08 -06 33 Interviewer depression rating.........ccceceeeeeeeernnieeenens 40 39 21 28 36 34 10 50 41 PSYCHIATRIC SYMPTOMS SCALE (PSS) 34 EL PE 65 43 56 78 75 72 78 80 35 Depression 65 53 63 it) 65 42 78 65 26 Table 7. Product-moment correlations of the major data elements with other Depression and Anxiety scales for total sample—Con. Peyohiansic College Health possond ymptoms MMPI | Zung Questionnaire gelings Scale (CHQ) Inventory fem (PSS) (PFI) num- Major data element Cur ber Art: De- De- De- rent Past AliR- De- Aries ity, [Bes | pres. | pres- der pres- | ety | PT | ety sion sion sion pres) ion sion sion MINNESOTA MULTIPHASIC PERSONALITY INVENTORY (MMPI) T SCORES Validity scales 36 (LY 0800. cviimmesisinnimismsinesnninsssiaperssbasirprsssinsaniers -23 -14 -02 -13 -23 -21 -26 -41 -31 37 {F} Validity .nuicnnat simi 62 60 59 62 62 58 46 60 56 38 (K) Correction -58 -53 -37 -50 -60 -59 -B1 -63 -52 Clinical scales 39 (Hs) HY POCRONGIIBSIS o.oo cinssmssssmsssnsrurnmvsasonnigs 39 30 44 51 40 36 31 27 25 40 UD) DODY EEE ON cx sxs sunsvsssissnnmmsnsnarnummissapasprsssssatanssns 43 53 Ca 72 50 40 26 65 45 41 UHY TY HYSIOrIA oc crsvimnimamnsinimisssismmm ssi 31 27 41 46 34 31 21 24 22 42 (Pd) Psychopathic 38 41 55 46 42 36 12 42 40 43 (Mf) Masculinity-Femininity Interests......ccccoe...... 02 09 11 -07 -07 -12 -18 10 -07 a4 APB) PATBIBIO. f1ssi ns iunissisommimsrsnbonasissionssibimossain 42 41 32 38 40 43 27 24 37 45 (Pt) Psychasthenia.. 41 52 66 57 42 36 30 60 53 46 (Sc) Schizophrenia. 54 55 62 64 55 50 39 59 58 47 AMIS) HY DOMAMB coiierssinreisnisarsransmssssssasn 30 22 -05 08 17 25 24 34 36 48 (Si) Social Introversion-Extraversion .........ccceeee.. 41 51 65 63 51 45 41 54 46 ZUNG DEPRESSION ITEMS 49 DoWnReartBd, DINE ......cusmniissremnnssvonmmassmissase 43 58 58 66 50 44 32 50 Morning, Tol IdESt. ...ccivimsmmmivirrscissssiosrrrinsisinios 01 -10 14 14 -05 -08 02 51 Cry ING SPOS ovsinsussrenseiitrmssirnnssss sss toes Gasser sates 43 39 27 52 49 51 38 52 Trouble sleeping > 35 18 13 34 33 35 43 B3 Et a8 MUCH AT USUABL ....oiccerrimsmiprsrmsssstsssssssansusenes 3] 25 27 52 31 30 21 54 SHIEONJOY SEX. vinsinissisimmeicisimsisnsssrrsistiarsssatsasnsss 29 41 30 51 34 28 12 55 Losing weight... 11 10 18 32 14 17 16 56 Constipated...... 26 18 34 39 29 27 12 57 Heart beats fast ......... 15 17 23 27 14 15 20 58 Get tired for no reason... 37 47 42 65 39 34 36 59 Mind clear as usual .... vy 42 45 47 62 44 38 31 60 BAY 10/0 NISL. cunmmsremmmarinerihnssshisssanebnisase 32 37 48 64 36 29 29 61 Restless, can’t keep still...........civeecrrsrssssssrsressannsans 41 33 30 47 38 37 22 62 Hopeful about future .... 32 46 57 67 42 31 26 63 More irritable than usual .. 29 39 31 46 43 44 25 64 Easy to make decisions.. 30 39 47 58 42 40 38 65 Feel useful and needed.. 46 52 59 73 55 45 27 66 Life is pretty full ....cevvcnvennnnnninnn i 28 38 57 61 35 24 13 67 Others better off if | were dead........cccevecnvneenennns 12 26 35 39 29 25 05 68 SI BNJOY TINGS cooviimmmivmmsrnissmvsnssvsirerebtbasssstimminte 29 30 49 63 82 26 20 69 Zang total score (SDS .c.u uummnsinsmmsirsiimainsi 56 63 72 66 59 46 COLLEGE HEALTH QUESTIONNAIRE (CHQ) 70 Current Depression .... ATA 78 71 50 66 AT: 96 63 71 Past Depression ... wy 75 65 40 59 96 oi sls 65 72 A IYXIBLY viii. isiare rin Ther Tenses et ines Suess bine 72 42 26 46 63 65 27 Table 7. Product-moment correlations of the major data elements with other Depression and Anxiety scales for total sample—Con. Psychiatric Personal Symptoms 1 vr | zu Collate Heat: Feelings Scale 9 gy e Inventory (PSS) (PFI) Item num- Major data element Cur- Past Der Ark De- De- De- rent d Any De- ARY ot pres- pres- pres- de- fet pres- . Y sion sion sion pres- pres ty sion inty sion sion PERSONAL FEELINGS INVENTORY (PFI) 73 Depression. ...csseisueses PARR RATS TATRA ECR 3 78 78 65 : ’ Ta 66 74 AVIS se rvsinsaunssnasshionssssiesinssonessn tas amin s iv E seta Hy 80 65 45 y 66 " NOTE: Decimals omitted before correlation coefficients. Table 8. Person-type cluster analyses descriptive statistics, by group type, sex, and scale Group 1 Group 2 Group 3 Group 4 Group 5 Sex and scale jo - w= co ph n X SD n X SD n X SD n X SD n X SD Male TTOLBN ciucinriversseissrmnnarersstantnmibbnnessisrensans 25 21 8 22 3 1. Free from health worry 13.5 1.7 12.7 1.6 69 | 1.4 10.7 | 29 7.0 7.2 2. Energy level ......c..ecreraer 15.4 2.2 12.2 1.8 109 | 4.0 103 [29 10.3 2.3 3. Satisfying, interesting life........... 6.7 1.6 5.3 1.7 7.4 1.2 44 113 33 2.5 4. Cheerful versus depressed mood. 20.7 2.7 17.4 2.2 186 | 22 14.1 |: 39 7.3 4.9 5. Relaxed versus tense, anxious . 20.2 2.8 15.9 3.3 136 | 3.3 135 | 3a 4.7 35 6. Emotional-behavioral control.. 14.0 1.2 125 1.9 12.7) 1.0 104 | 25 4.7 21 7: Total GWB ....oc.oonsarivissniasnass 90.5 8.1 76.0 7.6 70.1 7.9 63.4 | 6.8 37.3 8.3 8. Interviewer depression rating ..... 1.00 | 0.86 0.66 | 0.66 1.6 | 0.66 16 | 1.0 5.6 1.1 Female TOD. coun wnnriismrsrsmessamvensissmininnnss ix pussheh 39 30 1" 23 13 1. Free from health worry.. 13.6 1.2 10.5 24 ‘74 | 28 110 {- 2.1 7.9 4.2 2. Energy level ......uivien 15.0 2.3 124. | 20 81] 23 93 "25 6.5 23 3. Satisfying, interesting life..... 7.7 1.3 6.4 1.9 6.2 | 14 45 | 1.6 2.4 13 4, Cheerful versus depressed mood. 19.6 2.7 18.0 26 178 | 1.6 12.7 | 20 7.2 2.5 5. Relaxed versus tense, anxious .... 18.9 23 16.0 2.6 13.8 32 9.0 | 28 7.8 33 6. Emotional-behavioral control.. 13.1 1.1 12.7 1.0 98 | 21 88 | 17 6.4 2.0 7. Total GWB ve 88.1 8.7 75.9 5.4 63.1 3.7 55.3 1'85.2 38.1 6.4 8. Interviewer depression rating ............cceeeeveennn. 0.92 3.3 0.73 | 0.83 1.3 1.5 20 | 0.83 3.2 1.9 28 NOTES: n = number of students: X = mean; SD = standard deviation. APPENDIX CONTENTS Interest Inquiry and Debriefing sretsersenstnsnssnsaisistnstsasnsananseeens Thank-You Letter Assurance of Confidentiality Statement and Authorization for Release of Academic Records Subscale Items Psychiatric Symptoms Scale (PSS) sessccccstnsssasas General Well-Being Schedule (GWB) General Well-Being Case Record Summary Sheet Group 2 Subject Interview Form ARERR SAAT SARE Therapist Rating Zung Self-Rating Depression Scale (SDS) College Health Questionnaire Items (CHQ) Personal Feelings Inventory (PFI) ......ccueeee 29 30 INTEREST INQUIRY AND DEBRIEFING PSYCHOLOGY RESEARCH - 1020 Anyone wishing to participate in a program dealing with testing and/or treatment of psychological problems (e.g., depression, anxiety) may sign up for any day Monday through Thursday between 8:30 A.M. and 2:30 P.M. Each session must consist of a two hour block of time. Experimental credit will be given for your participation, with further appointments and credit op- tional. Your participation is voluntary, of course. We guarantee any infor- mation you provide will be kept strictly confidential through an elaborate numerical system. Due to the limited size of the project everyone cannot be accepted for consideration. If you are interested in this project, print your name, address, phone number, hours you can be reached at that phone number, and the day and hours you will participate. Be certain to include this information below and on the attached 4 x 6 card. If none of the times listed above are suitable, enter in days and times that you would like to participate; you will be contacted and an appointment will be made. NAME ADDRESS PHONE HOURS YOU CAN BE REACHED DAY AND TWO HOUR BLOCK OF TIME Please report to Sandburg W1020 at the time you indicated above. Keep this sheet and give the filled out 4 x 6 card to the assistant. Thank you for your cooperation. A. F. Fazio THANK-YOU LETTER LU LLM THE UNIVERSITY OF WISCONSIN—MILWAUKEE / MILWAUKEE, WISCONSIN 53201 DEPARTMENT OF PSYCHOLOGY PHONE: (414) 963-4746 June 29, 1973 Dear Participant: Thank you very much for your participation in our project dealing with psychological testing (in Sandburg Tower West 1020). All participants were requested to return for additional testing -- not because anyone was "dif- ferent," but because we were interested in many kinds of tests. In general, our testing permitted us to establish norms for these tests and to estimate which tests correlated with which other tests. The norms are described as having been obtained from "normal college students." Of course, all the data are anonymous and identification lists are destroyed after the last testing contact. If this experience has disappointed you regarding "psychological test- ing" or "clinical psychology" or "counseling," please be advised that not all testing programs or counseling services are conducted in the same manner. In no case was any test or other procedure used which would have any negative consequence - - other than to bore you! Hopefully, you had an opportunity to see what psychological tests, some used nationally, are like. If you have any additional questions, please contact me at 963-4710. Thank you, again, very much for your cooperation and interest. Sincerely, Anthony F. Fazio, Ph.D. Associate Professor 31 32 ASSURANCE OF CONFIDENTIALITY STATEMENT AND AUTHORIZATION FOR RELEASE OF ACADEMIC RECORDS ASSURANCE OF CONFIDENTIALITY STATEMENT I understand that all information which would permit identification of the individual will be held strictly confidential, will be used only by persons engaged in and for the purposes of the survey, and will not be disclosed or released to others for any other purposes. Signature Date AUTHORIZATION FOR RELEASE OF ACADEMIC RECORDS I authorize release of my academic records (e.g., grade point average, courses dropped, honors seminars) for use by Dr. Fazio in this particular survey, and I understand that these records will not be used for any other purpose and will be kept strictly confidential. Signature Date Dr. A. F. Fazio PSYCHIATRIC SYMPTOMS SCALE (PSS) Please answer each item with respect to its being True or False for you during the present or past month. (Score: number marked True). Depression Scale (7 items) 5. You sometimes can't help wondering if anything is worthwhile anymore. 13. Nothing ever turns out for you the way you want it to. 17. You have had periods of days, weeks or months when you couldn't take care of things because you couldn't "get going." 24. Most of the time you wish you were dead. 25. You have periods of feeling blue or depressed that interfere with your daily activities. 26. In general, would you say that most of the time you were in very low spirits. 39. Do you feel somewhat apart or alone even among friends. Anxiety Scale (10 items) 1. Are you ever bothered by nervousness, i.e., by being irritable, fidgety or tense--would you say often. 3. You are worried about sex matters. 4. You have personal worries that get you down physically, i.e., make you physically ill. 7. You have periods of such great restlessness that you cannot sit long in a chair. 8. You feel anxiety about something or someone almost all of the time. 22. Do you ever have any trouble in getting to sleep or staying asleep-- would you say often. 33. You have special thoughts that keep bothering you. 34. You have special fears that keep bothering you. 44. You have often taken sleeping pills or other drugs to calm your nerves. 45. Are you the worrying type--you know, a worrier. 33 34 GENERAL WELL-BEING SCHEDULE (GWB) DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE PUBLIC HEALTH SERVICE HEALTH SERVICES AND MENTAL HEALTH ADMINISTRATION NATIONAL CENTER FOR HEALTH STATISTICS HEALTH AND NUTRITION EXAMINATION SURVEY GENERAL WELL-BEING a. Name (Last, first, middle) b. Deck No. 171 d. Sex 1 [Male 2[ 1Female c. Sample No. e. Age READ — This section of the examination contains questions about how you feel and how things have been going with you. For each question, mark (X) the answer which best applies to you. . How have you been feeling in general? (DURING THE PAST MONTH) 1. 001 1 [J In excellent spirits 2] In very good spirits 3[ In good spirits mostly a[ 11 have been up and down in spirits a lot 5s [| In iow spirits mostly 6 [| In very low spirits strain, stress, or pressure? (DURING THE PAST MONTH) or stand 2] Yes -- quite a bit of pressure 3[ ] Yes -- some - more than usual 4] Yes -- some - but about usual s[] Yes - alittle 6 [| Not at all 1 [ | | | i | | | | 2. Have you been bothered by nervousness or your 2 | 1 [_] Extremely so -- tothe point where | ‘‘nerves’’? (DURING THE PAST MONTH) ! could not work or take care of things 2[] Very much so | I 3 1 Quite a bit : 4] Some -- enough to bother me SA little 6 [ |] Not at all | 1 3. Have you been in firm control of your behavior, 3. | 1] Yes, definitely so thoughts, emotions OR feelings? (DURING THE 1 PAST MONTH) ! 2] Yes, for the most part I 3] Generally so | I 4] Not too well ; 5] No, and | am somewhat disturbed | 6 (_] No, and | am very disturbed | 4. Have you felt so sad, discouraged, hopeless, or 4, | 1 [] Extremely so -- to the point that | have had so many problems that you wondered if I just about given up anything was worthwhile? (DURING THE PAST ! in MONTH) 2! Very much so : 3 [1 Quite a bit ; 4] Some - - enough to bother me : s [_] A little bit 6 [| Not at all | 1 5. Have you been under or felt you were under any 5. : 1] Yes -- almost more than | could bear i | | | | | [ I | I | I | How happy, satisfied, or pleased have you been with your personal life? (DURING THE PAST MONTH) 1 [] Extremely happy —could not have been more satisfied or pleased 2 [] Very happy 3 [_] Fairly happy 4 [] Satisfied -- pleased 5 [_] Somewhat dissatisfied 6 [|] Very dissatisfied . Hove you had any reason to wonder if you were losing your mind, or losing control over the way you act, talk, think, feel, or of your memory? (DURING THE PAST MONTH) 1 {J Not at all 2] Only alittle 3] Some -- but not enough to be concerned or worried about 4] Some and | have been a little concerned s[_] Some and | am quite concerned 6 [|] Yes, very much so and | am very concerned . Have you been anxious, worried, or upset? (DURING THE PAST MONTH) 1 [] Extremely so -- to the point of being sick or almost sick 2] Very much so 3] Quite a bit a] Some -- enough to bother me s [A little bit 6 [| Not at all . Have you been waking up fresh and rested? (DURING THE PAST MONTH) 1 [_] Every day 2 | Most every day 3[] Fairly often 4] Less than half the time s [| Rarely 6 [| None of the time 10. Have you been bothered by any illness, bodily disorder, pains, or fears about your health? (DURING THE PAST MONTH) 1 [1 All the time 2 [_] Most of the time 3] A good bit of the time 4 [|] Some of the time s [| A little of the time 6 [| None of the time . Has your daily life been full of things that were interesting to you? (DURING THE PAST MONTH) 1 [_] All the time 2 {| Most of the time 3] A good bit of the time a] Some of the time s J A little of the time 6 1 None of the time 12. Have you felt down-hearted and blue? THE PAST MONTH) (DURING 12. 1 All of the time 2 1 Most of the time 3 A good bit of the time 4 Some of the time s [| Alittle of the time 6 [| None of the time 35 36 13. Have you been feeling emotionally stable 13. ¥ 1 All of the time and sure of yourself? (DURING THE PAST 2 3 Most of the time MONTH) i | 3] A good bit of the time 1 4 [| Sone of the time s[_] A little of the time 6 [_] None of the time | 14. Have you felt tired, worn out, used-up, or 14. 1 All of the time P | exhausted? (DURING THE PAST MONTH) | 2 [] Most of the time : 3] A good bit of the time : a[_] Some of the time s[_] A little of the time : 6 [_] None of the time : For each of the four scales below, note that the | words at each end of the 0 to 10 scale describe ! opposite feelings. Circle any number along the i bar which seems closest to how you have gen- ; erally felt DURING THE PAST MONTH. | I 15. How concerned or worried about your HEALTH 15. ! 1 2 4 have you been? (DURING THE PAST MONTH) ; g : : : Pugin | heb Li } Not Very | concerned concernad at all d i 16. How RELAXED or TENSE have you been? 16. | & Fig Boa. 5G 7 8 Nie. Ag (DURING THE PAST MONTH) I | | | bol pad lege] J | ~~ J Very Very | relaxed tense I 17. How much ENERGY, PEP, VITALITY have 17. | 8.1 "2 3 Ww is. Pow 90 you felt? (DURING THE PAST MONTH) | SR Ree | No energy Very y AT ALL, ENERGETIC, \ listless dynamic | 18. How DEPRESSED or CHEERFUL 18. | 0 -%F. 203 48 6 7,18 9 0 have you been? (DURING THE PAST MONTH) re y Very Very i depressed cheerful 19. Have you had severe enough personal, 19. 1 [] Yes, and | did seek professional help I emotional, behavior, or mental problems that you felt you needed help DURING THE PAST YEAR? 2] Yes, but | did not seek professional help 311 have had (or have now) severe personal problems, but have not felt | needed professional help 4] | have had very few personal problems of any serious concern s_} | have not been bothered at all by personal problems during the past year Have you ever felt that you were going to have, or were close to having, a nervous breakdown? 1 he 1 [J Yes -- during the past year 2[] Yes -- more than a year ago 3[J No | | I I 1 21. Have you ever had a nervous 21. 1 [J Yes -- during the past year breakdown? 2[] Yes -- more than a year ago 3[J No I 22. Have you Sys bess a petisnt {5 Sulpationt) 22. } 1] Yes -- during the past year aot a mental hospital, a mental health ward o | re a hospital, or a mental health clinic, for any 2[] Yes =« more than a year ago personal, emotional, behavior, or mental problem.’ 3[J No 23. Have you ever seen a psychiatrist, psychologist, 23. V 1[] Yes -- during the past year or psychoanalyst about any personal, | s emotional, behavior, or mental problem g[).Yes-- more than ayes: ago concerning yourself? ! 3[JNo 24. Have you talked with or had any connection J with any of the following about some personal, I emotional, behavior, mental problem, worries, or ‘‘nerves’’ CONCERNING YOURSELF DURING | THE PAST YEAR? a. Regular medical doctor 24a. | (except for definite physical 2] No I conditions or routine check-ups) . ........ | @) 1] Yes I b. Brain or nerve specialist ............. b. 1] Yes 2[] No c. Nurse (except for routine medical conditions) . . ........ 0... c.! 1] Yes 2[JNo d. Lawyer (except for routine ; Yegal services) « visu v.00 nw ii wine elnie d. | 1] Yes 2[ No e. Police ( except for simple I Srafiic violations) iv viiiee eee 0 00m mw i0 0 w e. | 1] Yes 2[] No f. Clergyman, minister, priest, y rabbi, ete. coi tC EL ET ae f. 1] Yes 2[]No g. Marriage Counselor . ......... 2 g. LJYes 2[JNo h. Social Worker... .vovveureannnann.. h. 1] Yes 2[JNo i. Other formal assistance:. ............. ie 1 [_] Yes — What kind? 2] No 25. Do you discuss your problems with any members 25. 1 [J Yes - and it helps a lot of your family or friends? 3] Yes - but it does not help at all 4] No - | do not have anyone | can talk with about my problems s [_] No - no one cares to hear about my problems 6 [_] No - | do not care to talk about my problems with anyone I I | f I I I I | | | | | | 1 | | | 2[]Yes - and it helps some - | I | | | I | | I | | | i ) 7 [J No - | do not have any problems 37 GENERAL WELL-BEING CASE RECORD SUMMARY SHEET NAME (Last, First, Middle) Adjustment Factors g £§ @ Sample No. ER: 5 SITUATIONAL-BEHAVIORAL 5 20 ° : INDICATORS Ss Sex: M F Age: £ E o@ 8 (2 - s = @ = mo @ S38 Zl gE 218 egl2 - aR alle scl. (E5128|3% 1 £5lcs 2E|8_|28|5¢8|54]58 $523 ADJUSTMENT INDICATORS tele 2e|lea|Sz|2¢c E 22 ce 5 c2|3E|58I25 £5 won 8 2 cg Item Description Scoring Lolw2 wn tO cliwo Criterion Vanables @=ja 1. Good spirits *%'31''2° 3-4. 5.6 19. Psychologie Problems 3.2.3 cers *%* 5 3.210 Ee 20. Felt ncar nervous breakdown 12 3 FRR 21. Had nervous breakdown 23 ecm 2 Nervousness 1 2:% 45. 6 22. Clinical patient L 2.3 rel 0.12 3.4.5 23 Psychologic attn. 1.23 24. Other contacts reflecting 3 Firm control of ¥ 2.8 4.5.6 psych. problems: Yes No 5 ; 9 behavior, emotions 5 4 3.2.10 3. Regalar STUY. 1 9 4. Sad, discouraged, 1'2:'%3 4.5 6 b Deda nerss Shee. ! 5 — hopeless 12.8348 SI ET . ini d. Lawyer 1 2 ST 5. Stress, strain, L2 3:4-5.6 ¢. Police 1 2 ——v— 81 2 pressure 345 ee f. Clergy 1 2 6. Happy, satisfied aise ny g Manlage Counselor 1 2 SE ith life 5 1:89°1" 9 h. Social Worker I 2 et wi iam i. Other formal contact 1 2 PE 7. Afraid losi ind, 1-2 6 Li : ; ! a ar am 674 3 : 3 0 25. Social-Emotional Support Recode ‘ . 1. Yes-helps a lot 6 8. Anxious, worried, l] 2-3-4 5 6 2. Yes-helps some 1 upset 0 r2345 nn 3. Yes-but no help 1 4. No-have no one 2 9. Waking fresh, 1-2: 83'4 5 6 5. No-no onc cares 3 rested 5 43 22.10 a 6. No-do not care to talk 5 7. No-do not have problems 7 10. Bothered by 12% 45 6 bodily disorders 0 1-284 5 SH il. Interesting daily 1728 45 6 life 5 4 872 1 0 ne 12, Downhearted, blue 1 23456 86 0 42 °3 4.5 RL, 13. Emotionally stable, 1 2°34 5.6 sure of self 5 4.83 2.19 i 14. Feeling tired, 1 2. 3'¢ 5 6 wormout 0.1.2 3'4°5% RATING SCALES 15. Health concern, worry 0 1.28" ¢a'5°6 78:9 10 10 9 87 6 5-43 21 0 ease 16. Relaxed-Tense 0:1-28%8 4985867 .8 9 10 1009 8 7 6.5 43°21 0 oii 17. Energy level 012 345 6,789 10 ri 18. Depressed-Cheerful 01 2% 4 56178910 Sum of sub-scales u HH (22 3 4) (5 (6) Total Adjustment * - actual response *% - coded values NOTE: High scores indicative of 38 good or positive adjustment GROUP 2 SUBJECT INTERVIEW FORM Good morning (afternoon) . . . . . how are you today? (Pause) I'd Tike to thank you for coming and participating in this project. (Pause) Before I begin, I'd Tike to read to you this statement of confidentiality. (Read) If you understand and agree to this, please sign the statement. Thank you. Sex 1=M 2 =F 1. What is your present age and year in school? Age: (actual age scored) Year: 1 2 3 4 2. From what kind of school did you graduate: Public (1) ; Parochial (2) ; Private (3) 3. How many credit hours are you taking this semester? 4. Are you presently employed? If so, how many hours per week (on the average) do you work? Employed: 1 = Yes 2 = No Number of hours: 5. What is the source of support for your education? 6. Do you consider yourself to be a religious person? (If so, what is your religion?) How strong are your beliefs? Religion: Background: Strength: 7. What is your marital status? Married Single Divorced Separated Widowed 8. Are you satisfied with this status? If not, why? (If married) How many children do you have? . 39 10. 11. 12, 13. 14. 15. 16. 17. 18. 19. 40 (If single) Do you have a girlfriend (boyfriend)? On the average, how often do you see this person per week? Are you satisfied with the arrangement? If not, why? 2 = Yes 1 = No What are your present living arrangements? (at home with parents, dorm, etc.?) Do you like it that way? If not, why? 2 = Yes 1 = No How well do you get along with your mother? How well do you get along with your father? How well do you get along with your brothers and sisters? (If badly with anyone - ask: Can you please explain this more fully?) Are you satisfied with these relationships? If not, why? Are you presently taking any medication? If so, what type and for what reason? 1 = No 2 = Antidepressant Was this medication prescribed by a physician? 20. 21. 22. 23. 24. 25, 26. 27. 28. Are you taking any street drugs? If so, what type and how often? Have you ever received any psychological treatment? If so, when, for how long, and for what reasons? 2 = No 1 = Yes Would you say that you are making satisfactory progress toward your future goals? If not, why? 2=Yes 1=No Could you please describe one positive event in your life that you're presently conscious of; a pleasant condition or circumstance that you're happy about. How positive? On a scale from 0 (least positive) to 20 (more positive). Please describe a negative event; an unpleasant condition or circumstance that you find discouraging or uncomfortable. How negative? On a scale from 0 (least stressful) to 20 (more stressful). As you see yourself, what are some of your weak personality traits? What things about yourself might cause you No in coping with your environment? Now please list some of your strong personality traits: Things about yourself that benefit you in your daily life. What circumstances (i.e., external events) do you feel interfere or act as obstacles towards obtaining satisfaction in your life? Do you have any problems which seem to interfere with your present life, nagging or persistent problems which seem to occupy an annoyingly large amount of your thought-time? a. How does this concern interfere? (loss of sleep, preoccupied, can't eat, etc.) b. Can you estimate how many hours per week you are bothered by this problem? 41 29. 30. 42 c. To what extent has this problem interfered with your life? (forced to drop classes, etc.) Try to rate it from 0 (not at all) to 20 (interferes extensively). What other things may be of concern to you at this time? Would you like to talk to someone free of charge about your concerns? If yes: 0.K. (fine). However, because of the large number of people being interviewed, we cannot guarantee that all individuals will be able to be seen. If we are able to include you, you will be contacted most Tikely in the next couple of weeks. Until then, thank you very much for your participation in the project, thus far. If no: Thank you very much for your participation in this project. THERAPIST RATING The depression rating scale ranges from 0-10. Examples of some classification criterion are below: 0- Person seems pleasant and satisfied with his or her life at the present time. 1- Person is neither happy or depressed. This is the neutral category. 2- Person shows concern with his or her problems and is slightly depressed. 5- Person appears unhappy and is distressed with his or her life problems. 8- Person explicitly communicates distress and a desire for assistance. 10- Person has a hopeless, helpless attitude and extemporaneously displays extreme distress and shows no insight as to how he or she can deal with his or her problems. Persons who exhibit behavior more severe than this can be given a higher score. 43 ZUNG SELF-RATING DEPRESSION SCALE (SDS) Please answer these items as they pertain to you now. Response options and response values* A Tittle Some Good Most of the of the part of of the Time Time the Time Time 1. I feel down-hearted and blue. 1 2 3 4 2. Morning is when I feel best. 4 3 2 1 3. I have crying spells or feel like it. 1 2 3 4 4. I have trouble sleeping at night. 1 2 3 4 5. I eat as much as I used to. 4 3 2 1 6. I still enjoy sex. 4 3 2 1 7. I notice that I am losing weight. 1 2 3 4 8. I have trouble with constipation. 1 2 3 4 9. My heart beats faster than usual. i 2 3 4 10. I get tired for no reason. 1 2 3 4 11. My mind is as clear as it used to be. 4 3 2 1 12. I find it easy to do things I used to. 4 3 2 1 13. I am restless and can't keep still. 1 2 3 4 14. 1 feel hopeful about the future. 4 3 2 1 15. I am more irritable than usual. 1 2 3 4 16. I find it easy to make decisions. 4 3 2 1 17. I feel that I am useful and needed. 4 3 2 1 18. My life is pretty full. 4 3 2 1 19. I feel that others would be better off if 1 were dead. 1 2 3 4 20. I still enjoy the things I used to. 4 3 2 1 *The sum of these values are converted to a 25-100 score scale by dividing the raw score values by.80. COLLEGE HEALTH QUESTIONNAIRE ITEMS (CHQ) "Lately" or recently refers to the past six months; "past" more than six months. Read the questions closely and literally notice modifying words. (Item response score values are shown for each item as numbered.) Current Depression (7 items) 4. How has your mood been recently? 1. quite elated 2. happier than usual 3. average 4. somewhat low 5. quite Tow 10. Compared to usual, when you wake up recently, are you able to face the day or do you have to push yourself to get started? 4. push a lot 3. push a little 2. no trouble getting started 1. get started much more easily than usual 27. Have you maintained your normal social interest and activities recently, or have you avoided being with people (not counting times when you wanted to study)? 4. definitely avoided people 3. somewhat avoided people 2. about the same as always 1. much easier to be with people than usual 38. Have you recently felt that you have let either your parents, yourself, or others down in a major way? 2. yes ¥« no 59. How does the future look to you now? really black a little bad about average better than usual fabulous — NWP oOo 61. Compared to usual how has your energy been recently? . really great--more than I need! . good--about average . somewhat less energy than usual C 1 2 3 4 quite a bit less than usual 45 68. Have you recently tended to be more critical of yourself than usual? 3. a lot more 2. some more 1. not really Past Depression (2 items) 22. Have you had periods of feeling more irritable than usual? 4. frequent periods of irritability lasting two weeks or more 3. frequent periods lasting a shorter time 2. occasional periods of irritability lasting two weeks or more 1. no striking periods of feeling more irritable than usual 60. Has there ever been a period of time when your mood was low, apathetic, or depressed but only for a few days at a time? 4, often 3. sometimes 2. rarely 1}. never Current and Past Depression Items in Common (12 items) 1. Was there ever a time when you had unusual or severe trouble concentrating on schoolwork? J. Ap 2. yes, but only in the past 3. yes, just recently 4. yes, in the past and recently too 5. Have you had periods when it seemed to take a longer time than usual to fall asleep at night? Y.: 00 2. yes, but only in the past 3. yes, just recently 4, yes, in the past and recently too 13. Have you had periods in your life when you had thoughts of harming yourself? 1. no 2. yes, but only in the past 3. yes, just recently 4. yes, in the past and recently too 15, 17. 26. 30. 39. 46. 48. Have you ever had trouble waking up too early without being able to go back to sleep? 1. no 2. yes, but only in the past 3. yes, just recently 4, yes, in the past and recently too Have there been periods of more than a day or so in your 1ife when your appetite was unusually poor? Yo no 2. yes, but only in the past 3. yes, just recently 4, yes, in the past and recently too Have you ever been bothered by your sleep being less refreshing than usual for more than a day or two at a time? 1. no 2. yes, but only in the past 3. yes, just recently 4. yes, in the past and recently too Have you ever been bothered by periods in your life when you would sleep too much or want to sleep more than usual during the day? no 2. yes, but only in the past 3. yes, just recently 4, yes, in the past and recently too Have there been times when you felt (even if momentarily) that you might be better off dead? 1. no 2. yes, but only in the past 3. yes, just recently 4. yes, in the past and recently too Have you had periods in your life when you felt like crying more than usual? 1. no 2. yes, but only in the past 3. yes, just recently 4 yes, in the past and recently too Have you had periods (lasting two weeks or more) when you felt more tired than usual, no matter how much sleep you were getting? no 2. yes, but only in the past 3. yes, just recently 4 yes, in the past and recently too 47 55. 63. 21. 25. 49. 54. 48 If you ever tried to harm yourself physically, when did it happen? 1. doesn't apply 2. tried it in the past 3. tried it just recently 4. tried it in the past and just recently Have you had periods (lasting more than two weeks) of being low, depressed, down in the dumps, or blue? Yi 00 2. yes, but only in the past 3. yes, just recently 4, yes, in the past and recently too Anxiety (6 items) Have you felt your heart pounding or beating fast and at the same time fearful, tense, or jittery even when the situation you were in was not 5 stressful one (as in making a speech, etc.)? . no 2. yes, but only in the past 3. yes, just recently 4, yes, in the past and recently too Do you have marked fears of certain situations like being in a closed place, standing on heights, being in crowds, going outside, or into the dark to such an extent that sometimes it makes you avoid doing things you would otherwise like to do? 2. yes, but only in the past 3. yes, just recently 4. yes, in the past and recently too Have you had "attacks" of being "short of breath" or unable to catch your breath, and at the same time felt fearful or jittery? 1. no 2. yes, but only in the past 3. yes, just recently 4. yes, in the past and recently too Have you had marked feelings of weakness, tiredness, or fatigue when doing even a small amount of exercise? 1 no : 2. yes, most of my life, but haven't sought medical advice about it 3. yes, most of my 1ife, and have consulted a doctor about it 4 yes, occasionally 5 almost never 56. 73. Are you ever so tense, worried or upset before or during exams that it interferes with your performance on the test? 3. often 2. occasionally Te never Have you had painful or uncomfortable sensations in your chest that make you question whether you might have heart trouble or a heart attack? 1. no 2. yes, but only in the past 3. yes, just recently 4. yes, in the past and recently too 49 PERSONAL FEELINGS INVENTORY (PFI) The Personal Feelings Inventory was presented as a list of true-false questions in which the Depression and Anxiety subscales were mixed. The only instructions to the subject were "Please answer these items as they pertain to you now." ("True" responses scored) Depression subscale (45 items) 1. I have less interest than usual in things. 2. I have difficulty concentrating. 3. I am often sad or depressed. 5. I feel depressed most of the time. 6. I have trouble giving attention to ordinary routine. 8. I have felt life wasn't worth living. 0. I have difficulty coming to a conclusion or decision. 11. I feel overwhelmed with life. 12. My thoughts dwell on a few troubles. 14. I have kept up very few interests. 15. Little if anything interests me. 17. I spend less time at usual recreational activities. 19. I feel miserable or unhappy. 20. I can't concentrate when reading. 21. I am bothered by feelings of inadequacy. 23. I have too little energy. 24. I can't concentrate on movies or T.V. programs. 50 26. 28. 29. 30. 32. 33. 35. 37. 38. 39. 41. 42. 44, 46. a7. 48. 50. 57. 53. 55. 57. 58. 59. 61. I tend to depreciate or criticize myself. I don't seem to smile anymore. I enjoy almost nothing. I enjoy doing little if anything. I have had difficulty with my memory lately. I keep losing my train of thought. I think about my death. My thoughts get muddled. I have trouble remembering something I have just read or heard. I seem to be slowed down in thinking. I spend time sitting around or in bed. Recently I've been thinking of ending it all. My memory is impaired. My movements are slowed down. I can't make up my mind. I have thoughts about killing myself. I feel slowed down. I am discouraged about the future. I have lost interest in work. I can't concentrate on what people are saying. I feel worthless. I have little interest in movies or T.V. I spend almost no time at recreation. I feel i11 at ease with people in general. 51 62. 64. 65. 66. My future is bleak. I get angry with myself. I have a diminished appetite. I feel slowed down in my thinking. Anxiety Subscale (21 items) 4. 7 9. 13. 16. 18. 22. 25. 27. 31. 34. 36. 40. 43. 45. 49. 52. 54. 52 I have been uneasy or anxious in the past month. I have tried to avoid one or more situations in the past month. I tremble; my hands are shaky; I feel weak at the knees. My hands are sweating and clammy. I feel hot and cold, and blush or get pale readily. I have butterflies or a sinking feeling in my stomach. My heart pounds or flutters when I am uneasy or panicky. I have fear of a particular object or situation. I have a dry or coated mouth. My fears prevent me from participating in some activities. I have dizziness, faintness, and/or giddiness. I have difficulty in getting my breath, and have a choking, tightness in my chest. I have attacks of fear or panic and feel I have to do something to end it. I am uneasy when I go out alone or stay home alone. I avoid going out alone or staying home alone. I am uneasy when in an enclosed space. I am uneasy when in crowds. I avoid being in crowds. & E 56. I get attacks of sudden fear or panic. 60. I avoid being in an enclosed space. 63. I continually feel afraid of things. %U.S. GOVERNMENT PRINTING OFFICE: 1977— 260-937:31 53 VITAL AND HEALTH STATISTICS PUBLICATIONS SERIES Formerly Public Health Service Publication No. 1000 Series 1. Programs and Collection Procedures.—Reports which describe the general programs of the National Center for Health Statistics and its offices and divisions, data collection methods used, definitions, and other material necessary for understanding the data. Series 2. Data Evaluation and Methods Research.—Studies of new statistical methodology including experimental tests of new survey methods, studies of vital statistics collection methods, new analytical techniques, objective evaluations of reliability of collected data, contributions to statistical theory. Series 3. Analytical Studies.—Reports presenting analytical or interpretive studies based on vital and health statistics, carrying the analysis further than the expository types of reports in the other series. Series 4. Documents and Committee Reports.—Final reports of major committees concerned with vital and health statistics, and documents such as recommended model vital registration laws and revised birth and death certificates. Series 10. Data from the Health Interview Survey.—Statistics on illness; accidental injuries; disability; use of hospital, medical, dental, and other services; and other health-related topics, based on data collected in a continuing national household interview survey. Series 11. Data from the Health Examination Survey.—Data from direct examination, testing, and measurement of national samples of the civilian, noninstitutionalized population provide the basis for two types of reports: (I) estimates of the medically defined prevalence of specific diseases in the United States and the distributions of the population with respect to physical, physiological, and psychological charac- teristics; and (2) analysis of relationships among the various measurements without reference to an explicit finite universe of persons. Series 12. Data from the Institutionalized Population Surveys.—Discontinued effective 1975. Future reports from these surveys will be in Series 13. Series 13. Data on Health Resources Utilization.—Statistics on the utilization of health manpower and facilities providing long-term care, ambulatory care, hospital care, and family planning services. Series 14. Data on Health Resources: Manpower and Facilities. —Statistics on the numbers, geographic distrib- ution, and characteristics of health resources including physicians, dentists, nurses, other health occu- pations, hospitals, nursing homes, and outpatient facilities. Series 20. Data on Mortality. —Various statistics on mortality other than as included in regular annual or monthly reports. Special analyses by cause of death, age, and other demographic variables; geographic and time series analyses; and statistics on characteristics of deaths not available from the vital records, based on sample surveys of those records. Series 21. Data on Natality, Marriage, and Divorce.—Various statistics on natality, marriage, and divorce other than as included in regular annual or monthly reports. Special analyses by demographic variables; geographic and time series analyses; studies of fertility; and statistics on characteristics -of births not available from the vital records, based on sample surveys of those records. Series 22. Data from the National Mortality and Natality Surveys.—Discontinued effective 1975. Future reports from these sample surveys based on vital records will be included in Series 20 and 21, respectively. Series 23. Data from the National Survey of Family Growth.—Statistics on fertility, family formation and disso- lution, family planning, and related maternal and infant health topics derived from a biennial survey of a nationwide probability sample of ever-married women 15-44 years of age. For a list of titles of reports published in these series, write to: Scientific and Technical Information Branch National Center for Health Statistics Public Health Service, HRA Hyattsville, Md. 20782 4 7 4 4 1/4 a ny < ve STA ¥ oI 17 aL Cen 0 RS % E 3 p = bs e) he NCHS ~ e} &G on fe Sew @ ©) XH CE Cl Lely, ORL CRT EY CES CL LC CR OE EH TET An Intellectual-Development (ID) Index A Socio-Intellectual-Status (SIS) Index A Differential-Intellectual-Development (DID) Index U.S. Children and Youths, 6-17 Years U.S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE Public Health Service Health Resources Administration VITALand HEALTH STATISTI DATA EVALUATION AND METHODS RESEARCH Library of Congress Cataloging in Publication Data Dupuy, Harold J. The construction and utility of three indexes of intellectual achievement. (Vital and health statistics: Series 2, Data evaluation and methods research; no. 74) (DHEW publication; (HRA) 78-1348) Includes bibliographical references. Supt. of Docs. no.: HE20.6209:2/74 1. Intelligence tests. 2. Psychological tests for children. I. Gruvaeus, Gunnar, joint author. II. Title. III. Series: United States. National Center for Health Statistics. Vital and health statistics: Series 2, Data evaluation and methods research; no. 74. IV. Series: United States. Dept. of Health, Education, and Welfare. DHEW publication; no. (HRA) 78-1348. [DNLM: 1. Intelligence tests—Infancy and childhood—United States—Statistics. 2. Intelli- gence tests—In adolescence—United States—Statistics. W2 A N148vb no. 74] RA409.U45 no. 74 [BF431] 312°.07°23s [153.9°3] ISBN 0-8406-0106-9 77-608140 DATA EVALUATION AND METHODS RESEARCH Series 2 Number 74 The Construction and Utility of Three Indexes of Intellectual Achievement: An Intellectual-Development (ID) Index R Socio-Intellectual-Status (SIS) Index A Differential-Intellectual-Development (DID) Index U.S. Children and Youths, 6-17 Years A methodological report on the construction and utility of three indexes of intellectual achievement. The concept of partitioning a measure of intellectual development into measurable components and the method of criterion scaling are seen as providing a structure for use by behavioral scientists in general as well as in the particular case of the search for contributing and impeding conditions associ- ated with intellectual development. DHEW Publication No. (HRA) 78-1348 U.S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE Public Health Service Health Resources Administration National Center for Health Statistics Hyattsville, Md. September 1977 NATIONAL CENTER FOR HEALTH STATISTICS DOROTHY P. RICE, Director ROBERT A. ISRAEL, Deputy Director JACOB J. FELDMAN, Ph.D., Associate Director for Analysis GAIL F. FISHER, Associate Director for the Cooperative Health Statistics System ELIJAH L. WHITE, Associate Director for Data Systems JAMES T. BAIRD, JR., Ph.D., Associate Director for International Statistics ROBERT C. HUBER, Associate Director for Management MONROE G. SIRKEN, Ph.D., Associate Director for Mathematical S tatistics PETER L. HURLEY, Associate Director for Operations JAMES M. ROBEY, Ph.D., Associate Director for Program Development PAUL E. LEAVERTON, Ph.D., Associate Director for Research ALICE HAYWOOD, Information Officer DIVISION OF HEALTH EXAMINATION STATISTICS MICHAEL A. W. HATTWICK, M.D., Director HAROLD J. DUPUY, Ph.D., Psychological Adviser LINCOLN OLIVER, Chief, Psychological Statistics Branch ROBERT S. MURPHY, Chief, Survey Planning and Developing Branch Vital and Health Statistics-Series 2-No. 74 DHEW Publication No. (HRA) 78-1348 Library of Congress Catalog Card Number 77-608140 ACKNOWLEDGMENT This study was made possible through the support of Dr. Nicholas Zill of the Foundation for Child Development (345 East 46th Street, New York, N.Y. 10017) and of the Foundation itself. When the concepts of a Socio-Intellectual- Status index and a Differential-Intellectual-Development index were first men- tioned to Dr. Zill he immediately grasped their conceptual implications and their potential utility. He provided the assistance of Gunnar Gruvaeus for a 6-month period and the Foundation paid all costs attendant to Mr. Gruvaeus’ services. Mr. Gruvaeus’ statistical and programing expertise and his subject-matter knowledge were critical in carrying this study to, the scope and level of technical attainment it reached. Harold J. Dupuy, Ph.D. 3 i “ “EE. wil - . 5 3 ® hd igs Bh we. x Si asi! oy _ LP a “ns a ! po ) Sg wn oes iw lea wide 5% Hy - 3 ae Ble E fad Th Le na ar Ky AL (ae hic ol i LT x . ro iy = J Be ] nn ? gett, 3 os Lyf » tr Cain gle 1 4 : vy BT | nr et " : BA oy Los . hy ji 1 2 Ry Eh . Be ei i Ek as ) i E Fong) i piri - 0 ha Eo bre, es pa rly [Eons aA Sr rf peas om feel uri ¥ pair HE a el Bl i gs UE on ey A cee . . i . iy a or =. eh =i oa I" i 5 pride Coes fi od [Hn whan of fel pms RR wi ie w Ps . ee tik my gt are) Rol Ly Jit Jnl viral coi ily oe bs - FENN oi he oh 4 them Sl AT Li maf hE ns = aka py Set Sess dF ie. ah hg . ] - oo pride lL Ed i Hits ii i rpands Sided fein iss PA Chenin ; fh i ab hae Pri bik a Fi a an i «5 a ) o ol a kL TAT ® Al HE ] : io Eat tatpa sin ged fT 1 rien d ret Se A 5 i : Sa i =a hg B bl hE CONTENTS Acknowledgment Summary Method Utility Substantive Findings Index Development..... Introduction Criterion Scaling of Predictor Variables The Index of Intellectual Development (ID) The Index of Socio-Intellectual Status (SIS) The Index of Differential-Intellectual Development (DID) Race-Specific SIS and DID Indexes....... Examined Sample Compared to Population Estimates Intercorrelations of the Indexes vosns Substantive Findings Application of the ID and Race-Specific SIS and DID Indexes to Substantive Examination Findings from Cycle II, Children 6-11 Years of Age References....... List of Detailed Tables Appendix: Technical Notes LIST OF TEXT TABLES A. Response levels and percents of variance accounted for in general and in race-specific indexes, by race, of intellectual achievement by independent variables for children and youths aged 6-17 years with means and standard deviations of indexes B. Percent variance accounted for by four independent predictor variables C. Unweighted sample size, mean Intellectual-Development (ID) scores, standard deviations, and con- structed variables, by sum of both parents’ education in years, with percent variance accounted for and correlation ratios D. Unweighted sample size, mean Intellectual-Development (ID) scores, standard deviations, and con- structed variables, by annual family income per person under 21 years of age in household, with percent variance accounted for and correlation ratios E. Unweighted sample size, mean Socio-Intellectual-Status scores, means and standard deviations of Intellectual-Development scores and Differential-Intellectual-Development scores, by each value of the Socio-Intellectual-Status index, with percent variance accounted for and correlation ratios ....... F. Obtained means, standard deviations, range of scores, and Socio-Intellectual-Status and Intellectual- Development correlations for race-specific Socio-Intellectual-Status iNdEXES ...ceesseersrreecrsancsssaasesaanens G. Examined sample and population estimates summary statistics, by race and intellectual indexes .......... — = = td fd COIN NNNN 15 16 24 9 vi H. Matrix of product-moment intercorrelations of the indexes, by race ......... ores sesssssssnsaressrsersnsnesees J. Correlation coefficients, means, and standard deviations for intellectual indexes and selected variables.. K. Sample size and mean index scores of intellectual achievement, by number of pregnancies previous to birth of examined child, with percent variance accounted for and correlation ratios......ceseesssesascsessssss L. Sample size and mean index scores of intellectual achievement, by attendance at nursery school or kindergarten, with percent variance accounted for and correlation ratios.....c.... wevssees sseressussarsessenvavassnn M. Sample size and mean index scores of intellectual achievement, by nature of talking problem, with percent variance accounted for and correlation ratios N. Sample size and mean index scores of intellectual achievement, by twin status, with percent variance accounted for and correlation ratios O. Sample size and mean index scores of intellectual achievement, by school-judged intellectual level, with percent variance accounted for and correlation ratios P. Sample size and mean index scores of intellectual achievement, by recommendations for special school resources, with percent variance accounted for and correlation ratios ..c.ceieeesescseesssssssscssessens Q. Sample size and mean index scores of intellectual achievement, by diagnostic impressions of neuro- logical, muscular, or joint conditions by the examining physician, with percent variance accounted for and correlation ratios SYMBOLS Data not available-------------eneememommmmeem eee we Category not applicable---------emmmmmeemmmmmemmeeeee Quantity zero - Quantity more than 0 but less than 0.05--—- 0.0 Figure does not meet standards of reliability or precision---------------eeeeememeen 10 11 12 13 13 13 13 14 14 THE CONSTRUCTION AND UTILITY OF THREE INDEXES OF INTELLECTUAL ACHIEVEMENT Harold J. Dupuy, Ph.D., Psychological Adviser, Division of Health Examination Statistics and Gunnar Gruvaeus, M.A., Foundation for Child Development SUMMARY This report describes the construction of three indexes of intellectual achievement for use in analyses of the National Center for Health Statistics’ Health Examination Survey findings for U.S. children (aged 6-11 years) and youths (aged 12-17 years). Method The index of Intellectual Development (ID) was developed through the application of stand- ard psychometric procedures. However, the derivation of the other two new indexes, Socio- Intellectual Status (SIS) and Differential- Intellectual Development (DID), should be of major methodological significance to behavioral scientists who are concerned with advancing measurement capability into a heretofore in- tractable area. The elaboration and successful application of the method of criterion scaling as described in this report should encourage applications in many diverse areas of scale or index construction. A note of caution is in order. The numerical index values derived in this report are specific and limited to the data of the Health Examina- tion Survey Cycles II (children) and Cycle III (youths). However, the anticipated use of these data bases both within the National Center for Health Statistics (NCHS) and outside NCHS is the justification for presenting the obtained values and their incorporation, as individual examination components, into each examinee’s data tape record for these two national examina- tions. Copies of these tapes can be purchased from NCHS. Utility The index of Intellectual Development (ID) can be used as a surrogate measure comparable to the Full Scale IQ (intelligence quotient) of the Wechsler Intelligence Scale for Children (WISC), 1949. The Socio-Intellectual-Status (SIS) index can be used as a single control, moderator, or covariate index for determining the contribution of the SIS family background factor in analytical studies of other examination findings. The utility of the Differential-Intellectual- Development (DID) index is seen in terms of its potential for studying and identifying other examination findings that bear on intellectual development when the confounding intrusive- ness of SIS is removed. The DID index provides an indicator of intellectual achievement that is independent of the concomitant relationship of the index of Intellectual Development and the family background factors used to construct the Socio-Intellectual-Status index. Substantive Findings The use of the three indexes in studying some examination findings from the Cycle II children’s survey (aged 6-11 years) of 1963-65 helps to clarify some persistent issues related to intellectual achievement. The first-order analyses revealed statistically significant relationships between the index of intellectual development and (1) number of pregnancies previous to the birth of the ex- amined child, (2) twin versus nontwin birth status, and (3) attendance versus nonattendance at nursery school and/or kindergarten. However, these relationships were mostly accounted for by the family background factors reflected in the Socio-Intellectual-Status index. No im- portant amount of variance was found in the residual component of the index of Intellectual Development as measured by the Differential- Intellectual-Development index. Thus the first- order relationships with the index of Intellectual Development were accounted for by the differ- ential prevalence of these conditions among children coming from family backgrounds with different SIS index values. INDEX DEVELOPMENT Introduction This report presents the methods of con- structing three indexes of intellectual achieve- ment derived from data collected by the NCHS’ national Health Examination Surveys of U.S. children (6-7 years of age) and youths (12-17 years of age). The children’s survey was con- ducted from 1963-65; the youths’ from 1966- 70. These surveys have been described in pre- vious NCHS publications.! The applications of these indexes in the analyses of some data from the Cycle II chil- dren’s examination survey are also presented. While these findings may be of substantive inter- est to some readers, they are not exhaustive of the issues they reflect. The three indexes of interest in this report bear on the measurement of intellectual achieve- ment of our Nation’s children and youths. These are labeled descriptively as indexes of: Intellectual Development (ID) Socio-Intellectual Status (SIS) Differential-Intellectual Development (DID) The index of Intellectual Development (ID) is basically comparable to an Intelligence Quotient (IQ) index. The Socio-Intellectual- Status (SIS) index is somewhat analogous to a Socio-Economic-Status (SES) index. However, the components of SIS were rigorously cali- brated to reflect the contribution of certain family background factors to intellectual devel- opment which existed independently of the child’s or youth’s own control. The Differential- Intellectual-Development (DID) index is taken as reflecting intellectual achievement of the child or youth independent of the SIS family background contribution to the index of Intellec- tual Development. The concept of a SIS-type index emerged from the perception of the confounding or in- trusive relationship of certain family background characteristics in studying the associations among health-related variables within groups of individuals (in contrast to intra-individual associations). This seems to be especially rele- vant to studying the associations of certain somatic insults with intellectual development. For example, if a strong (negative) relationship were found between scarlet fever and intellec- tual development, the next question would be, Is this association accountable by a (possible) joint relationship of these two conditions with a common SIS-type family background? Also important in the conceptualization of SIS was the possibility of identifying a parsimonious set of family background factors which could be ordered along some dimension (scaled) so that none of the many other family background fac- tors, which are or may be associated with in- tellectual development at the single variable level, would show an association when the scaled dimension is taken into account. The given in- vestigator could then “control” on this one dimension rather than having to consider the many other singular variables. Thus SIS could serve as a moderator or covariate dimension in the study of associations among any health variables that also may covary along this family background dimension. As an example, if one wanted to study the association of the number of decayed teeth with diseased tonsils, the in- vestigator might want to “partial out” the com- mon variance of these two conditions with SIS. The conceptualization of DID was a rational extension of a more general concept to a specific application. The general concept is that the variance in common between two (or more) variables can be extracted and the residual vari- ance in the variable of interest can be rescaled as an index for use in measuring its singular dimensionality. For example, raw score perform- ances on a general vocabulary test are highly correlated with age from about age 2 to age 15. The age factor can be “taken out” and the vocabulary score achievement can be rescaled to be independent of age. Criterion Scaling of Predictor Variables The concept of criterion scaling is rather simple and its application straightforward. In this context it refers to the scaling of, or assign- ing weights or numerical values to, response options within an item or to the original values along a measured dimension (e.g., inches of height), in terms of certain numerical values of the criterion of interest. At least two conditions must be met. Within a given data set, at least one data element must be considered the criter- ion and at least one or more of the other data elements must have more than a zero correlation with the criterion. A criterion, in this context, is a variable that discriminates the sample of observations along some dimension, or into categories, of interest. The criterion can be viewed as the dependent variable and the other variables as independent, predictor, or discrim- ination variables. The Technical Notes section provides a more complete description of the method of criterion scaling and compares the results of criterion scaling with multiple linear regression. The Index of Intellectual Development (ID) The index of Intellectual Development (ID) was constructed from the Vocabulary and Block Design subtests of the Wechsler Intelligence Scale for Children (WISC). These two subtests were given to both the children and youths. The total examined sample for 6-17 years of age was 13,887. A number of NCHS reports describe these two tests, the basis for selection, and pro- cedures for examination and scoring.! Independent research studies have found that the sum of the scaled scores for these two subtests correlates about .85 to .88 with total WISC IQ scores.2 The raw scores on these sub- tests were transformed and normalized on the population estimates by 4-month age groups and within sex. The transformation was to T scores which are set to a mean and median of 50.0 and a standard deviation of 10.0 with the raw score population estimates of observations distributed according to the area under the nor- mal curve. The T scores for the two subtests are thus sex-age independent. That is, the variance attributable to sex and age was removed. The two T scores were then summed. This provided a mean of 100.0. The population estimates were then redistributed to have a standard deviation of 15.0. These two properties are similar to the WISC Total Scale IQ score. The obtained range of ID scores was 46-152 which was very similar to the obtainable range of 46-154 for the WISC Total Scale IQ. The sample skew value of -.08 and kurtosis value of -.14 indicate a very close distribution fit to the normal curve. In summary then, the high correlations found between the sum of the Vocabulary and Block Designs subtests with Total Scale WISC IQ, and the equivalence in means, standard deviations, ranges, and distributions provide sufficient support for accepting the ID index as a comparable measure of WISC Total Scale IQ and as suitable for making aggregate compari- sons of intellectual development. The Index of Socio-Intellectual Status (SIS) The next step was to select a set of variables out of the total number of variables obtained for each child and youth that would reflect family characteristics and demographic factors that a priori would seem to be independent of any personal contribution of the children or youths. Also excluded were any variables that would be of substantive interest in their own right in later analyses. Excluded under these two considera- tions were such variables as age of father and age of mother at birth of examined person, number of previous pregnancies of the mother, birth weight, attendance at kindergarten, any child- hood diseases, school questionnaire items, etc. The final selection included 4 ‘“‘control” vari- ables and 13 “predictor” variables that seemed to meet all specifications. Each of these 17 vari- ables was then subjected to an analysis of vari- ance computation with the ID index as the dependent variable for criterion scaling. The per- Table A. Response levels and percents of variance accounted for in general and in race-specific indexes, by race, of intellectual achievement by independent variables for children and youths aged 6-17 years with means and standard deviations of indexes General index Race-specific index Re- ID SIS DID SIS DID Independent veriskly Shonss White White White White White All and Black All and Black All and Black All and Black All and Black races other races other races other races other races other races races races races races Control variable Percent of variance accounted for Sex 2 0.01 0.00 0.09 0.12 0.08 0.00 0.02 0.03 0.13 0.16 0.07 0.00 0.03 0.02 0.13 Examination cycle (children, youths) ...........c.coormeicirinrcininiinnns 2 0.03 0.02 0.01 0.27 0.35 0.37 0.31 0.30 0.28 0.09 0.21 0.38 0.18 0.19 0.16 Age. 13 0.06 0.04 0.37 0.31 0.41 0.79 0.39 0.37 0.70 0.13 0.25 0.80 0.23 0.25 0.55 Vocabulary and Block Design Test qualifications.............cccvun. 5 0.17 0.30 0.03 0.58 0.82 0.41 0.08 0.06 0.20 0.38 0.84 0.41 0.04 0.06 0.10 Predictor variable First parent's education 21 24.52 21.35 12.61 74.22 74.20 64.95 0.55 0.51 4.69 67.63 78.09 64.40 0.32 0.39 1.18 Second parent's education. 21 21.23 19.53 8.66 60.49 62.35 42.30 0.54 0.31 4.05 53.91 64.39 41.25 0.33 0.31 1.62 Annual family income... 12 20.30 15.20 7.81 59.45 57.64 42.10 0.09 0.28 3.31 55.27 53.88 42.54 0.03 0.04 0.77 Rage .....cvrisericirasves 3 13.15 un re 10.70 vel ‘an 4.61 ew wae 36.54 xn e's 0.01 "v's on Number of persons i 10 7.69 4.92 5.11 23.40 20.31 21.08 0.16 0.34 1.22 20.21 17.25 21.44 0.12 0.13 0.60 graphic region 4 5.20 2.31 6.13 7.01 3.58 12.78 1.00 0.33 1.37 8.29 3.61 12.80 0.49 0.42 2.13 Both parents’ relationship to child/youth...... 5 3.54 1.46 0.76 5.92 3.38 3.14 0.47 0.23 0.36 8.10 3.31 3.10 0.16 0.26 0.21 First parent's relationship to child/youth. 1 3.46 1.50 0.84 6.29 3.60 4.97 0.63 0.48 1.26 8.37 3.49 4.94 0.41 0.47 0.65 Population change (1950-1960) ............... 4 3.08 3.25 5.26 5.06 7.65 4.81 1.48 0.97 1.15 3.47 7.32 4.81 0.76 0.95 2.52 Second parent's relationship to child/youth .. 10 2.83 1.00 0.46 5.61 297 4.14 0.48 0.35 1.29 7.66 2.89 4.14 0.30 0.33 0.59 Standard metropolitan statistical area (SMSA 3 1.52 1.49 3.97 2.95 4.47 6.27 0.73 0.23 0.16 292 4.26 6.30 0.07 0.21 1.32 Type of place and population siz 8 .94 1.64 8.27 3.25 5.10 12.28 0.36 0.23 1.18 1.42 4.92 12.32 0.21 0.21 2.99 Foreign language spoken in home. 3 71 2.27 0.51 3.23 6.70 0.73 0.06 0.00 0.03 1.55 6.95 0.72 0.02 0.02 0.16 Constructed variable Sum of both Parents’ @AUCALION ............uveuereissressnsnsemssnsssnsensns 13 27.38 25.03 13.48 85.07 85.73 78.04 0.04 0.16 6.33 75.78 90.20 77.34 0.05 0.07 1.12 Annual family income range per person under 21 years of age .. 12 2154 16.02 9.92 66.98 64.86 56.39 0.05 0.50 4.38 59.79 58.14 56.26 0.03 0.04 0.86 Index mean ................c..... 100.0 102.2 86.7 100.0 101.1 93.1 100.0 101.1 93.5 100.0 102.2 86.6 100.0 100.0 100.1 Index standard deviation. 15.0 14.3 19 8.62 8.11 7.69 12.34 12.18 11.25 9.04 7.52 4.87 11.98 12.16 10.87 cent of variance accounted for and the correla- tion ratio of each of these 17 variables with the ID index were also obtained. Table A presents the list of 17 variables and the percent. of vari- ance accounted for in the ID index for the total sample, and the two race categories of black and white and other races. The detailed tables (1-3) present the mean ID values for each response level for the 17 variables plus other detailed statistics. A number of analytical methods were then tried in a search for a procedure that could be used to combine the variables in a way that would account for the most variance in the ID index and that would also seem to be most meaningful in terms of the purpose to be achieved. A multiple regression of the 13 criterion-scaled predictor variables with the ID index was not performed. Instead a suggestion? was made to give first consideration to variables that would seem to reflect a “functional” fac- tor among parents. A variable was considered as functional if a given parent could have exer- cised some degree of control or influence in the development of that parent’s own life style or status attainment. Four of the first five pre- dictor variables shown in table A accounted for the most criterion variance and also seemed to aBy Lincoln I. Oliver, Chief, Psychological Statistics Branch, DHES, NCHS. be the most relevant under this functional direction. The fourth most important variable, race, was not considered as functional in the sense just used. Percent variance accounted for in the ID index is shown in table B. Again in order to simplify the more direct meaningfulness of these four functional vari- ables, they were combined into two ‘con- structed” variables: (1) sum of both parents’ education (X;) and (2) annual family income per person under 21 years of age in the house- hold (X,). The combined response levels were then subjected to analyses of variance with the ID index. The response levels were then grouped on the basis of approximately equal mean ID values with a progressive increase in mean ID for group division. The grouped response levels were then criterion scaled for response weights. A scrutiny of tables C and D should help to Table B. Percent variance accounted for by four independent predictor variables Percent vari- Variable ance ac- counted for First parent's otUCBtION ures sirmsinssmsrsssscessssssaonies 24.52 Second parent's education . 21.23 Family INCOMIB ..riviirnicvsssssnsisvsnisksrsaiossssssonss 20.30 Number in household under 21 years of age ............ 7.69 Table C. Unweighted sample size, mean Intellectual-Development (ID) scores, standard deviations, and constructed variables, by sum of both parents’ education in years, with percent variance accounted for and correlation ratios Mean Constructed variable XxX, Sum of both parents’ education n SD ID Value n Magn sD D Ota co cciiiniinssninrninsraninssnsreasssnnnessrnn sans RYR RASS FEE SER RH 13,887 | 100.0 15.0 52 82.4 10.3 8 90.5 11.4 37 79.1 11.2 42 81.9 11.6 080.7 402 80.7 11.1 83 | 78.1 10.9 51 81.1 14.0 129 80.9 9.4 53 89.6 13.2 151 85.7 12.3 111 87.5 12.8 085.7 640 85.7 12.8 BO YOBIS cco srusernivreniinnsrnsnermmrisissssnrsssrss sss sesso Ta sss TASER ATES TE AIRS TOIS 217 83.9 13.2 Ad WBAIS wires i isssstshuisnuenmeeinsnrsrhinhbunsesrtos sss AITIRII TASH ER ERR RRRERRRER SRF RRRRORS 108 85.3 12.6 AD VRAIS isos stsasinsssesssvasnrssnrivinssnsinironbassrssssssssessssssbe sass sent anit is snes 228 89.3 12.9 TBIYOAIS wo trsrssintvsnathoesssonsomissvsansninisstalinsunsSasinmiasosnbivasmiarsaitiaressdvasvan 165 87.3 11.3 } 088.5 793 88.5 12.7 VB Y OBIS cinsrrrssiarirsrisssssennissitinpinis bain suibivansdors sanshuones sends picrtinsassnnsverss 400 88.5 13.0 AB WBAIS «icc iiiiinisiuinssiunrensrns irsrasnrennnersss tessa Essa tRIIAR S050 00 Sa RRNA RH ER ERERSS 223 91.9 12.8 16 years .... 2) o> | 123) {ooze [113s | 928 | ns LY BBY ii nisnsssasssasesusiprion srs rvtsmmsnss iss protsssnorsnsnssaniimunsssnunsesisinases 389 93.6 11.6 TEBE eer for i rrr st Seo] ae | 1131] oma | 1038 | vas j24 AO NOON re cnisntisnsisiprirssissetoriiasissebmnitarintaamsherprnssgronginisadasenssstpdabises 514 96.5 12.9 20 years 1082 | 987 | 132} | 0980 | 1596 | 980 | 132 21 years 647 100.9 12.9 22 years 081 | 1002 | 12.8] | 1004 | 1628 [1004 | 129 23 years 638 | 102.0 12.7 on Bore A doa Ya? } 103.7 | 3,410 | 103.7 12.6 25 years 414 | 107.1 12.1 . 26 years 498 | 106.0 12.2 } Wes p12. | 108.5 122 27 years 218 | 109.4 13.6 28 years 603 | 108.3 Ta 1086 B21 1088 1B. 29 years 353 } 111.56 12.0 30 years 245 | 111.3 oe a 598 {1114 na 31 years 188 | 112.1 11.7 32 years 322 1122 a Hz 477 {1124 R25 BS VBR curios anirsinsss sits casms as Sa EES ATS AA AAA SEA EASA ASA SEER EAHA SAS 2 211 116.6 13.8 BA. YEAS BNT MOTE ciiirricimmsirimmsmrnmssstsrsirsrsnsessssvsiavses sar arta asso ras asso 127 1137.0 14.3 } nes 33841 1125 "ua Percent variance accounted FOr ....ccmanmisimsimirisis msn. 27.74 27.38 COTICIBTHONIBHIO civsrmrrsvinrinsssrsssssssssseasspssnssinvmiararmsasesnsrsssssarssegsorasad 53 52 NOTE: n = sample size; SD = standard deviation. Table D. Unweighted sample size, mean Intellectual-Development (ID) scores, standard deviations, and constructed variables, by annual family income per person under 21 years of age in household, with percent variance accounted for and correlation ratios Constructed variable (X,) Annual family income per person under 21 years of age Mean sD in the household 2 ID Mean Value n ID SD TOA) cic inion minima this se So ET SA ES EE SE SRT TA AT ens 13,887 | 100.0 15.0 $0-$124 148 83.6 12.4 083.6 148 83.6 | 124 $125-$374 706 85.0 127 085.0 706 85.0.}'12.7 $375-$624 ... 859 88.4 12.5 088.4 859 88.4 | 125 $625-$874 ... 1,054 92.2 14.0 092.2 | 1,054 92.2 | 14.0 $875-$1,124.... 588 94.1 13.1 094.2 588 94.1 | 13.2 [1] $1,125-$1,374 915 97.3 13.8 097.3 915 97.3 | 13.8 $1,375-$1,624 1,027 99.4 13.3 $1,625-$1.,874 oa | 1070 |143f| 0909 | 1572 | 1000 | 139 2) $1,875-$2,124 ... 789 | 101.9 13.1 $2,125-$2,374.... 817 .} 102.2 125 102.2 { 1,878 | 102.2 | 13.2 [3] $2,375-$2,624 270 | 102.9 14.7 $2,625-$2,874 808 | 105.2 12.5 $2,875-$3,124 ... 581 | 102.7 12.7 $3,125-$3,374... 461 | 106.1 12.8 104.3 111937 1 1042 | 129 $3,375-$3,624 87 97.9 13.8 $3,875-$4,124 66 | 109.0 14.5 $4,125-$4,374 ... 1,249 | 106.5 12.8 $4,375-$4,624 ... 100 | 100.3 14.3 106.2 | 1,828 | 106.2 | 13.3 $4,875-$5,124 ... 186 | 110.1 12.0 $5,875-$6,124 227 | 102.8 14.7 SOA 288B:37 0 i. sovi i nrianitisimms iris rasa roams es dn Eran rashes enn 504 108.0 12.4 $6,625-$6,874.... 281 1 1135 13.5 $8,325-$8,674 ... 259 | 106.4 12.3 $9,875-$10,124. 262 | 110.6 12.9 109.2: "1.597 | -'W0B.2 | 129 $12,375-$12,624... 190 | 107.4 12.8 $19,875-$20,124 101 | 109.8 12.5 “Don’t know income’’ and number of persons under 21 years of age 1 person... 51 99.3 11.9 2 persons . 118 100.4 13.8 1 3 persons. 121 98.9 16.3 0998 3652 $99 9 'i2) 4 persons 72 :101.3 14.9 5 persons 67 93.9 14.7). 6 persons. 47 90.8 12.8 7 persons 26 91.8 13.0 8 persons 17 88.6 16.8 091.4 178 11 [143 9 persons ..... 8 85.1 12.4 10 persons or more 13 84.2 13.9 Blank or refused on income and number of persons under 21 years of age 1 person 56 | 105.8 12.8 2 persons . 57 1103.7 15.5 1 Boiron. 49 98.9 14.1 102.2 196 | 102.6 (3. 113] 4 persons .... 34 | 101.0 15.0 5 persons . Ser sraasrs TTS Sasa RARER SA AR A SAR SAREE 19 98.6 8.9 6 persons . 26 93.6 16.7 7 persons. 13 95.7 16.7 1 : 8 perions 9 90.6 7.4 094.2 71 94.5 er 11 9 persons ....... » oh oF vale 10 persons or more 4 86.2 6.2 Percent Variance BCCOUIIEN FOF «i. srr raiseiinianiis rian ssisrsssssesnssssenerpsssesonnts sta seizsssse 2253 21.54 COTTEIRHION FRU 2cceiss sensirsisresinrorssassnsssessnisstseisvivisssesRATEs RH HISAR RAFTS sR E ISI SAER RU RI PRR ERT HEY 47 .46 1Standard deviation not computed. NOTES: n =sample size: SD = standard deviation; | | = grouped together in final variable construction. clarify these procedures. The resultant outcome for each of these two constructed variables was to reduce response levels in (1) from 35 to 13 with only a slight decrease in percent variance accounted for from 27.74 percent to 27.38 per- cent and in (2) from 45 to 12 with about a 1-percent decrease in accounted for variance from 22.53 percent to 21.54 percent. Table A presents the percent variance accounted for by the two constructed variables. A linear multiple regression equation of the two criterion-scaled constructed variables with the ID index was then computed. The values of the equation were: Y' (ID) =.7382 (X,) + .5598 (X,) - 29.80=SIS 1 2 The “predicted” values of the ID index (Y”) were then taken as SIS index values. The product- moment correlation between SIS and ID was 5676 and the correlation ratio was .5690. Since these two values are so close, a linear rela- tionship between the two variables is indicated. The mean value for SIS was 100.0 which is the same as the mean for the ID index; the median was 102.0. The standard deviation of SIS was 8.52 compared to 15.0 for ID which reflects the remaining unaccounted for variance in ID. The range of SIS index values was 76.6-115.9 and the distribution of observations was clearly skewed toward the lower values of SIS. However, the skew value of -.53 is not so great as to pre- clude the use of the SIS index as a dependent variable in an analysis of variance design. A description of the skewness and kurtosis tests used is presented in the Technical Notes. The Index of Differential-Intellectual Development (DID) The construction of the Differential-Intellec- tual-Development (DID) index was straightfor- ward. The DID index score was obtained by simply subtracting the SIS index score from the ID index score for each individual and adding a constant of 100.0: DID = ID- SIS + 100.0. Thus if an ID score was 120 and SIS was 110, the DID index value would be 10 + 100.0 or equal to 110.0 which indicates a differential intellectual development of 10 ID index scores higher than expected based on the SIS index value. The constant of 100.0 was added to give the DID index the same mean as the ID and SIS indexes; it also eliminates negative values and permits a readily perceived comparison of DID performance compared to ID and SIS. Thus a DID score, for example, of 100.0 indicates that the person’s ID score was the expected value based on the person’s SIS score. The product-moment correlation between DID and ID was .8225 and the correlation ratio was .8215. The closeness of these two coeffi- cients indicates an almost perfect linear relation- ship between DID and ID. The mean and median for DID was 100.0 and the standard deviation was 12.34. The product-moment correlation be- tween DID and SIS was -.0015, which indicates a near zero relationship. An analyses of variance test was computed using SIS as the independent variable and DID as the dependent variable. SIS accounted for only 0.19 percent of the vari- ance in DID; the correlation ratio was .04. In- spection of the mean DID values for each value of SIS in table E, also reveals only slight random variations of mean DID values across the whole SIS range of values. The range of the DID index values was 47- 143; the skew and kurtosis values of -.03 and .14 respectively indicate an almost normal dis- tribution of observations on DID. Race-Specific SIS and DID Indexes The SIS and DID index values were entered in the data tape file of each child and youth and analyses of variance were then run for all con- trol, predictor, and constructed variables. The amount of variance accounted for in the DID index was 4.61 percent by race, 1.48 percent by population change, and 1.00 percent by geo- graphic region. None of the remaining variables accounted for as much as 1 percent of the vari- ance in DID (table A). Several procedures were used in trying to take out the race variance in DID without using race. These included adjust- ment of criterion weights by geographic region and population change jointly and the recalibra- tion of the two constructed variables by optimal criterion scaling within race. None of these worked. The final procedure used was to com- pute race-specific (white and other races and black) multiple regression equations for race- Table E. Unweighted sample size, mean Socio-Intellectual-Status scores, means and standard deviations of Intellectual-Development scores and Differential-Intellectual-Development scores, by each value of the Socio-Intellectual-Status index, with percent variance accounted for and correlation ratios SIS ” Mean Mean ID Mean DID SIS ID SD DID SD TOLD rns staat sa A TARE SA TER Aas SR aE esa aps WAAR RAIS EAE 13,887 | 100.0 100.0 15.0 | 100.0 12.34 121 71.2 77.6 11.3 | 100.4 11.3 82 79.3 78.2 9.2 98.9 9.2 30 80.3 81.1 12.0 | 100.8 12.0 243 81.1 82.2 11.01 101.1 11.0 38 82.4 83.6 12.8 | 101.2 12.8 264 83.0 82.7 11.5 99.8 115 47 84.3 87.4 10.9 | 103.1 10.9 177 85.0 86.1 11.6 | 101.1 11.6 214 86.2 85.3 12.1 99.0 12.1 222 87.1 86.3 10.8 99.2 10.8 263 88.2 89.2 11.9 | 101.0 11.9 183 89.2 88.6 11.6 99.4 11.6 306 90.2 89.5 12.0 99.3 12.0 413 91.3 91.4 12.9 | 100.1 13.0 219 92.1 91.6 12.3 99.5 12.3 195 93.1 93.3 12.7 | 100.2 12.8 452 94.1 93.8 13.2 99.7 13.2 321 94.9 95.2 13.5 | 100.3 13.5 467 95.9 95.4 12.4 99.5 12.4 523 97.0 97.3 12.9 | 100.3 12.9 708 98.3 98.1 12.8 99.8 12.8 338 99.1 99.6 12.2 | 100.5 12.2 572 | 100.0 99.8 13.0 99.8 13.0 819 | 101.2 101.5 12.1 | 100:3 12.1 206 | 102.0 101.0 13.3 99.0 13.3 868 | 102.8 103.1 12.0 | 100.4 12.0 990 | 103.9 103.3 12.3 99.4 12.3 934 | 105.1 105.4 11.9 | 100.3 11.9 797 | 106.2 106.7 12.3 | 100.5 12.3 186 | 107.2 106.7 12.2 99.5 12.2 699 | 108.0 107.6 11.8 99.6 11.7 198 | 108.8 109.2 13.5 | 100.3 13.5 521 | 109.9 109.3 12.2 99.4 12.2 342 | 111.0 110.8 12.6 99.6 12.7 296 | 112.1 112.9 12.5 | 100.8 12:8 44 113.1 112.7 15.9 99.6 15.9 445 | 113.9 114.3 11.8 | 100.4 11.8 144 | 115.9 116.1 13.9 | 100.2 13.9 Percent variance acCoUINIBL TOF oi iiisimisirsssrssssrmmessissrsssssnsserssssns 99.94 32.38 To 0.19 COITRIAIONT FRI vrai sfrrrvisisisssivsnmribusssssisssssssesnnsizsmssassndarerasivssosnionionsene .9997 .5690 bo .0361 NOTE: n = sample size; SD = standard deviation. specific SIS indexes. The resultant equations were: SIS (white and other races) = .7488 (X,) + .4293 (X,) - 16.53 SIS (black) = .4625 (X;) + .3613 (X,) + 8.62 The obtained summary statistics for race-specific SIS indexes are shown in table F. These mean SIS values were now comparable to the mean ID values within race whereas the Table F. Obtained means, standard deviations, range of scores, and Socio-Intellectual-Status and Intellectual-Development correlations for race-specific Socio-Intellectual-Status in- dexes SIS-ID Race Mean SD Range | correl- ation All races.......... 100.0 | 9.04 | 76-116 .6011 White and other races...... 102.0 | 7.52 | 80-116 5258 BACK TA0B. cess srs seentrrannss 86.6 | 4.87 | 76-101 .4034 original SIS values were not (table A). SIS was still skewed for all races, for white and other races, but not for blacks. The DID index values were obtained from the race-specific SIS indexes as before. The mean race-specific DID values were equal to about 100.0 for both race groups, while the original DID means were quite different for the two race groups (table A). Analyses of variance were run for the race-specific SIS and DID in- dexes with all 19 variables. It is apparent in table A that differences in mean Intellectual Development (ID) among the predictor and con- structed variables were due to SIS influences. Less than 1 percent of the variance in the race- specific DID index was accounted for by any of the 19 variables for all races and white and other races. Among blacks, about half of the predictor and constructed variables accounted for over 1 percent of the variance in DID. Inspection of the mean DID values by response levels for blacks (see detailed tables) did not reveal strong con- sistent trends sufficient to justify carrying the race-specific SIS index construction any further. The race-specific DID index for all races had a mean of 100.0, standard deviation of 11.98, and a range of 44-142, and was still almost normally distributed. Examined Sample Compared to Population Estimates Since the examined sample (n = 13,887) was used in the development of the SIS and DID in- dexes, a comparison of the results from the examined sample was made with the sample weighted population estimates. No important differences emerged between the sample and the population estimates within all races, white and other races, and blacks for means, standard deviations, skewness, and kurtosis (table G). However, the statistical values shown in this re- port should not be taken as population estimates; they are sample values only. Intercorrelations of the Indexes The product-moment intercorrelations among the indexes are shown in table H. The race-specific SIS and DID index coefficients with ID in the total sample was .601 and .798, respectively. SIS and DID correlated -.003. Analyses of variance were run with ID as the de- Table G. Examined sample and population estimates summary statistics, by race and intellectual indexes Examined sample Sample weighted population estimates Race and index Mean SD skew | KU" | Mean SD Skew | Kur- tosis tosis AN TBCEE U1) tiie ciiniirimsvmsiisrsnssssninesmansioiodansussssiassisssss (13,887) (46,476,063) UD ctasosseimmnmneirusdasssvnnmiiasieniasdansnsnis 100.0 | 14.99 -.08 | —.14 | 100.0 | 15.00 —-.09 =15 SIS (general) ...... 100.0 8.52 -53 | -.27 1 100.0 8.67 -.54 -31 DID (general)........ 100.0 12.34 -.03 .14 100.0 | 12.30 -.02 15 SIS (race-specific) .... — 100.0 9.04 -.51 -57 100.0 9.11 -52 ~.58 DAD (raco-SPaCIFICY. conicis ioisissivninsssiinrinmmssssvrsasssssstonnssssss brio sanani 100.0 11.98 -.04 .20 99.9 11.95 -.03 .20 White and other races (n)......cccccevereeiereinirinennnnenensnnnnn (11,901) (40,180,771) HD) coneinvinsnnsensiupsinasimsnsunssnivaiirnnepesviti sous ns ie sonra saa STEERER AHR 102.2 14.29 -33 .07 102.1 14.31 -.14 .05 SIS (general) ...... 101.1 8.11 -.68 .14 101.1 8.29 -.69 .09 DID (general)........ 101.1 12.18 -.06 .18 101.0 { 12.13 -.08 .18 SIS (race-specific) .... whew 102.2 7.52 -.65 A2 1 102.2 7.68 - 87 .07 DID (raeR-8PEIFICY.. comivnistninvevisicimmmnsiiinmieinsma iiesas esis 100.0 | 12.15 -.06 .18 999 | 12.10 -.05 .18 BHBONC ATI oo. nies fovcprimmmsotonsssssseontoinss ss saan ines ses son hans’ (1,986) (6,295,292) BE sein isa snags ah RP A ER ET SANT TTA GT 86.7 11.88 17 .00 86.5 | 11.98 .18 .01 SIS (general) ...... 93.1 7.69 33 |-=:50 93.1 7.78 14 52 DID (general)........ 23.5 11.26 .06 37 93.4 11.29 .06 40 SIS (race-specific) ........ ro 86.6 4.87 JA3 | —.80 86.6 4.93 14 -.52 DAD {rar e-S DBC HC) Siri rsrinmsniiriesmmmssssos mass siins nan ninsnissnnprs eset snes 100.1 10.87 a2 23 100.0 10.92 13 25 Table H. Matrix of product-moment intercorrelations of the indexes, by race Race and index ID SISg DIDg | SISgg | DIDRg All races (n = 13,887) 3 EE CE po 1.000 SS BNE Al) Lv Tr civrrromrc rr ere Te AR passe nly mE es ARs Rp A RE Te lveaven ee Te Rs a tes .568 | 1.000 DD AGEIBIA sii svi vstasesss sevnrs sinsiaiobi ch svmmninsnssons ie mia vrs STs sap Ina ST SA ASR Tr TOA EA .822 | —.002 | 1.000 SIS BRO SIC IRICY oss ve siiimieanesnseesssnmivhasisimmnmsissvpbenansinnnisnns Ess EARLS RES ASR RISA ERS RS A a SA RES SRR .601 .944 .078 1.000 DID (800-8000 suriisinsissssiessiunssisessivmisasssssiarsssnsnsosimminsitbussssvnsssnssssanisstnnmsninrsisoummiiinnninn .798 | —.003 970 |. =.003 1.000 White and other races (n = 11,901) ND suinccnseresinrermsmmmsisnninssssssnessnssiinsbiiensnivannsssvnunsssmnmmrsbsvssssnsesisssssstnssasiesssnesnsnssnnanunssnsobusse 1.000 SIS (general) .... Tied .524 | 1.000 DID AGENBIAN). ou. cviisiimissciniiinsessinoseshsssssiniirms sais reser CR TE SRE REFS RARE e Sans saa wins .824 | —.051 1.000 SIS {T00-SPROIEICY co civinisvuissivmmrmsrisesissstiessiisonasvieinssssvsins st iunsriasenssnsnessinntivammennioy esses .526 .998 | -.048 1.000 DE BEB IBOIRIC Yu civ iuorsidicioormnssirrisniinegiionins nsstn unt isinse vanes mass SEER EIA Sy Te Ari 850 | —.001 .998 -.001 1.000 Black (n = 1,986) WD cers dssnnseitariieninesion i ionsnsiadionsilvin teva nninnmiukentn asnins in EAT FT AA EVR RR pera eae 1.000 EE 0) SE I SE ie EO A= I Se .403 | 1.000 DVD {QBRBTAIY ins sismisivusinstunsssiismmsscvmennesissinssrianrrsnsrskhnrsssunmeessmmsinunnbssisissomhessannstinsovavanens .780 | —.258 | 1.000 SIS (race-specific) ...... oa .403 | 1.000 | —.258 1.000 IN AE BBPBEIEICY .. sever saviantssnshreriisssnsn diva tesiinsnhvsss bs slpiirmasn sin cieTiss seer TS Ore rE Es ai an 912 | —.008 .968 “007 1.000 NOTE: G = general, RS = race-specific. pendent variable with race-specific SIS and DID indexes. SIS accounted for 36.26 percent and DID accounted for 63.79 percent of the variance in ID for a total of 100.05 percent. Since these SIS and DID indexes were essentially indepen- dent indexes (r = -.003), this indicates that the total variance in ID was separated into two nonoverlapping independent components. As a check on the stability of these index values across diverse groups, the results from the analyses of variance with the four control vari- ables were inspected (table A and detailed table 1). No significant variance occurred across these subgroups for any of the indexes. A further check on the limits of possible shrinkage of the strength of relationship of SIS and ID was made. Analyses of variance were made of the full-range variable sum of parental education, None-34 years and more, with ID for Cycles II and III separately. The percent of variance accounted for in ID was 28.04 and 27.96 and the correla- tion ratios were .530 and .529 respectively for the two cycles. These checks support the posi- tion that the strength of relationships reported for the combined sample would have been very close had one cycle been used to develop the in- dexes and then cross-validated on the other cycle. 10 Since the correlation between ID and race- specific SIS was .60 and since other studies? in- dicate a correlation of IQ of about .55 between siblings reared together, the position is taken that the SIS index is measuring a generalized sociological family background factor relating to intellectual achievement. However, DID cannot be taken, at least at this time, as inde- pendent of other intrafamily characteristics, orientations, and interactions. Future research investigations into family contributors to children’s intellectual achieve- ment should include direct measures of parental intellectual achievement as well as intellectual achievement orientations and supports within the family. SUBSTANTIVE FINDINGS Application of the ID and Race-Specific SIS and DID Indexes to Substantive Examination Findings from Cycle Il, Children 6-11 Years of Age About 500 data elements were available on an extended data tape for the 7,119 children 6-11 years of age examined in Cycle II. Sixteen data elements or variables were selected to “test out” the indexes. The follow- ing nine variables were selected for which product-moment correlations were computed with the three indexes. The two constructed variables 1. Sum of parental education 2. Annual family income per household person under age 21 The two Wechsler Intelligence Scale for Chil- dren (WISC) subtests used in constructing ID 3. T-scored Vocabulary subtest 4. T-scored Block Design subtest Two tests from the Wide Range Achieve- ment Test (WRAT) 5. T-scored Reading Test 6. T-scored Arithmetic Test The Harris-Goodenough Draw-A-Person Test (DAP) 7. T-scored DAP Test An educational achievement composite score of the two WRAT tests (mean 100.0, stand- ard deviation 15.0—the same as ID) 8. Education achievement A total measured performance index made of the two WISC, two WRAT, the DAP Test scores (mean 100.0, standard deviation 15.0) 9. Total performance The correlation coefficients are shown in table J. The intercorrelations among the three in- dexes were almost identical to those found on the combined Cycles II and III sample. Neither one of the two constructed variables that were used for deriving the SIS index correlated with DID. The WISC Vocabulary subtest contributed more to SIS than Block Design contributed, and the reverse occurred for DID. The WRAT tests had slightly higher correlations with SIS than with DID; the reverse was true for the Draw-A- Person (DAP) Test. The correlations of SIS with the WRAT and the DAP Test are reasonable expectations. The DID correlations with these three tests indicate that it has a meaningful measurement property and is not just a random residual component of Table J. Correlation coefficients, means, and standard deviations for intellectual indexes and selected variables Index and variable! Race-specific ID Mean SD SIS DID Sum of parental eAUCATLION .......cueeiireeniiireeiereeee ie erar ee erseaerassserassnaseses Annual family income per household person under age 21 wisc T-3corad Vorabulary SUBST ...uusvimmaritsssssssmsmmsinrserssrssessssrssnsr en siasiase T-scored Block Design SUBTEST ......cucuiuiuiireririrurmrurcrssensiessrnnsnnssesseassens T-SCOIet- BR eACIHIG OSE oss ssssisesssternasssarinsssesservornegpravesassmasprssasintnnsasnsosnmns T-300r00) AtIINMELIC BBL. ovissrrssirisissssiasshiuvessararnsnnsssevssssasassaissssavassnaiane Correlation coefficient 1.000 .603 .793 | 100.2 14.91 .603 | 1.000 | —.009 99.7 9.09 .793 | —.009 | 1.000 | 100.5 11.90 extras neamns Reena 523 .880 { ~.016 ‘{' 100.7 7.83 .486 .790 .006 99.0 6.99 siapesinsvitssstyTR Ess Riay .859 .581 633 50.3 9.82 uknrers ers arpreReS .857 454 727 50.2 9.76 633 .505 .408 50.2 9.81 SRR eR 612 463 413 50.2 9.77 DEawW=A 1. Denoting the standard deviation S, then §2 = U,. It can be shown that for a wide class of fre- quency distributions, Pearson’s S, can be ex- pressed exactly in terms of Uy, Ug, and Uy. Us itself is also a measure of skewness. Clearly, if the distribution is symmetrical, Ug vanishes and the ratio Us /S3 will give some indication of the extent of departure from symmetry. Ob- viously, all symmetric distributions are not nor- mal. As a measure of the peakedness or flatness of the distribution (kurtosis) ratio U,/S* is 26 used. For a normal distribution this ratio has a value of 3 and thus we can define our measures of skewness and kurtosis as: 2 = Us [S3 and boy = U,/S* - 3 For normal distributions b; and by, equal zero. A nonsymmetric distribution is negative or positive skewed depending on the sign of b;. If by < 0 the distribution is flat (platykurtic) and if by > 0 the distribution is peaked (lepto- kurtic) in comparison with the normal. This kurtosis test should be used only when the distribution is symmetric. For testing pur- poses the null hypothesis assumes that the popu- lation distribution is normal. Then the standard error squared for b; and by is 6/n and 24/n re- spectively where n is the sample size. See Kendall® for further statistical detail. For Cycle II and Cycle III combined, n was 13,889 and the standard error would be .02 for by and .04 for by. For the index of Intellec- tual Development (ID) 6; was -.08 which indi- cates that the distribution had a significant (but considering the sample size) slight negative skew- ness. For the Socio-Intellectual-Status index, b, was —.53 and the distribution was markedly neg- ative skewed. Both b, values were significant and indicate a platykurtic distribution. For the Differential-Intellectual-Develop- ment index, b; was -.03 which is not signifi- cantly different from zero. On the other hand, bo, was .14 and thus the distribution is signifi- cantly leptokurtic (peaked). For all practical purposes, however, this distribution cannot be distinguished from a normal distribution. %U.S. GOVERNMENT PRINTING OFFICE: 1977—260-937:33 Series 1. Series 2. Series 3. Series 4. VITAL AND HEALTH STATISTICS PUBLICATIONS SERIES Formerly Public Health Service Publication No. 1000 Programs and Collection Procedures.—Reports which describe the general programs of the National Center for Health Statistics and its offices and divisions, data collection methods used, definitions, and other material necessary for understanding the data. Data Evaluation and Methods Research.—Studies of new statistical methodology including experimental tests of new survey methods, studies of vital statistics collection methods, new analytical techniques, objective evaluations of reliability of collected data, contributions to statistical theory. 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Data from the Health Examination Survey.—Data from direct examination, testing, and measurement of national samples of the civilian, noninstitutionalized population provide the basis for two types of reports: (I) estimates of the medically defined prevalence of specific diseases in the United States and the distributions of the population with respect to physical, physiological, and psychological charac- teristics; and (2) analysis of relationships among the various measurements without reference to an explicit finite universe of persons. Series 12. Data from the Institutionalized Population Surveys.—Discontinued effective 1975. Future reports from these surveys will be in Series 13. Series 13. Data on Health Resources Utilization.—Statistics on the utilization of health manpower and facilities providing long-term care, ambulatory care, hospital care, and family planning services. Series 14. Data on Health Resources: Manpower and Facilities. —Statistics on the numbers, geographic distrib- ution, and characteristics of health resources including physicians, dentists, nurses, other health occu- pations, hospitals, nursing homes, and outpatient facilities. Series 20. Data on Mortality.—Various statistics on mortality other than as included in regular annual or monthly reports. Special analyses by cause of death, age, and other demographic variables; geographic and time series analyses; and statistics on characteristics of deaths not available from the vital records, based on sample surveys of those records. Series 21. Data on Natality, Marriage, and Divorce.—Various statistics on natality, marriage, and divorce other than as included in regular annual or monthly reports. Special analyses by demographic variables; geographic and time series analyses; studies of fertility; and statistics on characteristics -of births not available from the vital records, based on sample surveys of those records. Series 22. Data from the National Mortality and Natality Surveys.—Discontinued effective 1975. Future reports from these sample surveys based on vital records will be included in Series 20 and 21, respectively. Series 23. Data Wom the National Survey of Family Growth.—Statistics on fertility, family formation and disso- lution, family planning, and related maternal and infant health topics derived from a biennial survey of a nationwide probability sample of ever-married women 1544 years of age. For a list of titles of reports published in these series, write to: Scientific and Technical Information Branch National Center for Health Statistics Public Health Service, HRA Hyattsville, Md. 20782 whl Cen, $ % 8 J 2 $ n a— NCHS 4 bel 5 9) b) Bu) (§y 5 LASTS RS 2-Number be Synthetic Estimation of State Health Characteristics CECT RL Health Interview Survey U.S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE Public Health Service DATA EVALUATION AND METHODS RESEARCH VITAL and HEALTH STATIST NOS Library of Congress Cataloging in Publication Data United States. National Center for Health Statistics. Synthetic estimation of State health characteristics based on the health interview survey. (Vital and health statistics: Series 2, Data evaluation and methods research; no. 75) (DHEW publication; (PHS) 78-1349) Bibliography 1. Health surveys—Statistical methods. 2. Estimation theory. 3. Health surveys—United States—States. I. Title. II. Series: United States. National Center for Health Statistics. Vital and health statistics: Series 2, Data evaluation and methods research; no. 75. III. Series: United States. Dept. of Health, Education, and Welfare. DHEW publication; (PHS) 78-1349. RA409.U45 no. 75 312°.07°23s [614.42] 77-22219 ISBN 0-8406-0107-7 For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 Stock No. 017-022-00596-4 DATA EVALUATION AND METHODS RESEARCH Series 2 Number 75 Synthetic Estimation of State Health Characteristics Based on the Health Interview Survey This report discusses the various methods that have been proposed or used for obtaining estimates of health characteristics for local areas. Particular emphasis is given to discussion and evaluation of synthetic estimation procedures developed originally at the National Center for Health Statistics for purposes of estimating levels of health characteristics obtained from the Health Interview Survey for each State and the District of Columbia. DHEW Publication No. (PHS) 78-1349 U.S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE Public Health Service National Center for Health Statistics Hyattsville, Md. October 1977 NATIONAL CENTER FOR HEALTH STATISTICS DOROTHY P. RICE, Director ROBERT A. ISRAEL, Deputy Director JACOB J. FELDMAN, Ph.D., Associate Director for Analysis GAIL F. FISHER, Associate Director for the Cooperative Health Statistics System ELIJAH L. WHITE, Associate Director for Data Systems JAMES T. BAIRD, JR., Ph.D., Associate Director for International Statistics ROBERT C. HUBER, Associate Director for Management MONROE G. SIRKEN, Ph.D., Associate Director for Mathematical Statistics PETER L. HURLEY, Associate Director for Operations JAMES M. ROBEY, Ph.D., Associate Director for Program Development PAUL E. LEAVERTON, Ph.D., Associate Director for Research ALICE HAYWOOD, Information Officer OFFICE OF THE ASSOCIATE DIRECTOR FOR MATHEMATICAL STATISTICS MONROE G. SIRKEN, Ph.D., Associate Director Vital and Health Statistics-Series 2-No. 75 DHEW Publication No. (PHS) 78-1349 Library of Congress Catalog Card Number 77-22219 PREFACE The investigations on which this report is based have been supported by con- tracts between the Measurement Research Laboratory, Office of Research, National Center for Health Statistics (NCHS), and the School of Public Health, University of Illinois at the Medical Center, Chicago. Dr. Monroe G. Sirken, Associate Director for Mathematical Statistics, NCHS, served as project officer for the Center on these investigations. Dr. Sirken and Ms. Patricia Royston, mathematical statistician, Office of Mathematical Statistics, NCHS, provided considerable input throughout the course of this project. Dr. Wesley L. Schaible and Dr. Dwight Brock, Office of Research, NCHS, reviewed an earlier draft of this report and made many helpful suggestions. wg) gio Jaap o i A - a tg gag b f be Ba Ds, ng 2 Ry oh : 14 i le = af fine, pur : hd it oe 4d i CONTENTS Preface » Introduction Review of the Literature ..... Alternative Methods of Obtaining State Estimates Background Nearly Unbiased Estimator Synthetic Estimator Regression-Adjusted Estimator Evaluation of Synthetic Estimates Background wos Estimation of the Mean Square Error (MSE) and Average Mean Square Error (AMSE) of Synthetic Estimates Evaluation of HIS Synthetic Estimates for Alternative a-Cell Grids .......... RRA IRR ORS esas tree References sreprast Appendix: Proofs of Lemmas and Theorems LIST OF TEXT TABLES A. Interpretation of the components of the square of the bias of the “nearly” unbiased eSUIMALe wurivires B. Distribution of percentage absolute differences between the nearly unbiased estimate and the true value among 42 States in the North, Central, South, and West Regions for total deaths, deaths from major cardiovascular-renal diseases, and deaths from motor vehicle accidents, 1960 ......cceeeueres C. Maximum contribution to the relative variance of x s of sampling variation in the Psa w—otw ve D. Mean proportional absolute differences between the synthetic estimate produced by the total 50 a- cell grid and that produced by other a-cell grids for selected Health Intervi i Hl , erview Survey (HIS) varia- E. Maximum proportional absolute differences between the synthetic estimate : produced by the total 50 a-cell grid and that produced by other a-cell grids for selected Health Interview Sos (HIS) variables, 1969-71 ’ F. Correlation coefficients between the synthetic estimate produced b i v y the total 50 a-cell grid and that produced by other a-cell grids for selected Health Interview Survey (HIS) variables, 1969-71 MEL iii 10 14 14 15 Lai ee SYNTHETIC ESTIMATION OF STATE HEALTH CHARACTERISTICS BASED ON THE HEALTH INTERVIEW SURVEY Paul S. Levy, Sc.D., School of Public Health, University of Illinois at the Medical Center, Chicago, and Dwight K. French, Statistical Methods Staff, National Center for Health Statistics INTRODUCTION Statisticians, demographers, economists, and others have long been aware of the critical need for accurate small area statistics. While the U.S. decennial census provides accurate local statis- tics of many characteristics once every 10 years, the accuracy of these statistics becomes ques- tionable as time elapses from the last census and, in addition, characteristics other than those found on the census questionnaire are often desired. Although a rather extensive system of ongoing general purpose surveys is conducted by Federal agencies, they are almost always designed to produce estimates for the United States as a whole or, at most, for rather large geographic regions or divisions: For reasons of sample size and design, direct estimates for such subdivisions as cities, counties, States, or other minor civil divisions, which are so critically needed, can rarely be obtained from these sur- veys. The National Center for Health Statistics, one of the Federal agencies responsible for main- taining a system of sample surveys and other data collection systems, has long recognized the need for good small area statistics, and for the past decade has investigated alternate strategies for obtaining such estimates. In particular, NCHS has developed a procedure known as “synthetic estimation” for obtaining small area statistics. This procedure obtains small area esti- mates of characteristics by combining national estimates of the characteristics specific to demo- graphic subgroups with estimates of the propor- tional distribution of the local population into the subgroups. The subgroups would be chosen for their relevance to the characteristic being estimated. For example, if it were desired to estimate the prevalence of the sickle cell trait in a particular county having a racial distribution of 30 percent white and 70 percent black, and if a hypothetical national survey estimated that the trait was prevalent among 10 percent of U.S. blacks and virtually nonexistent among U.S. whites, one would estimate that 7 percent of the population in the county had the trait (30% X 0% + 70% X 10%). This is a synthetic estimate. / The advantages of the synthetic-estimation approach to local estimation are its intuitive appeal, its simplicity, and its low cost relative to a direct survey of the local population. A major disadvantage is its lack of sensitivity to certain local characteristics. For example, in the above illustration, it may happen that the white popu- lation in that area are all of Mediterranean des- cent and have more than a negligible amount of persons with the sickle cell trait. Much research on the synthetic estimation procedure has emerged since an NCHS report on synthetic estimates of disability for States was published in 1968.1 The purpose of this report is to examine critically the various methods for obtaining local estimates that are in the litera- ture and, in particular, to examine synthetic estimation from a methodological point of view. REVIEW OF THE LITERATURE The need for methods of obtaining valid and reliable estimates of characteristics of local populations has been recognized for a long time by statisticians and demographers. In particular, much effort has been expended by statisticians associated with the U.S. Bureau of the Census and their contractors, especially in the use of symptomatic variables such as births, deaths, and school enrollment, which are available on a local level, to measure changes in population size since the most recent decennial census. Methods such as the vital rates technique, censal ratio method, Census Bureau Component Methods I and II, ratio correlation method, and others have been described extensively in the literature.2 Basically, these methods use the relationship between the population size of the local area at the most recent census and the measure of the symptomatic variable or variables for that year, in conjunction with the value of the sympto- matic variable(s) at the date for which the esti- mate is desired, to produce the desired local estimate of population size or change. An elaboration of the use of techniques based on symptomatic variables has been developed recently by Ericksen.3-5 His elaboration involves use of sample data from the Current Population Survey in conjunction with symptomatic vari- ables to obtain estimates of population size for local areas. Although health statisticians have long felt the need for valid and reliable estimates of health characteristics for local areas, only in the past decade has serious attention been given to the development of methodology for obtaining local area estimates of such health characteris- tics as morbidity, mortality, disability, and utilization of health care services. The methods developed by demographers for estimating local population sizes could not, however, be directly applied to the estimation of health characteris- tics for local areas; hence, methodology for estimating health conditions for local areas has developed along different lines from those discussed above for local estimation of popula- tion size. A major advance in estimation of health characteristics for local areas came with an experiment conducted by Walt R. Simmons and his staff at the National Center for Health Statistics (NCHS) during the mid-1960’s and published in 1968.1 In this experiment, three different estimation techniques were used to produce estimates of long- and short-term dis- ability for each State in the United States for the 2-year period beginning July 1, 1962, and ending June 30, 1964. The NCHS data used for estimating disability were from the Health Inter- view Survey (HIS), and the population data were from the Current Population Survey update of the 1960 Decennial Census. One of the methods used was proposed originally by Woodruff to produce local esti- mates of retail trade;® the other two, namely, the synthetic estimator and the nearly unbiased estimator, were developed at NCHS. These methods will be discussed in greater detail. Of the three methods investigated, the synthetic estimator was judged to be the most promising for estimating disability on the State level, and the estimates finally published! were obtained by this method. The NCHS publication on synthetic estimates of disability! seemed to stimulate further efforts to apply and evaluate synthetic estimation. Within NCHS, an evaluation of the synthetic estimation procedure was conducted in which synthetic estimates of death rates in 1960 from four causes (motor vehicle accidents, major cardiovascular-renal diseases, suicide, and tuberculosis) were calculated for each State and for the District of Columbia.” These synthetic estimates of death rates were then compared to the known true death rates for each State and, in general, agreement between synthetic esti- mates and true death rates was good for one of the causes examined (major cardiovascular-renal diseases), fair for another (suicides), and poor for the other two (motor vehicle accidents and tuberculosis)./The general conclusion from the study was that the validity and reliability of synthetic estimates might differ from character- istic to characteristic. As part of the NCHS study of death rates, an alternative estimation procedure was developed. The resulting estimator, called the regression- adjusted estimator, uses the synthetic estimate in combination with ancillary data available on the State level and thought to be correlated with the health characteristic to be estimated.” This estimate, for at least one of the causes of death examined, seemed to be an improvement over the synthetic estimator. After the NCHS publication on synthetic estimates of disability, the Bureau of the Census produced synthetic estimates of unemployment rates and number of dilapidated housing units that had all plumbing facilities for States, SMSA’s, and counties.8-10 In addition, extensive studies were undertaken to evaluate the syn- thetic estimates. An important result of these studies was the emergence of a criterion, called the average mean square error (AMSE), as a proposed measure of the accuracy of a set of synthetic estimates, and the development of a method for estimating the AMSE.%:!1 These methods will be discussed in greater detail later in this report. Most recently, Namekata, Levy, and O’Rourke!? investigated the use of synthetic estimation in obtaining estimates of complete and partial work disability for States based on data from the 1970 census. The synthetic esti- mates were obtained and compared with the direct estimates that were available from the 1970 Decennial Census for each State. Their general conclusions were that the synthetic estimation technique was fairly good for partial work disability but fairly poor for complete work disability. ALTERNATIVE METHODS OF OBTAINING ESTIMATES Background In the original NCHS investigation of alternative procedures for small area estimation of health characteristics from the Health Inter- view Survey (HIS), several procedures were con- sidered.! In this section, we will discuss in detail two of the methods, namely, the nearly unbiased estimator and the synthetic estimator. In addition, we will discuss an estimator, called the regression-adjusted estimator, not considered in the original investigation but developed in a later study.’ One of the problems in obtaining estimates for States of health characteristics based on HIS data is the fact that the basic design of the HIS does not lend itself to unbiased estimates for States. In the basic HIS design, a primary sam- pling unit (PSU), which is generally a county or SMSA, is chosen to represent a stratum consist- ing of one or more demographically similar PSU’s. Those strata consisting of more than one PSU are called non-self-representing strata, and their component PSU’s may not be from the same State, although they would be from the same census region (Northeast, North Central, South, or West). Thus, the estimate from a sam- ple PSU when inflated to represent the entire stratum might cut across State boundaries, and hence, it would be impossible to combine the unbiased estimates for strata into unbiased esti- mates for States. Nearly Unbiased Estimator One of the methods considered in the origi- nal NCHS investigation is called the nearly un- biased estimator and yields an estimate for a State that is technically nearly unbiased. Basi- cally, this procedure takes the usual HIS stratum estimate for an aggregate and allocates it to a State in relation to the proportion of the total stratum population coming from the State. In other words, the nearly unbiased estimate X, of the mean level of characteristic X for State s is given by X= 1) din: X 7=1 where xX; = unbiased HIS estimate for the mean level of X for stratum j, d Rs = . Rg, j=1 = the number of persons in State s, ~ <2, Ni. = Ly Msji 2 i — = the number of persons in that portion of stratum j which is in State s, nj; = the number of persons in the jth stratum, 3 Siate, 7th PSU; s=1...., 8; 7~L,.... J; =1,. wos Lj and I; = the number of PSU’s in stratum j that are in State s. Some properties of the nearly unbiased estimate X, are given below. The proofs are presented in appendix I. Lemma 1: The expectation E(X, ;) of the nearly unbiased estimator X,. is given by i. X. L =r (2) where 7, sf, = average level of X in stratum j, n S <. I Me $f © n — = number of persons in stratum j, Ij n ed va -~ ji 57% xX. & bh ng; i=1 " average level of X in that portion of stratum j which is in State s, and yd ly x) j=1 1n2 I j= 1n2 J Xj; = average level of characteristic X in that portion of State s which is in PSU 7 of stratum j. Lemma 2: The bias B(X]) in the nearly un- biased estimate X, can be expressed by I ng (X,-X, 3! 7. oJ SJ. a Pa (3) j= Ses or equivalently by = don, JX. Rit iver BTY=-3, 7% (7 - LX, J (4) j=1 ""s.. i=1 5] SJ. Lemma 3: Let us assume that the ratio gj; inj, is the same for all PSU’s in the same State, which implies that nn... A for i=1, . : » Lj. (5) 57. BN Then the bias B(X,) in the nearly unbiased esti- mate X| has the form given by <. J 1 & B(X!) = j= 1 -. I — n Theorem 4: If =L = ae for ¢=1,..., I_;, then sje Lj B2%(X;), the square of the bias in X,, is given by the expression sj? ati. 3d Bs. 1 bg 2, -Lu) {n2 2; oe J. Xyji) Jo > 3ft So, 3 Xi) : (7) — Te J. Xji Xond) Table A. Interpretation of the components of the square of the bias of the ‘nearly’ unbiased estimate Component Interpretation J p2 si. = 2 . 1 hb rn Xs -X J 7 icmnginesinsdassessinibissies raise AA RAS Represents difference between the average level of X for a stratum J=1 ng Is and the average level of X for the portion of the straum that is in State s. Jh2 vo: 2 d= Cl itiivibmsemi——————— Represents variance in X among PSU’s belonging to the same State =. 1s and stratum. / / J sj sk nen 2h = 3.12 9. sk, (X; =X) Xi - ¥ ireinsate Represents a “between-strata’’ covariance. 1 J. “sji’ 4 R.~ ski j=1 k N Me |e Represents a “Retween-PSU" covariance. 0%; A (XX X;.)? 1; i=1 Theorem 4 implies that under the condition that n;;/n,; is the same for all PSU’s within the same stratum and belonging to the same State, the square of the bias of the nearly unbiased estimate X, consists of four components speci- fied in table A. It can be shown that the third component of B2(X,) can be transformed to the equivalent algebraic form given by 2 : ne Zeitsh: Xo. X;.-X;.) (Xsp.~X 1.) J nz, Thus, an equivalent expression for the square of the bias in the nearly unbiased estimate X, is given by L nZ 02; J n VI IB . B? (Xs) ii ). 2 J + x 2d i=1 7g Ig; j=1 75 I; Variance and mean square error of the near- ly unbiased estimate.—The variance oF can be obtained directly from its definitional formula. This is given by oi 5 ng; =, — 02, 9) *% min? % where 0%, the unbiased 7 estimate of the mean level of X in stratum j. It follows that the mean square error MSEx: is the variance of Xj, of the nearly unbiased: estimate X, is given by = = 04 2 MSEx: o% + B2(X,) where 0%, is given by relation (9), and BZ (X;) . s is given by relation (8) (under the condition that n/n; = 1/1). Evaluation of the nearly unbiased esti- mator.—In the original NCHS investigation of methods for obtaining local estimates, the nearly unbiased estimate did not emerge as the method of choice for producing these local area HIS esti- mates of health characteristics primarily because examination of the estimates produced by this method showed evidence that they were un- stable.l A later study was performed at NCHS to determine the extent to which the nearly un- biased estimator might be biased. The data base chosen for this study was mortality data in 1960 for the 42 States in the North Central, South, and West Regions of the United States. In par- ticular, nearly unbiased estimates of total deaths, deaths from motor vehicle accidents, and deaths from major cardiovascular-renal diseases were obtained from each State using the same stratification that is used in the Health Interview Survey. These nearly unbiased estimates were then compared with the true number of deaths in each State in the three regions examined, and the biases of the estimators were evaluated by ©’ 100/X,-X, | X Sea the percentage absolute difference Table B. Distribution of percentage absolute differences between the nearly unbiased estimate and the true value among 42 States in the North Central, South, and West Regions for total deaths, deaths from major cardiovascular-renal diseases, and deaths from motor vehicle accidents, 1960 Cause of death Major Percentage absolute difference cardio- Mot between nearly unbiased All vascu- he estimate and true value lar- Mele causes ronal acci- dis- dents eases Frequency Total siievesciminmmmiirnrons 42 I 42 42 QO. oi reiiiiininninnimriesesiinmsns 16 15 12 0-1. an 6 8 6 A 6 5 4 4 5 3 1 1 2 3 1 2 3 3 2 1 0 1 2 2 0 5 2 4 5 Percent Median percentage absolute dif- JOVBNCE oo. civeriveisniorrintersrivssssndine 1.78 | 1.70 | 2.70 The distribution of percentage absolute differ- ence is given in table B. The median percentage absolute difference was 1.78 percent for total deaths, 1.70 percent for major cardiovascular- renal deaths and 2.70 percent for motor vehicle accident deaths. The small biases obtained from this empirical study would yield the interpreta- tion that for the stratification used in HIS, the nearly unbiased estimator is in fact an estimator having small bias. However, in a given year, the number of households interviewed in a particular stratum might be quite small for the Health Interview Survey. It is, therefore, anticipated that oz, and hence 02, the sampling variance of the nearly unbiased estimator might be quite large. In addi- tion, the 0%, are difficult to estimate from the 7 (data. Hence, in terms of sampling variance, the My ' nearly unbiased estimate X] might not be the method of choice. ’ Synthetic Estimator Background.—The other method for obtain- ing local estimates of health characteristics investigated in the original NCHS study! is known as synthetic estimation and was the method finally chosen for producing local esti- mates of HIS health characteristics for States in 1963-64 and again in 1969-71.13 The underly- ing rationale for synthetic estimation is that the distribution of a health characteristic does not vary among populations of States except to the extent that States vary in demographic composi- tion. In other words, the method assumes that the incidence or prevalence of a health charac- teristic would be the same for two States if their composition were the same with respect to such demographic variables as age, sex, race, family income, family size, place of residence, and in- dustry of the head of the family. Conceptually, synthetic estimation uses the model given by k X= 2 P.% (10) a=1 where X s = mean level of characteristic X for the sth State, P,, = proportion of the population who are members of population cell «a (alpha), which is the socioeconomic demographi- cally bounded class of specified age, sex, race, income, etc. The sum over all a cells of P, = unity. X, = mean level of characteristic X for persons in cell « in the United States as a whole, and k= number of a cells utilized. In the original NCHS investigation, the X,, were national estimates of HIS variables for the period July 1962-June 1964. The population estimates P,, were obtained from tabulations of a H-percent sample questionnaire of the 1960 Decennial Census of Population for the 50 States and the District of Columbia. The popula- tion « cells were defined by cross-classifications of the following variables: 1. Color: white; all other 2. Sex: male; female 3. Age group: under 17 years; 17-44 years; 45-64 years; 65 years and over 4. Residence: standard metropolitan statis- tical area (SMSA)-central city; SMSA- not central city; not SMSA 5. Family income: under $4,000; $4,000 and over 6. Family size: fewer than seven members; seven members or more 7. Industry of head of family: Standard In- dustrial Classification codes 1 through 17 (Forestry and Fisheries, Agriculture, and Construction) and codes 19 and over (All Other Industries) The 384 possible cross-classification cells were collapsed to 78 so that reliable estimates could be obtained from the Health Interview Survey for each «a cell. For the synthetic estimates for the years 1969-71, HIS data from the three surveys of 1969, 1970, and 1971 were used to obtain the rates or percentages of the health characteristics measured. The populations of the 50 States and the District of Columbia were obtained from a sample described in a publication of the U.S. Bureau of the Census entitled Public Use Sam- ples of Basic Records From the 1970 Decennial Census, Description and Technical Documenta- tion, published in 1972. Of six such samples, the one used was the State Public Use Sample from the b5-percent questionnaires. Persons in the military or confined to institutions were not included in the population estimates produced for each State. Thus the restriction of the HIS samples to the civilian noninstitutionalized pop- ulation was carried over to these synthetic esti- mates. Of the seven variables used to produce the 78 a cells for the original report,! only six were available in the Public Use Sample used to produce these synthetic estimates. The variable that was not available was residence in standard metropolitan statistical areas. The six variables can produce a possible 128 cells of data. These were collapsed to 50 a cells for which reliable national estimates from the Health Interview Survey could be provided. A regional adjustment (as specified below) was employed for the State estimates within each of the four geographic re- gions of the United States to make these esti- mates consistent with the regional estimates produced by the probability design of the Health Interview Survey. In summary, the synthetic estimates pro- duced for HIS health characteristics for the years 1969-7113, use the same basic method as was used in the original NCHS investigation. However, in addition to estimates of long- and short-term disability, estimates of utilization of medical services were provided as well as esti- mates for subdomains of the population of each State (age, sex, color, and family income). Also, a methodology has been developed for providing sampling variances of synthetic estimates. Detailed synthetic estimate.—The detailed synthetic estimate X; of the mean level of characteristic X for State s is given by I > oS $s fof (11) $ LZ +P t=1 >i where ~y X, = final synthetic estimate of the mean level of characteristic X for State s, X, = the usual HIS final estimate of the mean level of characteristic X for region r (where region r contains State s), P,, = proportion of the population (from the 1970 Decennial Census) of region which is in State ¢ (¢=1,..., T), T = number of States in region r, = first-stage synthetic estimate of character- istic X for State s, X,, = final HIS estimate of the mean level of characteristic X for demographic cell a for the United States, P,, = estimated proportion of the 1970 popula- tion in State s belonging to cell a (as esti- mated from the 1970 U.S. Census 1- Percent Public Use Tapes), and k = number of « cells. Synthetic estimates x. for subdomains (age, sex, color, and income) are given by the estimator FR Ii le T 12 “Tr. 49 u where X,, = the final synthetic estimate for the mean level of characteristic X for subdomain « within State s, = 2. 2X0 = preliminary synthetic estimate for the mean level of characteristic X in sub- domain u of State s, P,, = the estimated proportion (as estimated for the U.S. Census 1970 1-Percent Public Use Sample Tapes) of the population of State s belonging to cell a, and =2 Pl, Qeu = the estimated proportion of the popula- tion of State s belonging in subdomain u, except for synthetic estimates of work- loss days per person per year in age groups. By definition, HIS excludes all persons under 17 years of age from the employed population. Therefore, the fac- tor f;, in the denominator of the ratio ad- justment for these statistics is redefined as the estimated proportion of the popula- tion age 17 and over in State s that be- longs to subdomain (age group) u The synthetic estimates for subdomains as given by equation (12) are ratio adjusted so that the aggregates are consistent with the final syn- thetic estimates for the State as a whole. The «a variables were limited to those listed below: Color: white; other than white. Sex: male; female. Age group: under 17 years; 17-44 years; 45- 64 years; 65 years and over. Family income: under $5,000; $5,000 and over. Family size: fewer than seven members; seven members or more. Industry of head of family: Standard Indus- trial Classification Codes 1 through 17 (agri- culture, forestry, fisheries, mining, and con- struction); 18 and above (all others). The 128 cross-classification cells produced by these variables were collapsed into 50 a cells for which reliable national estimates from the Health Interview Survey could be made. Zz The ratio adjustment X./) PX, was in- t=1 cluded in order to reflect a regional component in final estimates. It is the ratio of the published regional figure to the preliminary, derived re- gional rate calculated from the State estimates. Estimation of sampling errors of synthetic estimates for HIS characteristics 1969-71.—The synthetic estimates presented for the 1969-71 If P= minimum (Pg; x) and V2 = Rel- / HIS data are subject to sampling variability from : oy Xs . : variance of X_, we have two sources because they are based on HIS esti- ~~ 5 mates and estimated population proportions. (When synthetic estimates are computed from k known proportions and population means they 2 P2 02, +2 pi PP Cov(Z.X) are not subject to sampling error, since there pz = esl * 2p (1-P,)= x X2 p2 £2 -— is Q SO sa a sa X,,, then the variance of X, given a=1 a=1 Pee by equation (13) reduces to 1-Pm k 1-Pn[ k 2 k <== (£P F a 7] wp = == > 0% % Y na, sly XZ (1-F.,.)7,, Pr a=1 “x pr a=] Sor a Ss a=1 XxX. Ss a=1 i and +2) PP, Covi, .X.) (14) a P, QEu Equations (18) and (19) were the expres- sions used to compute sampling errors for the estimates in the report.!3 Almost all the esti- mates had sampling errors that were very small relative to the size of the estimates themselves. The relative standard error (RSE), defined by and was 5 percent or less for virtually all statistics in the report, even for the smallest States. The only important exceptions occurred for estimates of the proportion of persons in certain population subgroups who were unable to carry on major activity. The most variable subgroup was the under-45 age group, where the RSE ranged from 7.4 percent for the entire United States to 10.4 percent for Alaska. The highest single RSE was 11.6 percent for white persons in Alaska. Al- though it may seem strange for State estimates to have such small sampling errors, these esti- mates were essentially weighted averages of national HIS estimates based on 3 years of data wo) ov =5 2 ( X, - AMSE Bop S > % . (26) s=1 This statistic has been used with certain elabora- tions by Census Bureau investigators as the major criterion for evaluating synthetic esti- mates. A shortcoming of this criterion, however, is that it does not yield an estimate of the mean square error for a specific synthetic estimate (e.g., estimated unemployment in Ohio, 1976). Rather, it gives the average mean square error a set of synthetic estimates. Evaluation of HIS Synthetic Estimates for Alternative o-Cell Grids Investigators at NCHS originally hoped to evaluate the 1969-71 HIS synthetic estimates by means of the AMSE criterion. However, there was no unbiased estimate uncorrelated with the synthetic estimate that could be used in equa- tion (26). Although it is thought that the bias of the nearly unbiased estimate discussed above is likely to be small for HIS variables, and that the correlation between the synthetic estimate and nearly unbiased estimate is also likely to be small, the task of obtaining a reasonable esti- mate of its variance is difficult since it is often based on data from one or two primary sampling units. The main thrust in the evaluation of the 1969-71 HIS synthetic estimates was an empiri- cal investigation comparing synthetic estimates based on the 50 a-cell grid used to obtain the published, 1969-71 synthetic estimates with those obtained by collapsing the 50 cells into a smaller grid. In particular, synthetic estimates were obtained for the 50 States and the District of Columbia based on (1) the total 50 a-cell grid, (2) a 2 a-cell grid based only on sex, (3) a 4 a-cell grid based on age alone, (4) an 8 d-cell grid based on sex and age, (5) a 16 a-cell grid based on color, sex, and age, and (6) a 16 a-cell grid based on family income, sex, and age. The synthetic estimates produced by each of the collapsed grids (sex, age, sex by age, sex by age and color, and sex by age and income) were compared with theg synthetic estimates produced { by the total 50 a-cell grid by use of the follow- ing summary statistics: 1. The mean over all 50 States and the District of Columbia of the proportional 5g X, | fg between Xs the synthetic estimate 3 based on a particular grid and the synthetic estimate ¥ based on the total 50 «-cell grid (table D). 2. The maximum over all 50 States and the District of Columbia of the proportional absolute difference defined above (table 3. The correlation coefficient over all 50 States and the District of Columbia be- tween the synthetic estimate produced by a collapsed grid with that produced by the total grid (table F). absolute difference The mean proportional absolute difference (table D) is a measure of the average relative difference between synthetic estimates produced by a collapsed grid and those produced by the total grid. For the HIS variables considered in this study, synthetic estimates produced by each of the collapsed grids agreed closely by this cri- terion with synthetic estimates produced by the detailed 50 a-cell grid. For most of the 14 vari- bles in this study, the mean proportional abso- lute difference was less than 5 percent, and the worst agreement by this criterion was shown by the synthetic estimates produced by the a-cell grid based on sex. In most cases, the synthetic estimates based on age by sex, age by sex and | color, and age by sex and income did not show’ ) substantially better agreement by this criterion with those based on the total detailed grid than - the synthetic estimates based on age alone. The maximum proportional absolute differ- ence (table E) gives a feeling of the extent that a single synthetic estimate based on a collapsed grid might differ from the comparable synthetic estimate based on the detailed 50-cell grid. The magnitudes of some of the statistics shown in table E imply that in individual States, the grid used to compute the synthetic estimates might affect the size of the estimate, even though the 13 Table D. Mean proportional absolute differences between the synthetic estimate produced by the total 50 a-cell grid and that produced by other a-cell grids for selected Health Interview Survey (HIS) variables, 1969-71 \ a-cell grid Sex So HIS variable Sex by in Sex Age by color come age by by age age Mean proportional absolute difference RESTLICIOCHBCIIVILY YS cri isrsrssssmsnigiivassnsssnsomsmarssnrassenmmmsssnios sass omins Va ses Amana Sa FoR eRe Rs 028 .{ .017 | 017 .024 .020 Bed disability days ... .029 | .026 | .025 032: 1? 1029 WOT KAGSSCIAYS. oi vserrraersnsstsnensnnienssinsnsessmmrmssinnssisiotesshmmsriviinih sos suerivnsiias si tssmmpnsinsuisissonmmsntomannesnnse .039 | .026 | .025 .032 .021 Hospital discharges per TOD POrSON YEAS ..........cieisssesssssssressrssssorsserarssnnsrsnssporsssassssssssssissniavereses .021 | .008 | .008 .008 .008 Average 1ength: of hOSPIANZANION seiwuimirisissariviniesssssnsssssssssssesssnsipinnnssonssrvinsbnsnnsassessoninaibneninge .035 | .034 | .034 .028 .023 Percent of persons having one or more hospital episodes iN @ Year ........ccccecereereerennrrieeseeseennnnnne .018 | .008 | .008 .007 .006 Percent of persons having one or more physician Visits iN @ Yar .......ccccccvvvevnrnennererreeneererensenenes .008 | .008 | .008 .005 .007 Number of Physician VISITS D8r PEESOI YAN ...uivrsessrssissssrsnvsinsnnsssesprrsnamssssnssssssssasusssnnatossstonssrnses .021 .016 | .016 .015 017 Percent of persons having one or more dental Visits iN @ Yar ........cccocereevmmemrmmnnennenreeeessenesenenanns .031 .031 .031 .016 .027 Number of dental Visits DEF PRISON YOAF .....ccrcirerrisrrsvisrssnssassssssssssssssssssssssssssgsensniaressnrsnnssssssssssss .066 | .055 | .055 .032 .062 Percent not IHTiter) In GEHIVIIY ivviiiscncsmimmmssnisissssisspimivssssvsssrmisseississersvionsiniessvs nis veiopissinias .008 | .003 | .003 .003 .004 Parcorit HmItod in ACEIVITY ol. un criserisistvitse sits ane rn riv svt bois ss Gas ve EIT Sp REN Tae Rn as ne Emevnttren ins .061 | .021 | .021 .029 .026 Percent limited in amount or kind of Major @CtiVity ......cccccereevesreesienerssessseneeessssnneessssssssssasnns .064 | .024 | .024 .025 .027 Percent unable 10 Carry On Major GCHIVILY (vv cirrrmssmmirmmsrrmssssisssssssssssssrsisssserrorvsssabnsisssrsnsssss .094 | .058 | .061 .081 .057 Table E. Maximum proportional absolute differences between the synthetic estimate produced by the total 50 a-cell grid and that produced by other a-cell grids for selected Health Interview Survey (HIS) variables, 1969-71 a-cell grid Sex Sox HIS variable Sex by Sex Age by color - come age by by age age Maximum proportional absolute difference ReSiricIod aCHIVILYIORYS coves siisithessacessssioniansmmmsssosssisssnsssssssasssssnusnisvasseniininsnsmvsssssnsystsssossonnss 03 | 073 1.073 .099 J36 Bod ISADHILY BAYS ..cinirmimsimmisimmnnissirisemmmsnissmssmsmsssssissrssssistsnssstessasssssissinamnaivsssrsitsesssssssssess .134 | .088 | .089 114 170 WWOTK VOSS HAYS ovorsncninrssrisavmsisrunstonisimsansssns abs Riss iiss am Reiss RoR SARA S S AS oa annem nS Ss Seba R sa ea ee 216 | .047 | .140 071 211 Hospital discharges per 100 person years w | A271 J0B5 ; 070 .034 .024 Average 1ength Of NOSPHBHZATION virocissssscssscsissssssermnisssaisssssrsssssssvssssssssssssasssssssssibosrsersesss - [4-789 §{ 2071 ; 203 .083 .266 Percent of persons having one or more hospital episodes iN @ Yar .........cccceeevrvrveeeneeeenenes we 2703.1 057.1 O73 .026 .020 Percent of persons having one or more physician visits in a year . .042 | .041 | .042 .019 .027 Number of physician visits per Person year.......cccccceeveverereeerennes .104 | .084 | .088 .050 .048 Percent of persons having one or more dental visits in a year ... weil 229 2358 1..237 .058 .241 Number of dental Visits per Person Year .........c.cccccceeererenneeeens wn i «382 4 393 )::~398 L101 402 Percent not limited in activity ............. ei. 037 | 013] .013 .014 .021 Percent IME IN GCLIVILY .cnisiiniresisssssnisissssssssmssnarassravssensernbessivssssssnssssssinansnaidnsssvbusssornsssbsesors 454 | .094 | .092 .130 .184 Percent limited in amount or Kind Of Major aCtIVILY ...c.coe ems smmissrisiisssssissserssssvssssssssssssssassees 493 | .088 | .091 J22 .154 Percent unable to Carry On. MAJOT ACTIVILY ‘wicaivsvscsissmnimensrsiisisisisssnssissiosmnsenivasssvisosoressresy B95 | .233 {| .192 .264 494 14 Table F. Correlation coefficients between the synthetic estimate produced by the total 50 a-cell grid and that produced by other a-cell grids for selected Health Interview Survey (HIS) variables, 1969-71 a-cell grid Sex fox HIS variable Sex by Dy Sex Age by color ims come age by by age 206 Correlation coefficient BESErCIoa aCTIVITY CAYS cco vers icsrissssssisans isnrapesianisssisrianiosphssssssrsnsrorpesdesssesarsroninsetiiobsssssimpuimb asses 89 96 .96 94 93 BE CISOIIRY TBYS ./iiliicriiishinindrnitomint hiss pesssteihrassssbeibsssssassunsisssser thin ss esssnnssbassssssarsasusbnsss 94 .95 .96 95 .94 WORK 1088 AYE. ..viiiniiiseisciinrrinssreisiirbrmmsassssssiessssssivasivinshunssosrrnss dorms sess TR REAR 81 .89 .90 .96 .85 Hospital discharges per 100 person years 88 98 .97 99 99 Average length of hospitalization ........ccueeeinineeiinniinininen, 89 89 .89 96 87 Percent of persons having one or more hospital episodes in a year ... 90 98 98 99 99 Percent of persons having one or more physician visits in a year ... 81 82 81 95 91 Number of physician visits per person year........ Heian sessirereiety 93 96 .96 98 98 Percent of persons having one or more dental visits in a year . 91 90 .90 98 92 Number of dental visits per person year..... 96 95 .95 99 96 Percent not limited in activity ............. 63 95 .96 95 92 Percent limited iN aCtIVITY ......crcivrrinsiiinionsssssssosiobibin 61 95 95 93 93 Percent limited in amount or Kind of Major 8CHIVILY ......ccccciveiiiieieiieierieinniinnnnnnesnnersiinrsseeeeeseen, 50 94 94 94 93 Percent unable 10 Carry ON MBO ACTIVITY .i.civvisiiseissivessissitonisvisiinsssiinpstvisissssrsssssressssssssnsvansnvars 85 94 94 93 91 average proportional absolute differences are small. The correlation coefficient between syn- thetic estimates based on the detailed 50-cell grid and those based on a less detailed grid (table F) measures the strength of the relationship be- tween the two sets of estimates. It is a measure OO that is particularly appropriate when it is desired to rank a set of estimates and when the absolute values of the estimates are of secondary interest. In general, the correlations were quite high, with estimates based on the sex grid showing the lowest correlations with those based on the de- tailed grid. 15 REFERENCES INational Center for Health Statistics: Synthetic State Estimates of Disability. PHS Publication No. 1759. Public Health Service. Washington. U.S. Government Printing Office, 1968. 2U.S. Bureau of the Census: The Methods and Materials of Demography, by H. S. Shryock, J. S. Siegel, and associates. Washington. U.S. Government Printing Office, 1973. 31.8. Bureau of the Census: Developments in statisti- cal estimation for local areas, by E. P. Ericksen. Statistical Methodology of Revenue Sharing and Related Estimated Studies. Census Tract Papers, Series GE-40, No. 10. Washington. U.S. Government Printing Office, 1974. pp. 51-56. 4Ericksen, E. P.: A method for combining sample survey data and symptomatic indicators to obtain popu- lation estimates for local areas. Demography 10: 137-160, 1975. 5Ericksen, E. P.: A regression method for estimating population changes of local areas. J. Am. Stat. Assoc. 69: 867-875, 1974. 6 Woodruff, R. S.: Use of a regression technique to produce area breakdowns of the monthly national estimates of retail trade. J. Am. Stat. Assoc. 61: 496-504, 1966. TLevy, P. S.: The use of mortality data in evaluating synthetic estimates, in Proceedings of the American Statistical Association 1971, Social Statistics Section. Washington. American Statistical Association, 1974. pp. 328-331. 8Gonzalez, M. E., and Hoza, C.: Small Area Estima- 16 tion of Unemployment. Presented at meeting of Inter- national Statistical Institute, Warsaw, Poland, 1975. 9 Gonzalez, M. E., and Waksberg, J. E.: Estimation of the Error of Synthetic Estimates. Presented at the first meeting of the International Association of Survey Statisticians, Vienna, Austria, Aug. 1973. 10Simmons, W. R.: Adjustment of Data-Synthetic Estimates. Presented at the first meeting of the Inter- national Association of Survey Statisticians, Vienna, Austria, Aug. 1973. 11U.S. Bureau of the Census: Use and evaluation of synthetic estimates, by M. E. Gonzalez. Statistical Methodology of Revenue Sharing and Related Estimated Studies. Census Tract Papers, Series GE-40, No. 10. Washington. U.S. Government Printing Office, 1974. pp. 46-50. 12Namekata, T., Levy, P. S., and O'Rourke, T. W.: 9 thetic estimates of work loss disability for each State and the District of Columbia. Public Health Rep. 90: 532-538, 1975. 13National Center for Health Statistics: State Esti- mates of Disability and Utilization of Medical Services, United States, 1969-71. DHEW Pub. No. (HRA) 77-1241. Health Resources Administration. Washington, U.S. Government Printing Office, Jan. 1977. 14Gonzalez, M. E.: Small area estimation of unem- ployment, in Proceedings of the American Statistical Association, Social Statistics Section. Washington. American Statistical Association, 1975. 15Hansen, M., Hurwitz, W., and Madow, W.: Sample Survey Methods and Theory, Vol. 1. Methods and applications. New York. John Wiley & Sons, Inc., 1953. Proofs of Lemmas and Theorems Lemma 1 APPENDIX Lemma 2 Lemma 3 Theorem 4 Theorem 5 Theorem 6 Theorem 7 17 APPENDIX PROOF OF LEMMAS AND THEOREMS Lemma 1: The expectation E(X) of the nearly unbiased estimator X, is given by 1 EX)= n,; Xn, (1A) where S XxX, = 3 Nj. Xn, = average level of X in stratum j, n o o I Me 57. © i — = the number of persons in stratum j, Ig; Xs. = 2 ngiXsjilns;. = = average level of X in that portion of stratum j which is in State s, and Xi = the average level of characteristic X in that portion of State s which is in PSU ¢ of stratum j. 18 Proof We note that the expectation of X| is give since X, i is an unbiased estimator of X ; . QED vv! Lemma 2: The bias B(X;) in the nearly un: biased estimate X, can be expressed by B(X;) = 2 ng. X,. = Xin. (2A) = or equivalently by Proof Since, by definition, the bias B(X,) of X] equal to B(X;) = E(X;) - X;, where J — = S ng; Xj Ing i=1 = average level of X in State s, relation (2A) follows directly from lemma 1 and the definition of z J We note that Lemma 3: Let us assume that the ratio n/n; is the same for all PSU’s in the same stratum in the same State, which im- plies that Wei 1 —L = — fori=1 Ls Nj. 4; RE Pe (54) Then the bias B(X.) in the “nearly” unbiased estimate X| has the form given by I coqdy LL RK (60) J D4, Fi on Z. < v z _ go ni X,ji Proof Je sy 4 702 ] BL, The results follow directly from relation y I 1% (5A) and lemma 2. i —li Msji i= - 3 Rj %) hie QED Therefore, relation (3A) follows from relation os? 1 7 > 3 : die = - (2A) by substitution of relation (4A) into rela- Theorem 4: If i for i=1,..., I, then tion (2A). oS 2 . . QED . B2(X!), the square of the bias in X 5» 1s given by the expression Lind gold pd 2 sj ’ v oe) ng 1 - 3 B2X)=) FF FL+ == = (X -X.)2+ 2 oe X.-X x. =X ’ J=1 ng, I Z n?, I; . X ng 1% i=1 i' - +2 2, 2 I.1 x (X Xi) (Xx X:rt) (7A) J=1 k 2 (X, Je - Xo +X. - Lait) (8A) 19 Squaring the right-hand side of relation (8A), we obtain 2 ' d nj, 1 2 } B X= 2 n, rg LL 3:3 + Xy Xi) J pn? Is; 2 74 Is; Io = sj. 1 X Msi Msk TT w= Sr =) x [(X,;-X,;)+(X,;-X i} +2 ! X > 8.3, # n} 1 a nn os #5 Lilo Li abel i=1 Xo Xon) = gd = (X,~X,, +X. -X..,)+2 8 (X;-X:) (X; -X iv) 7=1 n2, IZ prey 5 5p j=1 ng, 1% iE Be "I J ng; Ng, Is Ish 52. SK. vd Ed vd +23 3 n2 1.1 0 ( J X.Y (Xx Xeni) (9A) JEL & P32, 0: + y > X2 ( l-P sy Po 5 a=1 X a Ss a=1 +2 3 P,P, Cov (X,,X.). a s EX; - X,) X, - X,) = Cov (X,, X,) +B(X!)B(X,)=0 § since X, and X, are uncorrelated and B(X]) = 0. ol = the variance of X. Proof BX - XR =P UT, ~-X) + (Z,~Z))F -E(X;- X,)? +E, - X* = 2E(X; of X,) (X Vi X;) but BE - Xf =o, and 22 QED Theorem 7: If X, is an estimate of X, with bias given by B(X,), if X| is an un- biased estimate of X ; uncorrelated with X,, and if 62 is an unbiased xg estimate of 0%, then the estimate Ss 2 MSEZ given by 7 os a MSE; = (X, - X,)? - 62, Xs (21A) Si is an unbiased estimate of MSE%.. Ss Proof Proof follows directly from theorem 6. QED # U.S. GOVERNMENT PRINTING OFFICE: 1977 260-937:35 Series 1. Series 2. Series 3. Series 4. Series 10. Series 11. Series 12. Series 13. Series 14. Series 20. Series 21. Series 22. Series 23. VITAL AND HEALTH STATISTICS PUBLICATIONS SERIES Formerly Public Health Service Publication No. 1000 Programs and Collection Procedures.—Reports which describe the general programs of the National Center for Health Statistics and its offices and divisions, data collection methods used, definitions, and other material necessary for understanding the data. Data Evaluation and Methods Research.—Studies of new statistical methodology including experimental tests of new survey methods, studies of vital statistics collection methods, new analytical techniques, objective evaluations of reliability of collected data, contributions to statistical theory. Analytical Studies. —Reports presenting analytical or interpretive studies based on vital and health statistics, carrying the analysis further than the expository types of reports in the other series. Documents and Committee Reports.—Final reports of major committees concerned with vital and health statistics, and documents such as recommended model vital registration laws and revised birth and death certificates. Data from the Health Interview Survey.—Statistics on illness; accidental injuries; disability; use of hospital, medical, dental, and other services; and other health-related topics, based on data collected in a continuing national household interview survey. Data from the Health Examination Survey.—Data from direct examination, testing, and measurement of national samples of the civilian, noninstitutionalized population provide the basis for two types of reports: (1) estimates of the medically defined prevalence of specific diseases in the United. States and the distributions of the population with respect to physical, physiological, and psychological charac- teristics; and (2) analysis of relationships among the various measurements without reference to an explicit finite universe of persons. Data from the Institutionalized Population Surveys.—Discontinued effective 1975. Future reports from these surveys will be in Series 13. Data on Health Resources Utilization.—Statistics on the utilization of health manpower and facilities providing long-term care, ambulatory care, hospital care, and family planning services. Data on Health Resources: Manpower and Facilities. —Statistics on the numbers, geographic distrib- ution, and characteristics of health resources including physicians, dentists, nurses, other health occu- pations, hospitals, nursing homes, and outpatient facilities. Data on Mortality. —Various statistics on mortality other than as included in regular annual or monthly reports. Special analyses by cause of death, age, and other demographic variables; geographic and time series analyses; and statistics on characteristics of deaths not available from the vital records, based on sample surveys of those records. Data on Natality, Marriage, and Divorce.—Various statistics on natality, marriage, and divorce other than as included in regular annual or monthly reports. Special analyses by demographic variables; geographic and time series analyses; studies of fertility; and statistics on characteristics -of births not available from the vital records, based on sample surveys of those records. Data from the National Mortality and Natality Surveys.—Discontinued effective 1975. Future reports from these sample surveys based on vital records will be included in Series 20 and 21, respectively. Data from ihe National Survey of Family Growth.—Statistics on fertility, family formation and disso- lution, family planning, and related maternal and infant health topics derived from a biennial survey of a nationwide probability sample of ever-married women 1544 years of age. For a list of titles of reports published in these series, write to: Scientific and Technical Information Branch National Center for Health Statistics Public Health Service Hyattsville, Md. 20782 : Us (2. DATA EVALUATION AND METHODS RESEARCH National Survey of Family Growth, Cycle I: Sample Design, Estimation Procedures, and Variance Estimation U.S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE Public Health Service Library of Congress Cataloging in Publication Data French, Dwight K. National survey of family growth, Cycle I. (Vital and health statistics; Series 2, Data evaluation and methods research; no 76) (DHEW publication; (PHS) 78-1350) Includes bibliographical references. Supt. of Docs. no.: HE 20.6209:2/76 1. Family size—United States—Statistical methods. 2. Fertility, Human. 3. Birth con- trol—United States. I. Title. II. Series: United States. National Center for Health Sta- tistics. Vital and health statistics: Series 2, Data evaluation and methods research; no. 76. III. Series, United States Dept. of Health, Education, and Welfare. DHEW publication; (PHS) 78-1350. RA409.U45 no. 76 [HQ766.5.U5] 312'.07'23s [301.42'1] ISBN 0-8406-0116-6 77-608168 For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 Stock No. 017-022-00604-9 DATA EVALUATION I Series 2 AND METHODS RESEARCH Number 76 National Survey of Family Growth, Cycle I: Sample Design, Estimation Procedures, and Variance Estimation This report describes the procedures used to select the sample, esti- mate population parameters, and estimate sampling variances for Cycle I of the National Survey of Family Growth. DHEW Publication No. (PHS) 78-1350 U.S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE Public Health Service National Center for Health Statistics Hyattsville, Md. January 1978 NATIONAL CENTER FOR HEALTH STATISTICS DOROTHY P. RICE, Director ROBERT A. ISRAEL, Deputy Director JACOB J. FELDMAN, Ph.D., Associate Director for Analysis GAIL F. FISHER, Associate Director for the Cooperative Health Statistics System ELIJAH L. WHITE, Associate Director for Data Systems JAMES T. BAIRD, JR., Ph.D., Associate Director for International Statistics ROBERT C. HUBER, Associate Director for Management MONROE G. SIRKEN, Ph.D, Associate Director for Mathematical Statistics PETER L. HURLEY, Associate Director for Operations JAMES M. ROBEY, Ph.D., Associate Director for Program Development PAUL E. LEAVERTON, Ph.D., Associate Director for Research ALICE HAYWOOD, Information Officer STATISTICAL METHODS STAFF, DATA SYSTEMS E. EARL BRYANT, Chief DIVISION OF VITAL STATISTICS JOHN E. PATTERSON, Director ALICE M. HETZEL, Deputy Director WILLIAM F. PRATT, Ph.D., Chief, Family Growth Survey Branch RITA U. HOFFMAN, Chief, Programming Branch COOPERATION OF THE NATIONAL OPINION RESEARCH CENTER In accordance with specifications established by the National Center for Health Statistics, the National Opinion Research Center at the University of Chicago, under a contractual agree- ment, participated in the design and selection of the sample and carried out the data collection. Vital and Health Statistics-Series 2-No. 76 DHEW Publication No. (PHS) 78-1350 Library of Congress Catalog Card Number 77-608168 PREFACE This report presents a detailed description of the sample design, estimation procedures, and variance estimation method used in Cycle I of the National Sur- vey of Family Growth. The survey was designed and conducted by the National Opinion Research Center (NORC) of the University of Chicago under a contrac- tual arrangement with the National Center for Health Statistics (NCHS). The sampling plan was developed under the supervision of Martin Frankel and Benja- min King of NORC, in consultation with E. Earl Bryant, Monroe G. Sirken, and William F. Pratt of NCHS. Much of the report, prepared by Dwight K. French of the Statistical Methods staff, is based upon survey specification documents prepared by NORC and upon internal NCHS memoranda. Dr. Frankel, Dr. King, Mr. Bryant, and Dr. Pratt, along with Drs. Gordon Bonham and Dwight Brock of NCHS, were the primary resource persons for methodological questions. In addition to internal review, NCHS policy stipulates that methodological reports are to be given a peer review for technical merit and readability by one or more persons who are familiar with the subject matter area of the report but are not involved in producing the report. Mr. Garrie Losee of NCHS carried out the peer review of this report and made many constructive suggestions. ie Es irs oo efit mE AL. - oy El ul 1a pwd et ame ath gid Le apt Se Tu oa anc EIA sa AR mi dE “dap oo oo 3 . . om . gn LR Haz - - bk BE " 2H, oo gE H er . - ‘gr = r, me ree a Te + hy CONTENTS DE Cl ra i mse TTY ETI SETI ATP ATER SS SESH FRA SHAE APH S S HATTA PR NRE R sons RR ann SAAR ERs Ome NAAT SOA TER TE w Introduction ........... " PERERA ” TN Design SPeCIfiCALIONS w.cccerrrrssrrrsssssssssssrsnssersssssssssssssesssstnssssessssss assess ssssss seen sess sssssssssneess Sample Design ETE EERE HEPES ESTEE SESE HET E Ses ETE RUS SHAVER VORY a STUINIMMATY vr irsseereverssnseonisriisstrssieuninssstiscsmroseacansasssssssnsmmersssssannersssshsnssoseesssrsmessss mses Determination of SAMPIE SIZE .rerecccrsesssssrsssrsssssssssomssssssrssssssssssissssssisassarssssrssassessasss Stratification and Selection Of PSU'S wcssmsvivsicsssssssmsisssssnssmsissrsssssssinsssssnissrsasssssvnsss Selection of Second-Stage Units ........ _ Selection of Third-Stage Units .....cossrvvnsrssssessensscnnn seers sss rErse rT s ELSI SSS se ESS eS AEST SES Se A BATS ee ee Selection of Fourth-Stage Dwelling Units ......cccccveeericnnneeennn. Fifth-Stage Selection of Sample Persons .........cucueee Characteristics of the Sample ..... Estimation siccessessssmsss I — Sevesty Weighting Procedure cssiseremisicmcmisisssvsnsimsississsssisssrssssesssssssysssssnsensevssssasssssssss Estimating Equation Variance Estimation Background ...... wor Summary of Applicable Theory ” ApplHcation to the NSFC .......cvccvnisiitenssinrssimsimmmsinssivrssossssininissimnsive ve OE eR errr assinassen Appendixes I. Glossary Of Terms werecossssssesivssvorsesssssssesessensasosonsssnmmoesssssssesssssuassonsssenissessssasassasoes II. Evaluation of Alternative Estimators III. Household Screener .. won Ferm LIST OF FIGURES 1. Geographic divisions of the United States, and their order for the first-stage sample .......... weve win 2. Relative standard errors for aggregates of women, by race 3. Relative standard errors for percent of total and white women (base of percent shown in curve 0 thOUSANAS) wsisrmssssrmrsmmssrmmsssirsrsssramssissserssssnrssseniissdepsssnirsansrss snore 4. Relative standard errors for mean numbers of births expected by women of all races and white LIST OF TEXT TABLES A. Standard error tolerances of estimated proportions for selected population subgroups......ceseeeeseees B. Sample PSU’s for the National Survey of Family Growth — w iii bt © WO 00 ~J Ls LLL 26 28 29 18 21 22 vi Ordering of States for sampling from the National Opinion Research Center non-SMSA frame ..... Example of sampling table on the Household SCIeener ...c.c.cmsisnssimssenssmmssssssssisessesssrsssssmsenss Fors Actual and expected number of sample DU’s, number of completed screeners, and screener com- pletion rates, by 1ace and SHAUN. «urmmsisimisssimsissisnses ERAT ere Teena Rh Lie Chea Ta Tra st irarase rar Number of sample women, actual and expected number of completed interviews, and interview completion rates, bY race Gnd SIIALIIL ciermscsisiimmsmsstrmsassmissirsssarssssmresmsessssssesanses ertnserss sates Screener and interview completion rates and combined response rates, by Stratum ..... isvevEv sys Comparison of standard error tolerances with the corresponding values obtained from the Na- tional Survey of Family Growth (NSFG) ..ccumnminmmmimsinmnimsinrerisliwiivirseis Poststratification adjustment factors (ratio of September 1973 population control totals based on Current Population Survey data to National Survey of Family Growth weighted estimates), BY EA0R SIE ARE sisvsm ses tinepieiinamsssassns matt shaivisninsesssaahnnssessnnsnssmsesinsnssansnsisasvossassersstiosssaissstonanes Example of how to determine 4, from PSU response data wissen Example of a hali-sample replication PALLET wuss assassins is issoisss assy Estimates of A and B for relative standard error curves, by race w.eoocveceveeinuernnieneinsieeninesssnnnssinees ‘ SYMBOLS Data not available-------------sseeee --- Category not applicable------------eeerereaeneeee Quantity zero - Quantity more than 0 but less than 0.05------ 0.0 Figure does not meet standards of reliability or precision (more than 30 percent relative standard error)----------- * id 12 12 13 13 14 16 17 19 NATIONAL SURVEY OF FAMILY GROWTH, CYCLE I: SAMPLE DESIGN, ESTIMATION PROCEDURES, AND VARIANCE ESTIMATION Dwight K. French, Statistical Methods Staff INTRODUCTION The primary mission of the National Center for Health Statistics (NCHS) is to collect and publish statistics relating to the health of the U.S. population. In carrying out its mission, NCHS collects data on vital events registered in the United States, conducts inventories of health facilities and manpower, and conducts probabil- ity sample surveys based on household inter- views, health examinations, and medical records. Data collection programs are supplemented by research projects which investigate new tech- niques of data collection and evaluate currently operating programs. In response to the need for current informa- tion on the interrelated topics of fertility, family planning, and their effects on population growth, the National Survey of Family Growth (NSFG) was established as an integral part of the NCHS program in 1972. Since the purpose of the survey was to collect data relating to natality and the process of family formation and dissolution, it was placed within the Division of Vital Statistics. The NSFG is designed as a cyclic survey; that is, data are to be collected every few years by means of a sample survey. The target population for Cycle I of the NSFG consisted of civilian noninstitutionalized women living in the conterminous United States who were less than 45 years of age and who were currently married, previously married, or single mothers with children living in the household at the time of interview. Data were collected by means of personal interviews with a probability sample of these women. The inter- views furnished information for determining trends and differentials in fertility, family plan- ning practices, sources of family planning advice and services, effectiveness and acceptability of various methods of family planning, and aspects of maternal and child health that are closely related to family planning. The sample design and data collection for the first cycle of the NSFG were contracted to the National Opinion Research Center (NORC) of the University of Chicago. The sample con- sisted of 10,862 eligible women, of whom 9,800 (90.2 percent) were interviewed during the 8- month period from July 1973 through Febru- ary 1974. Other reports will discuss the findings of the survey. This report describes in detail the sample design and sample selection procedures used in Cycle I, the techniques used to estimate population parameters, and the procedure used to estimate sampling variances. DESIGN SPECIFICATIONS The development of an efficient sample design must take into account the primary sur- vey objectives, amount of funds available, logis- tical problems, time limitations, organized spec- ulation concerning population parameters and unit operating costs. These requirements dic- tated a stratified multistage probability sample design for the NSFG, based essentially on the following set of specifications: 1. The target population was defined to be civilian noninstitutionalized women liv- ing in the conterminous United States who were less than 45 years of age and who were either (a) currently married, (b) previously married, or (c) single mothers with one or more of the children born to them currently living in the household. 2. The sample would consist of approxi- mately 10,000 women, selected from an initial probability sample of households. Trained field staff were to conduct a screening interview with a responsible member of each sample household to determine if there were any eligible « women (the screener questionnaire is re- produced in appendix III). When a household contained one eligible woman, she was included in the sample. In house- holds with more than one eligible woman, the staff member would ran- domly select one woman for the sample. 3. Data were to be collected from the sample women by means of personal interviews lasting an average of 1 hour. 4. All interviewers were required to be female. 5. The interviewer would collect informa- tion on fertility, family planning prac- tices, sources of family planning services, | and related maternal and child health practices. The fieldwork would be completed in approximately 6 months. The target interview rate for the total sample and both major subsamples by race was 90 percent of the expected number of women from all sample households (i.e., screener and interview nonresponse combined would ideally be no more than 10 percent). Neither screener nor interview response was sup- posed to fall below a minimum rate of 90 percent. The contractor would design and imple- ment procedures to measure and control the quality of data collection and data preparation. For the population subgroups shown in table A, the sample design should yield estimated proportions whose standard errors are within the tolerances given in the rightmost column. The tolerances were based on a sample of 3,600 Negro women and 6,400 women of other races, and a design factor of approximately 1.4 (that is, it was assumed that the standard Table A. Standard error tolerances of estimated proportions for selected population subgroups Expected proportion Standard error Population subgr of sample women in Estimated proportion tolerance for dik group the race group who within the subgroup estimated proportion are in the subgroup as specified by NCHS Education: Parity: Education: Parity: Negro Less than high school .......csresrisrsess BERRA ARSE High school and MOR ....o.cosusssiisssrcrmrssveserssnmisssrsmssrssssrs 0 CINE cv srsssremssssswssvrsson spre rT ROR TOT PRA RTE PA RTA AAES 3 children or more Other races Less than high school. .... High school and MOre ........ceeeeeevueeeeiniiriieeceecceree ee seenneeas 0-2 CHIIAEBI...0visssssisesssirivsiersssensavenrsevessnsnenbnmmsmivenisrbissooens 48 42 0164 52 .25 .0139 .50 19 .0128 .50 B51 0163 30 .23 .0133 .70 .15 .0074 59 .10 .0068 41 33 0127 error of statistics based on the NSFG design would be about 40 percent larger than their standard errors based on a simple random sample of the same size). SAMPLE DESIGN Summary The sample design for Cycle I of the National Survey of Family Growth (NSFG) was a five- stage probability design based on the National Opinion Research Center's (NORC) 1972 Master Probability Sample.! The counties and independent cities that make up the total land area of the conterminous United States were combined to form a frame of primary sampling units (PSU’s). From this frame, the first stage of sampling yielded 203 PSU’s which were divided into four replicate groups, three containing 51 PSU’s and the fourth having the remaining 50. Two of these replicate groups, containing 101 PSU’s, were chosen for the NSFG sample. The next two stages resulted in the selection of sev- eral segments (clusters of about 100 dwelling units) from each sample PSU. A member of the NORC field staff listed the dwelling units (DU’s) within each segment, and a fourth-stage systematic sample of DU’s was selected. At each sample DU, an NORC interviewer attempted to complete the Household Screener questionnaire shown in appendix III and list the names of all eligible respondents. From this list one eligible woman was randomly selected for interviewing. Determination of Sample Size After the NSFG contract was awarded to NORGC, they agreed to design the sample to pro- duce the race allocation that NCHS suggested in their precision requirements—3,600 Negro women and 6,400 women of other races. Once the allocation was fixed, NORC proceeded to calculate the number of sample dwelling units that were needed to produce the final sample of women. They started by collecting 1970 cen- sus information on the number of occupied DU’s with Negro heads and the number with heads of other races, as well as population counts of eligible women in the two race classes. The ratio of occupied DU’s to eligible women for both race groups was adjusted to account for the following three factors: 1. 1970 census data indicated that 8 per- cent of all DU’s in the United States were vacant. 2. Data from the NCHS Health Interview Survey indicated that 5 percent of all eligible women lived in households con- taining two or more eligible women. 3. Combined screener and interview nonre- sponse was expected to be 10 percent. The adjusted DU-person ratios represented the expected number of DU’s that would have to be screened in order to find and interview one sample woman in each race class. By multiply- ing the final ratios by the desired number of sample persons, NORC calculated the expected minimum number of DU’s that would need to be screened to yield 3,600 completed interviews with Negro women and 6,400 completed inter- views with women of other races—9,141 Negro DU’s and 18,091 DU’s of other races, or a total of 27,232 DU. These minimum numbers of DU’s, however, do not represent the actual number that were re- quired to be screened for the NSFG. In areas where a large proportion of the population was Negro, DU’s were oversampled to attain the re- quired number of Negro women. In order to keep the sample essentially self-weighting for women of other races, DU’s of other races were subsampled in these areas. However, it was necessary to screen all DU’s in order to deter- mine their race. This subsampling procedure in- creased the number required to be screened from the minimum 27,232 to 31,842. Stratification and Selection of PSU's The PSU’s in the NORC master sample were selected from separate sampling frames of stand- ard metropolitan statistical areas (SMSA’s) and nonmetropolitan areas in the conterminous United States. The SMSA frame consisted of the 246 SMSA’s as defined by the U.S. Bureau of the Census in March 1971. The frame was ordered in the following manner, based on ad- vance 1970 census population data: 1. The SMSA’s were first sorted by the nine census geographic divisions as shown in figure 1. 2. Within each geographic division, the SMSA’s were sorted into three size classes: 1,000,000 persons or more, 200,000 to 999,999 persons, and less than 200,000 persons. 3. In divisions 1, 2, 3, 4, 8, and 9, the SMSA’s in each size class were sorted by State, with the States placed in geo- graphic order from northwest to north- east to southeast to southwest. Within each State the SMSA’s were ordered in the same way. In divisions 5, 6, and 7, the SMSA’s in each size class were placed in descending order of the number of residents of races other than white, in order to increase the likelihood of select- ing an appropriate number of southern SMSA'’s with large Negro populations. The total population of the SMSA frame based on preliminary 1970 census data was 138,789,636. After the ordering was completed, the frame was divided into 139 sequential zones, each having 1 million population (the 139th zone contained 789,636 persons and 310,364 “blanks’). In each zone the numbers from 1 to 1 million were assigned in ordered intervals to the SMSA’s that were totally or partially in- cluded, each SMSA receiving an interval equal to its population within the zone. A ‘hit number’ between 1 and 1 million was randomly and independently selected for each zone, and the SMSA whose assigned interval included that number was the PSU selected to represent the zone. The selection of a hit number was not Figure 1. Geographic divisions of the United States, and their order for the first-stage sample Daca ARK South — Central TENN 6. East Yer 7. West South Central TEXAS ) ia { necessary for zones that were completely cov- ered by one SMSA. This selection procedure differs somewhat from classical sampling with probability proportionate to size in that SMSA’s that overlapped zones could be selected more than once, and very large SMSA’s had to be selected several times. For example, the New York City SMSA represented 11 zones, all of which it covered completely. It was not selected to represent two other zones that it did not cover completely. After the PSU’s were selected, the 139 zones were systematically separated into four groups (zones 1, 5,9, . . ., 137 constituted group 1; zones 2, 6, 10, . . ., 138 constituted group 2; etc.). Groups 1 and 3 were randomly selected, and the SMSA’s that represented the zones in those two groups became part of the NSFG sample. The remaining two groups were held in reserve, but were not used in the NSFG. The sample of the SMSA population consisted of 70 PSU’s, containing 56 distinct SMSA’s (see table B). All areas in the United States that were not Table B. Sample PSU's for the National Survey of Family Growth l SMSA’s Akron, Ohio Allentown-Bethlehem-Easton, Pa.-N.J. Appleton-Oshkosh, Wis. Atlanta, Ga. Baltimore, Md. Birmingham, Ala. Boston, Mass. Buffalo, N.Y. Chicago, Ill. (represented by 4 PSU's) Cleveland, Ohio Columbia, S.C. Columbus, Ohio Dallas, Tex. Denver, Colo. Des Moines, lowa Detroit, Mich. (represented by 2 PSU's) Flint, Mich. Fresno, Calif. Gary-Hammond-E. Chicago, Ind. Great Falls, Mont. Hartford, Conn. Houston, Tex. Indianapolis, Ind. Jersey City, N.J. Knoxville, Tenn. Little Rock-N. Little Rock, Ark. Los Angeles-Long Beach, Calif. (represented by 3 PSU's) Miami, Fla. Minneapolis-St. Paul, Minn. Nashville, Tenn. New Britain, Conn. New Orleans, La. New York, N.Y. (represented by 5 PSU's) Newark, N.J. (represented by 2 PSU's) Norfolk-Virginia Beach-Portsmouth, Va. Oklahoma City, Okla. Orlando, Fla. Pensacola, Fla. Philadelphia, Pa.-N.J. (represented by 2 PSU's) Phoenix, Ariz. Pittsburgh, Pa. Portland, Oreg.-Wash. Racine, Wis. Reading, Pa. Rochester, N.Y. St. Louis, Mo.-lll. (represented by 2 PSU's) San Bernardino-Riverside-Ontario, Calif. San Diego, Calif. San Francisco-Oakland, Calif. (represented by 2 PSU's) Santa Rosa, Calif. Springfield-Chicopee-Holyoke, Mass.-Conn. Stamford, Conn. Tacoma, Wash. Topeka, Kan. Washington, D.C. Wichita Falls, Tex. Non-SMSA PSU's Auglaize Co., Ohio Burnett Co.-Washburn Co., Wis. Carroll Co., Mo. Columbiana Co., Ohio Colusa Co., Calif. Florence Co., S.C. Gogebic Co., Mich. Houston Co., Ala. Iredell Co., N.C. Knox Co., Ohio Lincoln Co.-Rock Co., Minn. Long Branch-Asbury Park, N.J. Madison Co., S.C. Manitowoc Co., Wis. Marion Co., W. Va. Marquette Co., Mich. McDowell Co., W. Va. Meklenburg Co., Va. Mesa Co., Colo. Newaygo Co., Mich. St. Lucie Co., Fla. Schuylkill Co., Pa. Smyth Co., Va. Sumter Co., Ga. Sussex Co., N.J. Upshur Co., W. Va. Victoria Co., Tex. Washington Co., Ala. Wilkes Co., N.C. Willacy Co., Tex. Yuba Co., Calif. included in the SMSA frame. can be classified either as counties, independent cities, or, in New England, portions of counties (for convenience, all such areas will hereafter be referred to as “counties’’). In certain instances, sparsely popu- lated counties were linked to provide an ade- quate population base for later stages of sam- pling. The non-SMSA frame consisted of the conterminous United States minus the 246 SMSA'’s, with the individual and linked counties ordered as follows: 1. Counties from census divisions 1 and 2 with 50,000 persons or more, arranged in descending order of population (DOP). 2. Counties from divisions 3 and 4 with 60,000 persons or more, arranged in DOP within State. The order of States for divisions 3 and 4 is given in table C. 3. Counties from divisions 3 and 4 with populations between 30,000 and 59,999, where the proportion of the population living in urban areas (as defined by the U.S. Census Bureau) was greater than or equal to 40 percent, arranged in DOP within State. 4. Counties from divisions 3 and 4 with populations less than 30,000, where the urban proportion was greater than or equal to 50 percent, arranged in DOP within State. 5. Counties from divisions 5, 6, and 7 with populations greater than or equal to 30,000, where the urban proportion was 30 percent or greater and the proportion of the population that was Negro was less than 20 percent, arranged in DOP within State. The order of the States is given in table C. 6. Counties from divisions 5, 6, and 7 with populations greater than or equal to 30,000, where the urban proportion was 30 percent or greater and the Negro pro- portion was 20 percent or greater, arranged in DOP within State. 7. Counties from division 8 arranged in DOP. 8. Counties from division 9 arranged in DOP. 9. Counties from divisions 1 and 2 with populations less than 50,000 arranged in DOP. 10. Counties from divisions 3 and 4 with populations between 30,000 and 59,999, where the urban proportion was less than 40 percent, arranged in DOP within State. 11. Counties from divisions 3 and 4 with populations less than 30,000, where the urban proportion was less than 50 per- cent, arranged in DOP within State. 12. Counties from divisions 5, 6, and 7 with populations greater than or equal to 30,000, where the urban proportion was less than 30 percent and the Negro pro- portion was less than 20 percent, ar- ranged in DOP within State. 13. Counties from divisions 5, 6, and 7 with populations less than 30,000, where the Negro proportion was less than 20 per- cent, arranged in DOP within State. 14. Counties from divisions 5, 6, and 7 with populations greater than or equal to 30,000, where the urban proportion was less than 30 percent and the Negro pro- portion was 20 percent or greater, ar- ranged in DOP within State. Table C. Ordering of States for sampling from the National Opinion Research Center non-SMSA frame mm Area Order of States North Central Region Ohio, Michigan, Wisconsin, Minne- sota, Indiana, Illinois, Missouri, lowa, Kansas, Nebraska, North Da- kota, South Dakota Divisions 3 and 4............ South Region Divisions 5, 6, and 7....... Delaware, Maryland, West Virginia, Virginia, Kentucky, Tennessee, North Carolina, South Carolina, Georgia, Alabama, Mississippi, Louisiana, Arkansas, Florida, Texas, Oklahoma. 15. Counties from divisions 5, 6, and 7 with populations less than 30,000, where the Negro proportion was 20 percent or greater, arranged in DOP within State. The total population of the non-SMSA frame based on preliminary 1970 census counts was 63,456,729. This frame was partitioned in the same way as the SMSA frame into 64 zones of 1 million persons (zone 64 contained 543,271 “blanks’’). The method of selecting a county to represent each zone was exactly the same method used for SMSA’s; however, the method of determining the primary and reserve PSU’s was different. The 64 zones were divided into 16 sets of 4 (zones 1-4 formed the first set, zones 5-8 the second set, and so forth). Each set of numbers was randomly permuted, and the counties representing the first two zones in the sequence were assigned to the NSFG sample. For example, the permutation of zones 1-4 was 3, 1, 4, 2. Therefore, the counties representing zones 3 and 1 were included in the survey, while the remaining two selections were placed in reserve status. Only 31 PSU’s were selected from the non-SMSA frame because a blank was selected as the hit number in zone 64, and zone 64 was listed second in the permutation of set 16. Thus the first-stage non-SMSA sample con- sisted of 31 counties, none appearing more than once. These 31 counties, when added to the SMSA sample, produced a total first-stage sam- ple of 101 PSU’s from 87 distinct localities. NORC’s methods of ordering SMSA’s and non-SMSA counties, selecting PSU’s from zones of 1 million persons, and subsampling to deter- mine primary and reserve PSU’s ensured a rea- sonable geographic, racial, and urban-rural balance among the PSU’s. Even after the pre- liminary ordering, NORC was concerned that a sample of four PSU’s from zones of 4 million persons would result in excessive geographic clustering. They therefore decided on the more detailed method of selection from smaller zones. The systematic group method of selecting pri- mary and reserve SMSA’s was changed to ran- dom selection within sets for counties because the cyclical ordering of the non-SMSA frame might have caused geographic clustering if sys- tematic sampling had been used. Selection of Second-Stage Units The units selected in the second stage of sampling were block groups (BG’s) in areas where census blocks were delineated and census enum- eration districts (ED’s) in other areas. Each of the 87 distinct localities was completely covered by a nonoverlapping frame of BG’s, ED’s, or a combination of the two. In order to reduce sampling error and ensure proportionate representation of women by race and income, the second-stage frame within each PSU was ordered by these variables prior to sampling. Because 1970 census income data were not available at the BG and ED level, NORC attached to each unit the income and racial characteristics of the next higher order census unit, which in most areas was the tract. In predominantly rural counties that were not tracted, the minor civil division (MCD) or census county division (CCD) was the next level unit. The National Opinion Research Center purchased from the National Planning Data Corporation of Ithaca, New York, population and housing data for ED’s and BG’s, and income and racial com- position data for tracts, MCD’s, and CCD’s within each of the 87 distinct localities. With these data the second-stage frame within each PSU was ordered in the following manner: 1. In SMSA’s the ED’s and BG’s in tracts with less than 10 percent Negro house- holds were placed before units in tracts with at least 10 percent Negro house- holds. (For this purpose, the race of the household was defined as the race of the head.) Within each race group, the units were arranged in ascending order of median tract income. Within each tract the ED’s and BG’s were arranged in numerical order, with BG’s preceding ED’s if both types of unit were present. 2. In non-SMSA PSU’s the above method of ordering was applied when at least 6 percent of the total population was Negro. In counties where Negroes con- stituted less than 6 percent of the popu- lation, the tracts, MCD’s, and CCD’s were either placed in ascending order by median income or, in sparsely populated counties, arranged from northwest to northeast to southeast to southwest. Within each higher order unit, the BG’s or ED’s (usually ED’s) were arranged in numerical order. After the ED’s and BG’s were ordered, small units were linked with the unit immediately following to assure a minimum unit size of 100 DU’s. The cumulative households in each PSU were then divided into 18 zones of equal size. Within each of these second-stage zones, the numbers between 1 and the zone size were grouped into ordered intervals representing BG’s and ED’s in the same way that the intervals in first-stage zones represented SMSA’s and coun- ties. A random hit number was selected for each zone to determine the ED or BG that would represent the zone. For SMSA’s that appeared more than once in the principal sample, this procedure was carried out for each first-stage appearance. Thus the Chicago SMSA, with 4 hits in the sample, was represented by 4 X 18 or 72 second-stage units. Of the 18 second-stage units associated with each PSU, a subsample of 12 was selected for the NSFG. The 18 second-stage units were put into 6 groups of 3 units apiece (group 1 con- sisted of ED’s and BG’s from zones 1, 2, and 3; group 2 included units from zones 4, 5, and 6; etc.). A random number was independently selected for each group to determine which second-stage units were to be eliminated from the NSFG sample. The second-stage sample now contained 1,212 second-stage units within the 101 PSU's. At this point NORC and NCHS decided to supplement the sample by selecting additional second-stage units in areas where the popula- tion was largely Negro, because the design re- quirements of the NSFG dictated an oversam- pling of Negro females. Without these additional units later-stage sampling rates in areas with many Negroes would have been much larger than the rates in areas with few Negroes. The resulting large cluster sizes would have greatly increased the variances of survey estimates. The first step in selecting the supplemental sample was to identify all second-stage units in tracts, MCD’s, and CCD’s with at least 10 percent Negro households (again, the race of a household was determined by the race of its head). The zones represented by these units were split into two half zones of equal size, say z. If the original hit number 4 for a zone fell into the first half zone, the number 4 + z was used to select a tentative supplemental ED or BG. If the original hit number fell into the second half zone, A - z was the supplemental hit number. The selection procedure had to be modified for Washington County, Alabama, and Sumter County, Georgia. The 36 original ED’s repre- senting these rural, predominantly Negro PSU’s encompassed virtually all of their population. Therefore, it was necessary to return to the first- stage non-SMSA zones represented by these PSU’s and randomly select an additional PSU from each. The two supplemental PSU’s were Hale County, Alabama, and Newton County, Georgia. Their BG’s and ED’s were ordered according to the procedure described earlier, and their cumulative DU’s were divided into 12 zones of equal size. The second-stage zone method was used to select 12 tentative supple- mental units from each PSU. To determine which of the tentative supple- mental units would be included in the sample, each one was paired with its corresponding origi- nal selection and the simple average percent of Negro households was computed for each pair. It was estimated by NORC that in order to pro- duce the required sample of 3,600 Negro women with a sample of 32,000 DU’s, the supplemental unit should be included when the average per- cent of Negro households was 43.4 or larger. Otherwise, only the original unit should be re- tained. The average exceeded 43.4 percent for 122 of the 1,212 zones. Therefore, the NSFG second stage consisted of 1,090 +2(122) = 1,334 ED’s and BG’s. For purposes of subsequent sampling, the units were divided into two Strata. Stratum I consisted of the 1,090 predominantly white units from the zones where the supple- mental unit was not used. Stratum II consisted of the remaining 122 pairs of units. Selection of Third-Stage Units The purpose of the third stage of sampling was to select from each ED and BG a subarea called a “segment” containing approximately 100 DU’s. When an entire second-stage unit contained only about 100 DU’s, no third stage of sampling was required. When a third stage was necessary, however, the logistics of selecting a segment from a BG and an ED were quite different. The BG is an urban geographic unit intro- duced during the 1970 census. It consists of a set of city blocks with the same highest order digit in the census block identification number. For the third stage of sampling, NORC subjec- tively split the BG into groups of blocks, each group containing approximately 100 DU’s according to 1970 census counts. One group was randomly selected with probability propor- tionate to its size relative to the size of the total BG. The ED is a census divisional unit generally used in nonmetropolitan areas. It is usually the lowest level unit for which decennial census information on households is available. In some instances, however, an area called an “ED” dur- ing the second stage was found to be covered by blocks. When that was the case, any necessary third-stage sampling was carried out in the man- ner described in the preceding paragraph. When blocks were not delineated and the ED had many more than 100 DU’s, the ED was split into pseudoblocks which were bounded by roads and other easily recognizable landmarks. Dwell- ing units within the pseudoblocks were field counted in order to get rough measures of size, and a segment of approximately 100 DU’s was selected with probability proportional to its size relative to the size of the entire ED according to the rough count. The final third-stage NSFG sample consisted of 1,334 segments, one corresponding to each sample BG and ED. Therefore, there were 1,090 segments in Stratum I and 244 in Stratum II. Selection of Fourth-Stage Dwelling Units Members of the NORC field staff listed the DU’s within each of the 1,334 segments. An independent, systematic sample of DU’s was selected from the listing sheet for each segment. The individual fourth-stage sampling rates were chosen so that the sample of DU’s was essen- tially self-weighting within Strata. That is, the overall probabilities of selecting all sample DU’s in Stratum I were approximately equal, as were the probabilities associated with sample DU’s from Stratum II. In order for NORC to determine the fourth- stage sampling rate for each segment, they first had to determine P| and Py, the uniform probabilities of selection for the two Strata. To do this, preliminary census data were used to estimate the proportion of households in each Stratum with Negro heads. These proportions, along with the required number of screened DU’s for Negroes and persons of other races, were the constraints used to calculate the re- quired number of screened DU’s for the two Strata (hereafter denoted by S; and Sp). Next, Dr, the number of occupied DU’s in the United States at the time of the survey, was projected from census housing totals for 1970 and 1972. The number of occupied DU’s in the United States which were in ED’s or BG’s that met the definition of Stratum I was estimated by " Lo # \1,219/ 77 where 1,090/1,212 was the proportion of orig- inal second-stage sample units that fell into Stratum I. A corresponding estimate of occu- pied DU’s for Stratum II units in the United States was 122 Dy = (2) Dr Because 1970 census data indicated that 92 per- cent of all DU’s in the United States were occu- pied, the selection probabilities for the two Strata were given by 8, 0.92 P=——— =.000276219 and D § S, +092 P= “Dn =.002207277 Once NORC had calculated P; and Py, the fourth-stage sampling rate for any segment could be obtained by dividing P; or Py; by the product of the known probabilities of selection at the first three stages. The fourth-stage rates yielded an average of 16.7 screened DU’s per segment in Stratum I and 56.9 in Stratum II. It is obvious from the difference between these average cluster sizes that oversampling of ED’s and BG’s at the second stage could not by itself produce the required oversample of Negro women. Further oversampling of DU’s was necessary within sample segments. Because the field listing sheet was the frame for the fourth-stage sample, DU’s that were missed during the field listing, or that came into existence between the time of field listing and interviewing, had zero probability of being sampled directly. In order to give these DU’s the same probability of selection as listed DU’s in their respective segments, NORC developed a set of rules based on the half-open interval pro- cedure.? These rules enabled the interviewer to link each missed DU and each new DU with exactly one existing line of the segment listing sheet. The set of lines for a segment was first di- vided into subsets that represented listings for individual blocks. In urban areas blocks were usually well-defined units, but in many rural segments “blocks” were of widely varying shapes and sizes. The only requirements for a rural block were clearly defined boundaries and a complete up-to-date listing of DU’s by address or location. Each line within a block repre- sented a structure or a subunit within a structure (such as an apartment or room). The listings were considered circular; that is, the last listing within a block was “followed” by the first. When a sample line represented a complete structure, the interviewer was instructed to com- plete a screener for any DU’s within that struc- ture as well as any DU’s between that structure and the structure on the next line. “Between” was defined in terms of address numbers when they were available, and in terms of location when they were not. If a sample line repre- sented a subunit within a structure, the inter- viewer's instructions depended upon the position of the sample line relative to the lines repre- senting the other subunits. Since the listings were ordered, each multiunit structure had a first- and last-listed subunit and any number (from 0 to n) of other subunits. If the sample 10 line was a first-listed subunit, the interviewer was instructed to complete a screener for all additional DU’s within the subunit and all DU’s in the structure that were in unlisted subunits. If the sample line was a last-listed subunit, the interviewer was instructed to complete a screener for all additional DU’s in that subunit and all DU’s between the structure containing the sub- unit and the next-listed structure. If the sample line represented any other subunit, the inter- viewer was only responsible for additional DU’s in the subunit. : In order to avoid large increases in sample size due to additional DU’s, NORC set an arbi- trary limit of four DU’s per sample line. If more than three additional DU’s were associated with the original sample listing, the interviewer was instructed to call headquarters, where a random subsample of exactly four DU’s was chosen to receive screeners. The procedures for listing additional DU’s and subsampling excess DU’s added 780 unlisted DU’s to the original sample, of which 439 were in Stratum I and 341 were in Stratum II. The subsampled DU’s were exceptions to the princi- ple of equal probability of selection within Strata. Additional exceptions to equal probability of selection were made for 10 segments in Stratum I which had grown rapidly from the time of the census DU count to the time of the NORC field listing. The field staff in these “fast-growth” segments returned their listing sheets to NORC’s central office. The central office reduced the fourth-stage sampling rates to keep the number of sample DU’s from ex- ceeding 50, so that the interviewer’s workload would not become overly burdensome. Fifth-Stage Selection of Sample Persons To avoid the high correlation of information from eligible women within the same DU, the NSFG design stipulated that no more than one eligible woman from any sample DU would be interviewed. During completion of the House- hold Screener, the NORC interviewer listed all members of the DU on the second page of the form and relisted the eligible females in order of age in item 13 on the third page (see appendix III). Item 13 provides space for listing up to six persons because six was considered to be a rea- sonable limit for the number of eligible females to be expected from a single DU. When the interviewer listed more than one eligible female she referred to the sampling table on the first page of the questionnaire to determine the per- son she was supposed to interview. The sampling table consists of five numbers that designate which person to interview when the number of eligible females is two, three, four, five, or six (see table D). National Opinion Research Cen- ter personnel filled in the table on every House- hold Screener by randomly ordering the 720 possible sets of numbers and systematically assigning them to screeners. This method of assigning interviews gave each eligible woman in a given DU the same probability of being selected. The oversampling in Stratum II at the sec- ond and fourth stages of selection led to the desired oversampling of Negro females at the fifth stage. However, since 35 percent of the DU’s in Stratum II were expected to be of other races, oversampling would also have produced an unnecessarily large sample of females of other races. NORC avoided that costly problem by subsampling DU’s of other races at a rate of 1 out of 7.991. This rate gave the subsampled DU’s the same probability of selection as all DU’s in Stratum I. Subsampling was accom- plished by systematically printing “interview regardless of race” on 1 of every 7.991 screeners used in Stratum II and “interview if Negro only” on the rest. For this purpose, the race of a DU was defined as the race of the person who pro- vided the information for the Household Table D. Example of sampling table on the Household Screener IF NUMBER OF THEN INTERVIEW ELIGIBLE FEMALES PERSON LISTED LISTED IN SUM- ON SUMMARY BOX MARY BOX IS: LINE y ¥ Two | Three 3 Four / Five 4 Six or more Screener because it seemed likely that the screener respondent would often be an eligible respondent for the survey and because it might have been difficult to determine the race of all household members in some instances. CHARACTERISTICS OF THE SAMPLE The first four stages of the design resulted in the identification of 32,818 sample DU’s. Dur- ing the screening process, the interviewers dis- covered that 3,820 of these either were vacant or did not meet the definition of a DU. Com- plete Household Screeners were obtained for 26,028 of the remaining 28,998 occupied DU’s, for a screener completion rate of 89.8 percent (table E). After 2,674 DU’s were removed from the sample by the subsampling procedure in Stratum II, the final sample of 23,354 DU’s yielded a fifth-stage sample of 10,879 women, of which 4,362 were Negro and 6,517 were of other races (table F). Complete interviews were obtained for 9,817 women, of which 3,868 were Negro and 5,949 were of other races, for an interview completion rate of 90.2 percent (88.7 percent for Negro women and 91.3 percent for women of other races). Combined screener and interview response rates cannot be computed by race because the race of the majority of nonre- sponding DU’s was unknown. Combined screener and interview response by Stratum is shown in table G. Seventeen women (10 Negro, 7 of other races) were eliminated from the sample after they were interviewed because it was discovered that they had passed their 45th birthday before the date of interview. In addition, data for three sample women who were less than 15 years of age (two Negro, one of another race) were ex- cluded from all tabulations so that analysis could be conducted for eligible women 15-44 years of age. Therefore, NSFG estimates are based upon data from 9,797 women, of which 3,856 are Negro and 5,941 are of other races. While the number of interviewed Negro women exceeded the desired sample size of 3,600, the number of interviewed women of other races fell substantially short of the target of 6,400. Most of the additional Negro sample was due to the unexpectedly large number of 11 Table E. Actual and expected number of sample DU’s, number of completed screeners, and screener completion rates, by race and Stratum Expected Numb f number of Number of Total DU'’s Vv | umes o legitimate, 08 tor Screener in the Scans of egitimate, occupied which a completion Race and Stratum sample hota Du Secipiec DU'’s from complete rate! s presurvey Sean Yes (percent) estimates obtaing (1) (2) (3) (4) (5) (6) All races Both Strata.. 32,818 3,820 228,998 29,295 226,028 89.8 ———— eee Stratum | .... 18,593 2,038 216,555 16,576 215,134 91.4 Stratum I1.. 14,225 1,782 212,443 12,719 210,894 87.6 Negro BOth SUBE.covmmmmtriohis r ERRE 9,005 8,410 8,546 3 Stratum |... 773 656 725 8 Stratum |1.. 8,232 7,754 7,821 3 .. BOA SIBLE. orci mac emaesssiaeriebits 18,438 20,885 17,328 J SIBIUM |... iesetsaese tee e ese be sea ssssssssss tsb bea seba se sese sarin 15,059 15,920 14,278 3. STRATUM Wat coitecrrrn cerrerncnirermrrimre rE Tere Eres TETirS 3,379 4,965 3,050 3. 1[(5) + (3)] X 100. Includes race unknown. 3 Appropriate screener completion rates by race cannot be derived because race information was not available for all legitimate, occupied DU’s. Table F. Number of sample women, actual and expected number of completed interviews, and interview completion rates, by race and Stratum Approximate number of Interview completed Numer of Numer 3 completion interviews sample complete: rate expectsd Race and Stratum WOE Interviews Phin) gig presurvey estimates (1) (2) (3) (4) All races gy AA SE, ate A Se Pe 10,879 9,817 90.2 10,054 Stratum | 6,758 6,164 91.2 26,451 Stratum 11 4,121 3,653 88.6 3,600 4,362 3,868 88.7 3,600 Stratum | 394 341 86.5 281 Stratum || 3,968 3,627 88.9 3,319 6,517 5,949 91.3 26,454 Stratum | 6,364 5,823 91.5 6,173 Stratum || 153 126 82.4 281 112) + (1)] X 100. 2The target sample size for women of races other than Negro was 6,400. However. the assigned probabilities of selection for DU’s of race other than Negro in Stratum I and Stratum II yielded a slightly larger expected sample size than the original target. 12 Table G. Screener and interview completion rates and combined response rates, by Stratum Screener | Interview Combined Strat comple- comple- SmBIne ratum Hon tion response rate rate rate (1) (2) (3) Percent Both Strata ......... 89.8 90.2 81.0 STEATUIT | vicisessnsssmmrroranens 91.4 91.2 83.4 SHUM corsenimmrmmsns 87.6 88.6 77.6 111) x (2)] + 100. Negro DU’s identified in Stratum II (table E). This oversample was enough to overcome the higher-than-expected vacancy and nonresponse rates. The number of DU’s of race other than Negro in Stratum II was correspondingly much lower than expected. However, because of the subsampling procedure the number of inter- viewed women of races other than Negro was only 155 less than expected. In Stratum I the number of identified DU’s was also somewhat less than the expected value, and the vacancy and interview nonresponse rates were higher than expected. These problems caused the re- maining sampling deficit for women of races other than Negro, but had little effect on the size of the Negro sample because less than 5 per- cent of the DU’s in Stratum I were classified as Negro. Table H shows that the precision of survey estimates was not adversely affected because the target number of women of races other than Negro was not interviewed. Standard errors for the estimated proportions in table A were cal- culated from NSFG data using the balanced half-sample replication technique described later in this report. For all population subgroups except Negro women of parity 3 or more, these standard error estimates are substantially lower than the corresponding presurvey error toler- ance. The estimate for higher parity Negro women is slightly larger than its tolerance, but the difference is unimportant, since the variance estimates themselves are subject to variance. ESTIMATION Weighting Procedure Since the NSFG is designed to produce un- biased estimates for the entire population of Table H. Comparison of standard error tolerances with the corresponding values obtained from the National Survey of Family Growth (NSFG) Proportion of women in the race Eetimaied Standard Estimated group who are in 3 Inte error standard Population subgroup the subgroup or ian tolerance error within ine from based on From | NSFG | SUP9™OUP | table A | NSFG data table A | estimate Negro Education: L288 han BION SCHOO) uiiismmmsainiiissmmmmssimn ss as mie mis ase panies .48 48 42 .0164 .0150 High school and more... sss B52 B52 25 .0139 .0121 Parity: 0-2 CIE iris inns or ER ET TE A SR SETA TA TREC EET .50 .58 19 .0128 0112 3 Children OF MOE cocvuiiieiiiiieeceie eee eee eraser eres e rans .50 42 51 .0163 .0170 Other races Education: Loss Han igh SCHOO. usw imitestissimssmimsismssimmvssrmisnissrvvnres .30 27 23 .0133 .0106 High SCHOO BIC MIO «cu cersrirrsssnsnsssrsrsssmsmsssnsss sessassasssasannassnanesnse .70 73 18 .0074 .0053 Parity: 2 CIIEIBRLsrrvsmssimcsrvmvesssrsarmssrnmmmms ss AT SEB HO SAIS .59 .64 .10 .0068 .0054 B CHTICPOTY OF TIDE vuvnsinmuissssvenissmmminsssss aspera AG aR A 08 41 .36 33 .0127 .0099 13 eligible women in the United States, the sample data must be inflated to the level of the popula- tion from which the sample was drawn. The in- flation factor, or weight, for each woman is the product of several adjustments, one or more at each stage of sampling. Three types of adjust- ments are involved. Inflation by the reciprocal of the probabili- ties of selection.—The weight for each woman within a sample PSU is the product of the re- ciprocals of the probabilities of selecting (1) the ED or BG, (2) the segment, (3) the DU, and (4) the eligible sample person. Because of the possi- bility (sometimes certainty) that certain SMSA’s and counties could be selected as sample PSU’s more than once, the first-stage weight is the reciprocal of the expected relative frequency of occurrence of the PSU. The first-stage weight is explained in more detail in the discussion of the estimating equation. Nonresponse adjustment.—Each ~~ sample weight is adjusted for nonresponse to the House- hold Screener (screener nonresponse) and nonre- sponse of sample women to the detailed NSFG questionnaire (interview nonresponse). These adjustments are necessary because the phenom- enon of nonresponse introduces bias into any probability sample. The respondents to a survey may have a much different distribution of demo- graphic or health characteristics than the nonre- spondents. Even if the distribution of demo- graphic and health characteristics is about the same for respondents and nonrespondents, the two groups are by definition different because the respondents participated in the survey while the nonrespondents did not. Nonresponse adjustments minimize the impact of nonre- sponse bias on final estimates by imputing to nonresponding DU’s and women the characteris- tics of “similar” respondents. Similar respondents were judged to be DU’s in the same PSU and Stratum, and women in the same age-race class and PSU. Screener response was 89.8 percent for the entire survey (91.4 percent in Stratum I and 87.6 percent in Stratum II) and ranged from 98.9 percent to 62.5 percent in individual PSU’s. Interview response was 90.2 percent for the sur- vey (91.2 percent in Stratum I and 88.6 percent for Stratum II) and ranged from 100 percent to 54.5 percent in individual PSU’s. ’ 14 Table J. Poststratification adjustment factors (ratio of Septem- ber 1973 population control totals based on Current Population Survey data to National Survey of Family Growth weighted estimates), by race and age Other Age Negro Oy 14-19 years 0.743 1.036 20-24 years 0.927 1.088 25-29 years 0.975 1.092 30-34 years 0.960 0.991 35-39 years 0.876 0.951 40-44 years 1.082 1.097 Poststratification by age and race.—The weight for each ever-married respondent is mul- tiplied by a poststratification adjustment factor that is determined by the woman’s age and race. The 12 adjustment factors shown in table J make NSFG estimates of ever-married women in each age-race class equal to independent control totals for September of 1973 (the approximate midpoint of data collection). The control totals are based on data from the U.S. Bureau of the Census’ Current Population Survey (CPS). No poststratification adjustment is applied to the weights for single mothers because reliable con- trol totals for this population are not available. Poststratification achieves much of the improve- ment in precision that would have been attained if the sample had been drawn from a population stratified by age and race. The method used to compute the CPS control totals is discussed in appendix II as part of the evaluation of alterna- tive estimators. NCHS decided to use a poststratified esti- mator instead of a simple inflation estimator after conducting research to compare the pre- cision of the two estimators. The methodology and results of the comparison are given in appendix II. Estimating Equation The estimate of an aggregate parameter Y is given by3 Y'=Y, +7}, where Y} is the estimate for ever-married women and Y; is the estimate for single mothers. ! ’ 2 Ya A = ST Ket a=1 al is a poststratified estimator. The nonresponse- adjusted estimates Y' for the 12 age-race classes are multiplied by the poststratification adjust- ment factor X,;/X.;. X,, represents the NSFG estimate of the number of ever-married women in age-race class « and X,; is an estimate of the same population group based upon the CPS. 12 Fo. ’ Yy = Yoo a= is simply the sum of the nonresponse-adjusted estimates for single mothers in the 12 age-race classes. The nonresponse-adjusted estimator for ever- married women in age-race class « is given by 103 Sh Yiu =4, 2, Wigs rr Hoi hi £ Wagnin Tygnin Wagni Waghi Dy FoR k=1 4ghijk*" 4ghijk *Wsansr * Sugnii * Yoguipe Y,,, the corresponding estimator for single mothers, is exactly the same, except that Sagnin 1s replaced by 1 = 8p p- Youun,™ the observed value of characteristic Y for the sample woman selected from DU k, segment j, ED or BG 7, Stratum hk, PSU g, and age-race class a. 1 if the sample woman whose ob- 5 = served value is Yer has ever aghijk | been married; | 0 otherwise. Wienin = the fifth-stage weight applied to the sample woman represented by Wig, ik Loin™ Fagron = A Hpi; = Wagnij = Y enjx- The weight is equal to the number of eligible women in her DU. = the reciprocal of the original fourth- stage sampling rate within seg- ment j. 7.991 if segment j is in Stratum II and the race of DU k is other than Negro; otherwise Tyg = 1. the subsampling rate that was ap- plied if segment j was one of the 10 fast-growth segments in Stratum I; otherwise, Fy, = 1, the subsampling rate that was ap- plied if DU k was associated with excess missed DU’s; otherwise, Rygnin = 1. the number of sample DU’s in seg- ment J. the reciprocal of the probability of selecting segment j, the segment selected from ED or BG 7. = the reciprocal of the probability of selecting ED or BG ¢ from PSU g and Stratum A. = the number of sample ED’s and BG’s in PSU g and Stratum A. an adjustment for screener nonre- sponse (DU’s for which it was im- possible to determine whether or not there were any eligible respond- ents). The value M,, represents the total number of DU’s from PSU g and Stratum 4, and My, is the num- ber of DU’s that were classified as either including or not including eligible respondents. a partial adjustment for person non- response, where n,, is the number of sample persons in PSU g, age- race class a, and n,, is the number of persons who respond. However, NCHS decided that nonresponse greater than 50 percent within a PSU should be adjusted at the class level rather than the PSU level. Therefore, when n,, is greater than Le so ; twice ng, the nonresponse adjust- Table K. Example! of how to determine A, from PSU response data Number Number Nonre- E of of re- sponse Xcess PSU number sample spond- adjust- | nenre- 3 spond- persons ents in ment in class a class a factor Bhi Totals for class a....... 43 31 ote 3 10 10 1 0 12 10 1.2 0 13 6 2 1 6 5 1.2 0 2 0 2 2 43 43 For this example, Ay = Br 43-3 40 ment is defined to be 2, and the ex- cess nonresponse is adjusted in fac- tor 4 , described below. Wi, = 2,000,000/P,, where ig is the 1970 P census population of su g. This first-stage weight is the reciprocal of the expected frequency of occur- rence of PSU g in the NSFG sample. For PSU’s that were completely contained in a single zone at the time of selection, W,, is the re- ciprocal of the probability of selec- tion. However, W,, deviates from the reciprocal of the probability of selection for PSU’s that overlap zones. For SMSA’s with popula- tions greater than 2 million W,, is less than 1, whereas the reciprocal of the probability of selection for any PSU is always greater than or equal to 1. A,= an excess nonresponse adjustment that compensates at the a-class level for nonresponse greater than 50 percent in individual PSU’s. Table K gives an example of how to de- termine 4, . VARIANCE ESTIMATION Background The balanced half-sample replication tech- nique described in detail in other NCHS re- 16 ports*® is used to estimate NSFG variances. An empirical study by Bean® gives evidence that the half-sample technique produces highly reliable, essentially unbiased variance estimates. There are three important practical reasons why half-sample replication is being used: 1. Programming difficulties are reduced be- cause half-sample variances are com- puted by taking a simple average of squared deviations of half-sample esti- mates from the estimate based on the full sample. Instead of having to pro- gram an exceedingly difficult variance formula, the programmer must simply adjust the estimation formula to com- pute estimates from appropriately chosen half samples. 2. The complete algebraic formula for NSFG variances is unknown because of the complexity of the design. Although algebraic expressions can be derived for particular subprocedures—such as the individual stages of sampling and the poststratification and nonresponse ad- justments—a single, exact variance equa- tion has not been developed. 3. As stated by McCarthy*: ‘Variance estimates based upon the replicated esti- mates will mirror the effects of all aspects of sampling and estimation that are permitted to vary randomly from replicate to replicate.” Also, replicated half-sample variances include some of the variability due to nonsampling (measure- ment) error, as well as sampling vari- ability. Summary of Applicable Theory The population of interest is classified into L strata, and two sample PSU’s are drawn from each stratum. Selection of exactly two sample PSU’s reflects an essential element of the theory. This requirement may be met for noncertainty PSU’s by collapsing two strata having one PSU each, or for certainty PSU’s by creating two arti- ficial, or pseudo, PSU’s by random methods from a single PSU. The collapsing method produces somewhat positively biased (overstated) variance estimates by introducing a between-stratum component of variance that does not exist.2 Let the parameter of interest be denoted by Y, for which an estimate Y’ has been obtained from the complete sample. Y' is a linear com- bination of the sample observations in fully rigorous developments, although several empiri- cal investigations indicate that the bias of half- sample variance estimates for certain ratio esti- mators and correlation statistics is negligible, if detectable at all.#:5,7,8 A half-sample replicate is defined as a col- lection of L PSU’s obtained by selecting one of the paired sample PSU’s from each stratum. If the PSU’s within each stratum are designated by the subscript z = 1 or 2 and there are K half samples, where K > L, the pattern may be sum- marized as in Table L. The “+” indicates that a PSU falls into a particular half sample, and the “~” indicates that it does not. Analogs of Y' corresponding to each half sample are then computed. That is, for the kth half sample, Y" is given by L Y, =2) Yi h=1 where 7 = either 1 or 2 depending on which PSU of the stratum is the half-sample k, and Y;; is, Table L. Example of a half-sample replication pattern Stratum Half- 1 2 3 i sample replica- PSU PSU PSU con | PSM tion 1{21{112]7).2 112 1 + -] -1 + - 1 + =A 2 - + | -|+ +] - = + 3 -l+ 1+] -1-1+ = 5 K + l=-1+]~ i+] ~- ¥ - in this example, a total. The estimator Y’ is L Y' =D (Vs + Yio) 1 and its variance is estimated by K 1 4 == ve k=1 Because it is impractical to compute the Y, for the entire set of 2L possible half samples when L is large, a subset of half samples is selected to produce the estimates. A set of side conditions relating to the selection of PSU’s for the half samples has been developed by McCarthy*:5 based on work by Plackett and Burman® and Gurney.10 These side conditions greatly increase the stability of s%+ by eliminating a between- strata component of variance that is otherwise present. The value of s%+ obtained from a sub- set of half samples that are chosen according to the McCarthy criteria is equal to the value that would be obtained using all 2L half samples. A set of half samples that satisfy the McCarthy cri- teria is called a “balanced set,” and the pro- cedure is referred to as “balanced half-sample replication.” Application to the NSFG In order to apply the balanced half-sample replication technique, NCHS grouped the 103 NSFG PSU’s into 48 strata. Seven of the strata were self-representing; that is, they consisted of SMSA’s that came into the sample with cer- tainty (except for Boston, which was lumped with 2 of the 5 New York City PSU’). Within each of these strata two pseudo-PSU’s were cre- ated by listing the PSU’s in numerical order and listing the segments in numerical order within each PSU. The first segment and every second segment thereafter was assigned to the first pseudo-PSU, and the remaining segments were assigned to the second pseudo-PSU. Within the other 41 strata, each of the 2 replication PSU’s consisted of 1 or more NSFG PSU’s (but never more than one locality). The PSU’s in each stra- tum belonged to the same geographic region and 17 *(uoriux g jo 1uad1ad °F) 000‘96 JO 10110 pIepuels I0 ‘quadiad gf JO 10110 pIepuels 3ATIE[21 © SBY S301 [[e JO (11BYD 3) JO UI0110q IY] JE 9[EdS IY] UO) USWIOM UoI[[iur g jo 91eSaid8e uy :24vyo fo asn fo apdwvxsy (SANVSNOHL NI) NIWOM 40 H3GWNN A31LVINILST 000°01L 000°L oot ol l 68.95 v € 2 Ves:os » £f =z Vecroc » £ z Vessos v ¢ z Vescoc v ¢ e y ~oSNgn Yo (LN3OH3d) HOHY3I AHVANVLS 3AILVI3YH aces Aq ‘uswom jo salebaibbe Joy S10112 piepuels anlle|ay ‘g ainbi4 18 were generally about the same size. The value 1 was assigned to one of the replication PSU’s in each stratum, and the value 2 was assigned to the other. Forty-eight half samples were then formed from the entries in successive columns of an orthogonal 48 X 48 matrix of 1’s and 2’s adapted from Plackett and Burman.’ In order to estimate the variance of an NSFG aggregate statistic Y', 48 half-sample ana- logs of Y' were computed. The formula for the kth half-sample estimate is ; _ xp! ’ Y= Yt where x Yon ’ al Xs A 1 Pe Yip = a=] and 12 r ’ Yo => Yam a=1 Yu od Xi were computed in exactly the same way as Y,; and X_,;. No additional weighting was necessary because of the poststrat- ification process. On the other hand, the Y,,, were computed after multiplying the weight for each single mother by 2 to compensate for the half-sample procedure. The variance of ¥’ was then estimated by 1 48 S2.,=—% (Y,-Y')? 48 k=1 Types of aggregate statistics produced from the NSFG include number of currently married women, number of ever-married women, num- ber of pregnancies for ever-married women, and total number of children born to ever-married women. Half-sample variances were not com- puted for all aggregate statistics because the time and money needed to do so would have been prohibitive. In addition, data reports would be much more cumbersome if a variance estimate were published for each statistic. To avoid these problems, variances for each type of statistic were computed only for selected population subgroups, which were chosen to represent a wide variety of demographic characteristics and a wide variation in the size of the estimates. Curves were fitted to relative standard error (RSE) estimates for number of currently mar- ried women and number of pregnancies, accord- ing to the model $24 B RSE (Y)= [—= [4+— (¥')? y’ A and B are parameters whose estimates deter- mine the shape of the curve. The rationale for the model and the iterative method that was used to estimate 4 and B are explained else- where. 11 Figure 2 shows relative standard error curves for estimates of women by race. The estimates of 4 and B for the curves are shown in table M. Although the curves for women were fitted to RSE’s for estimates of currently married women only, RSE’s for estimates of ever-married women fall close to the curves. Therefore, it is appropri- ate to obtain predicted RSE’s for estimates of ever-married women from the aggregate curves for women. Separate curves were needed for Negro women and women of all other race classifica- tions (women of all races, women of race other than Negro, and white women). Because Negro women were oversampled, an estimate of a given number of Negro women has a smaller RSE than an estimate of the same number of women of all races. The curves in figure 2 clearly show this relationship. ~~ For example, an estimate of 200,000 Negro women has an RSE of 9 percent, while an estimate of 200,000 women of all races has an RSE of 15 percent. Table M. Estimates of A and B for relative standard error curves, by race Curve A B 0.000017613 0.000040219 Total and white women .............. Negro women 4,493.7916 1,600.4393 19 Variances of aggregate statistics were used to derive variances of percents, which are ratios of two aggregates with the numerator being a sub- class of the denominator. Percent estimates usually show the proportion of a population that has a particular characteristic of interest. The RSE of the percent estimate is given by the expression! RSE (P')= 4/[RSE2 (Y') - RSE2 (Z')] B B A+ 4 + Y Z BZ'- BY' Y'z' _ [Bz'-BY' (PY) Y'Z'(P' [7 B(100 - P') “NTF where B is the least squares estimate from the error curve for Y' and Z'. The RSE of P’ is dependent upon the values of both P' and Z'. In order to account for the variation in error due to P' and Z', a set of per- cent RSE curves was derived from each aggregate RSE curve. Each curve in the set yields RSE’s for percent estimates with a fixed denominator. Figure 3 shows the set of curves for percent of total and white women, along with an exam- ple of how to use the error chart. Each curve satisfies the equation 4493.7916 (100 - P’ RSE (P') = A ns) ) P'Z' where P' is the estimated percent and Z' is the denominator of P’. Linear interpolation yields an acceptable estimate for the RSE of a per- cent whose denominator is not one of the values shown in figure 3. In addition to percents, the NSFG provides other types of ratio estimates where the numera- tor is not a subclass of the denominator, such as the mean number of expected births per woman, the mean number of expected additional births per woman, and the probability that a woman gives birth within a certain number of months following her last previous birth. Variances for these types of estimates could not be derived from variances of aggregate statistics, so they were computed directly by the half-sample tech- nique. The variance of the ratio estimate R' = Y'/W' is given by where R, is the kth half-sample analog of R'. As was the case for aggregate statistics, approximate error curves were fitted to selected variance estimates. The model for these more complicated ratio estimates was Il MA ge RSE (R') where A, B, and C were the parameters to be estimated. As with percentage estimates, the RSE varies with the size of the estimate R' and its denominator W'. The method of estimating A, B, and C is the same general method used for aggregate estimates.!! The RSE’s for each type of ratio statistic are represented by a set of curves, as was the case for percent estimates. Figure 4 shows the set of curves for mean number of births expected by women of all races, along with an example of how to use the error chart. The three curves in the chart satisfy the equation RSE(R') = 4/ 0.00002488 - 649.05239/R'W' + 1,733.8522/W' 20 Figure 3. Relative standard errors for percent of total and white women (base of percent shown in curve in thousands) 80 of percent (thousands) 100 20 A 0 OO NWO RELATIVE STANDARD ERROR (PERCENT) >» 0 oNwo= A 2 3 4 56789) 2 3 4 56789) 2 3 4 56789) 1 10 100 1,000 ESTIMATED PERCENT Example of use of chart: An estimate of 10 percent (from the scale at the bottom of the chart) of a population subgroup of 1 million women (fifth curve from the top) has a relative standard error of 20.0 percent, or a standard error of 2.0 percent (20.0 percent of 10 percent). where R' is the estimated mean and W' is the error curves for the various kinds of statistics estimated number of women (the denominator produced from Cycle I of the NSFG. Each re- of R'). Linear interpolation yields an acceptable port that discusses findings from Cycle I will in- estimate for the RSE of R’' when R' is not one clude similar charts for all types of statistics of the values shown in figure 4. presented therein. Figures 2-4 are examples of relative standard An estimate of the standard error of the dif- 21 cc Figure 4. Relative standard errors for mean numbers of births expected by women of all races and white women 100 90 70 60 Estimated 50 mean 5.0 40 2.0 30 1.0 nn oONOWOVWO RELATIVE STANDARD ERROR (PERCENT) vw oNno= w A 2 3 456789) 2 3 456789) 2 3 4 se789y 2 3 456789) 2 3 456789 1 10 100 1,000 10,000 ESTIMATED NUMBER OF WOMEN IN THE DENOMINATOR (IN THOUSANDS) Example of use of chart: An estimate of 2.0 births per woman (middle line on the chart) for a population subgroup of 900,000 women (read from the scale at the bottom of the chart) has a relative standard error of 4.0 percent, or a standard error of 0.08 (4.0 percent of 2.0). ference between any two aggregates, percents, or other ratio statistics is given by - 2 2 ry - 7) VERA S = 4/(Y])2RSE2(Y]) + (Y})2RSE2(Y}) This expression provides a good estimate of the standard error for uncorrelated statistics, but can only be considered a rough approximation otherwise. Because NSFG estimates are based upon a large sample of women, the distributions of Y| and Y, (and, therefore, Y] - Yj) are approximately normal. Frankel!2 shows empiri- cally that, using balanced half-sample replication estimates of variance, the test statistic ¥, -% t= T= (¥Y] - YY) approximates the student’s ¢ distribution under the null hypothesis of no difference between the parameters estimated by Y} and Y, against a two-sided alternative. The number of strata in the replication design (48 for the NSFG) can reasonably be used as the number of degrees of freedom for the t statistic, although the exact value for the degrees of freedom is unknown. Therefore, individual two-tailed significance tests of differences between NSFG statistics can be performed with an approximate significance level of a by computing ¢ and comparing it to the two-tailed 1 - « critical value for the ¢ distri- bution with 48 degrees of freedom. Example: Suppose 500,000 currently married Negro women expect an average of 2.46 births per woman and 5 million cur- rently married women of other races expect an average of 2.08 births per woman. To test this race difference at the a = .05 level of significance, compute yu 2.46 - 2.08 V (2.46)2 RSE? (2.46) + (2.08)2RSEZ (2.08) From figure 4, RSE(2.46) =~ .055 and RSE(2.08) ~ .018 so that ,_ 2.46 - 2.08 \ (2.46)2(0.55)2 + (2.08)? (.018)?2 =271 The two-tailed .95 critical value (1 - a) for a t statistic with 48 degrees of freedom is 2.01. Therefore, the difference is significant at the .05 level. 23 REFERENCES King, B. F., and Frankel, M. R.: Description of the Sample Design for the National Family Growth Survey. Unpublished manuscript. 2Kish, L.: Survey Sampling. New York. John Wiley & Sons, 1965. 3Brock, D. B.: Estimation and Variance Specifica- tions for the National Survey of Family Growth. Unpub- lished manuscript. 4National Center for Health Statistics: Replication: An approach to the analysis of data from complex sur- veys. Vital and Health Statistics. PHS Pub. No. 1000- Series 2-No. 14. Public Health Service. Washington. U.S. Government Printing Office, Apr. 1966. 5National Center for Health Statistics: Pseudorepli- cation: Further evaluation and application of the bal- anced half-sample technique. Vital and Health Statistics. PHS Pub. No. 1000-Series 2-No. 31. Public Health Serv- ice. Washington. U.S. Government Printing Office, Jan. 1969. 6National Center for Health Statistics: Distribution and properties of variance estimators for complex multi- stage probability samples: An empirical distribution. Vital and Health Statistics. Series 2-No. 65. DHEW Pub. No. (HRA) 75-1339. Health Resources Admin- istration. ~~ Washington. U.S. Government Printing Office, Mar. 1975. 24 7Simmons, W. R., and Baird, J.: Use of pseudorepli- cation in the NCHS Health Examination Survey. Pro- ceedings of the Social Statistics Section of ASA. Ameri- can Statistical Association, 1968. 8Kish, L., and Frankel, M. R.: Balanced repeated replications. J. Am. Stat. Assoc. 65:1071-1094, Sept. 1970. 9Plackett, R. L., and Burman, J. P.: The design of optimum multifactorial experiments. Biometrika 33: 305-325, 1946. 10Gurney, M.: The Variance of the Replication Method for Estimating Variances for the CPS Sample Design. Dittoed memorandum, U.S. Bureau of the Census, 1962. 11National Center for Health Statistics: Estimation and sampling variance in the Health Interview Survey. Vital and Health Statistics. PHS Pub. No. 1000-Series 2, No. 38. Public Health Service. Washington. U.S. Gov- ernment Printing Office, June 1970. 12Frankel, M. R.: Inference from Survey Samples: An Empirical Investigation. Ann Arbor. Institute for Social Research, University of Michigan, 1971. 13 French, D. K., and Bryant, E. E.: Sample- Dependent Estimation for the National Survey of Family Growth. Proceedings of the Social Statistics Section of ASA. American Statistical Association, 1976. APPENDIXES CONTENTS YL: .. Glossary of Terms: vuserensmsesssmmsssseerronmessssensmrnessressyrsssennss 26 II. Evaluation of Alternative Estimators ....cceeeerererereresseresssenens ATTRA TARAS SRA RA AR AAR RAR 28 III. Household Screener ’ 29 25 APPENDIX | GLOSSARY OF TERMS Conterminous United States.—The land area consisting of the District of Columbia and all States except Alaska and Hawaii. Dwelling unit (DU).—A single room, or group of rooms, that is intended for separate liv- ing quarters. The people who live there must live and eat separately from everyone else in the building (or apartment) and the room or group of rooms must have either 1. A separate entrance directly from the outside of the building or through a common hall, or 2. Complete kitchen facilities for the use of this household only. Complete kit- chen facilities include all of the follow- ing: a. a range or cooking stove, and b. a sink with piped water, and c. a mechanical refrigerator. Education.—The highest grade of school completed. Geographic region.—For the purpose of clas- sifying the population by geographic area, the U.S. Bureau of the Census has grouped the 50 States and the District of Columbia into four regions, as follows: Region States included Northeast......... Maine, New Hampshire, Ver- mont, Massachusetts, Rhode Island, Connecticut, New York, New Jersey, Pennsyl- vania 26 North Central... Michigan, Ohio, Indiana, Illi- nois, Wisconsin, Minnesota, Iowa, Missouri, North Da- kota, South Dakota, Kansas, Nebraska Delaware, Maryland, District of Columbia, Virginia, West Virginia, North Carolina, South Carolina, Georgia, Florida, Kentucky, Texas, Tennessee, Alabama, Missis- sippi, Arkansas, Louisiana, Oklahoma Montana, Idaho, Wyoming, Colorado, New Mexico, Ari- zona, Utah, Nevada, Washing- ton, Alaska, Oregon, Cali- fornia, Hawaii Alaska and Hawaii are not included in the NSFG sample design. Household. —A family living together, or five or fewer unrelated individuals living together in a DU. Parity.—The number of live births a woman has had. Screener interview.—A preliminary interview at the household to collect information about the DU and to determine whether or not the household includes one or more women who are eligible for the detailed interview. Standard metropolitan statistical area (SMSA).—A county or group of contiguous counties (except in New England) which con- tains at least one central city of 50,000 people or more, or “twin cities’ with a combined popu- lation of at least 50,000. In addition, other con- tiguous counties are included in an SMSA if, according to certain criteria, they are socially and economically integrated with the central city. Urban area.—As defined by the U.S. Bureau of the Census, the urban areas of the United States include all cities or “twin cities’ with at least 50,000 population in 1970 together with the surrounding closely settled area and all other incorporated or unincorporated popula- tion centers with 2,500 inhabitants or more. OQ0 27 APPENDIX II EVALUATION OF ALTERNATIVE ESTIMATORS An aggregate parameter Y for all eligible women less than 45 years of age in the United States can be written as Y=Y, + Y,, where Y, is the total for all ever-married women and Y, is the total for all single mothers with one or more of their children currently living in the house- hold. Alternative estimators of Y considered for the NSFG were tha +4] (1) and Ve=vi+v, @) where Y] and Y, are simple inflation estimators and 12 xX , a Yy = > You : XxX’ (3) a=1 al is a poststratified estimator. The X_, represent NSFG estimates of the number of ever-married women in each of 12 age-race classes and the X,1 are corresponding estimates for September 1973 (the approximate midpoint of NSFG inter- viewing) based upon the U.S. Bureau of the Cen- sus’ Current Population Survey (CPS). At the time the two estimators were pro- posed, it was decided that the choice of Y, or Yyp as the official estimator for the NSFG would be based on information from the sample data. Values of certain statistics would be cal- culated using both estimators, and variances of the two competing estimates would be com- puted using identical half-sample replication pro- cedures. If the variance of Y, was the lower of the two variances for many of the experimental statistics, and if Yp did not result in higher vari- ances for more than a few statistics, then it would be chosen; otherwise, Y},p would be used. Simple inflation and poststratified esti- mates of the number of currently married U.S. women and the relative standard errors (RSE’s) of both estimates were computed for more than 200 subdomains of the population. The post- stratified estimator had a smaller RSE than the inflation estimator for more than 80 percent of the domains. The improvement in precision was 20 percent or better for almost two-fifths of the domains. A more complete discussion of the design and results of the study can be found elsewhere.13 Because the RSE of Y, was much smaller than the RSE of Yj, for many aggregate esti- mates, and was no more than 10 percent larger than the RSE of Y},, for any parameter in the study, the decision was made to use Y, as the official NSFG estimator. NOTE: The list of references follows the text. O00 28 APPENDIX HI HOUSEHOLD SCREENER OMB No. 68 - S72170 NORC-4604 NATIONAL OPINION RESEARCH CENTER Expires: April 30, 1974 July, 1973 University of Chicago Collected for the National BEGIN DECK 21 Center for Health Statistics HOUSEHOLD SCREENER NOTICE: All information which would permit identification of any OFFICE USE ONLY individual will be held in strict confidence, will be used only by persons engaged in and for the purpose of the sur- 10 Poet, Sercum 0 vey, and will not be disclosed or released to others for Tel. Re-Check: any purpose, as in accordance with Section 305(a) of the Public Health Service Act, Section 1,103(a) of the Public 11 os Tom ) Health Service Regulations [42 CFR 1,103(a)] and under a Public Health Delegation of Authority Number 31 ASSIGNMENT BOX SAMPLING TABLE IF NUMBER OF THEN INTERVIEW ELIGIBLE FEMALES PERSON LISTED LISTED IN SUM- ON SUMMARY BOX MARY BOX IS: LINE Two Three Four Five Six or more INTERVIEWER: Is this address in a rural area or in some other kind of area? Rural . . . 1 Other . + . 2 12 INTRODUCTION Hello, I'm from the National Opinion Research Center. (SHOW ID BADGE.) A letter was sent to you recently explaining the study we are conducting for the U.S. Public Health Service. As you may recall from the letter, the study is being conducted all over the country and is about family size. RECORD OF ALL CONTACTS AT HOUSEHOLD Interv'r Da Y Date Time Per Results tials 29 HOUSEHOLD ENUMERATION 1. To start, how many people live in this household? on NUMBER TIME BEGAN BEGIN DECK 22 10 11 2, What is the name of the head of this household? (ENTER NAME ON LINE O01 BELOW, ) 3. And the other members of this household--what are their names? BE SURE PERSON INCLUDES (HIMSELF/HERSELF). everyone related to (HEAD). NAMES IN TABLE BELOW.) Let's begin with (ENTER 4, Are there other people living here who are not related to (HEAD)? 6. 7. 8. 9. IF 13 YEARS OR OLDER, ASK: Is oo old (PERSON) now married, widowed, di- What CoE oe vorced or annulled, separated or has is (he/she) never been married? IF NE- FP EAD Ares STING sae, . (PERSON) 'S Le Se VER MARRIED BUT REPORTED AS LIVING ASK QS. 6-9 FOR EACH PERSON relation- | ‘10 9; TOGETHER, CODE "INFORMAL." IF NEVER AS APPROPRIATE ship to Sor Wi s/nee) MARRIED AND NOT LIVING TOGETHER BUT (HEAD OF o5- last HAS OW] HILDREN, CODE "WITH OWN House. vious) birth- ELLE HOLD) ? en In Singlef La for usa. | DLv.| sepa-| With | Never] First Name Last Name F aree| wal dss) cates nite] ore: ren 12 13 1% 15 16 01 HEAD 1 2 1 2 3 4 5 6 7 17] 18 19 20 21 02 1 2 3 2 3 4 5 6 7 72] 23 7% 25 6 03 1 2 1 2 3 4 5 6 7 27 28 30 31 04 1 2 1 2] 3 4 3 6 7 32 32 34 35 36 05 1 2 1 2 3 4 5 6 7 37 38 39 40 41 06 1 2 1 2 3 4 5 6 7 w2| 43 Lh 45 46 07 1 2 1 2 3 435 6 7 47 48 42 50 51 08 1 2 1 2 3 4 5 6 7 52 53 54 55 56 09 1 2 1 2 3 4 5 6 7 57 58 59 60 61 10 1 2 1 2(| 3 4 5 6 % { IF MORE THAN 10 PEOPLE IN HOUSEHOLD, GO TO CONTINUATION BOOKLET, PAGE 30 10. Wi Yes No Is there anyone now away from home who usually lives here? 0 xe in United § Are any of the persons Armed Forces of the 3 DECK 21 CONTINUED 13, SELECTION OF RESPONDENT (CHECK ONE BOX) 1 OJ NO ELIGIBLE WOMEN UNDER 45 YRS, OF AGE, NO INTERVIEW REQUIRED; SKIP TO Q. 14. 13 ONE ELIGIBLE WOMAN UNDER 45 YRS, OF AGE 2 CURRENTLY MARRIED OR INFORMALLY MARRIED; Od CIRCLE R'S PERSON NUMBER ON P, 2; SKIP TO Q, 14; THEN USE [CURRENTLY MARRIED QUESTIONNAIRE] ONE ELIGIBLE WOMAN UNDER 45 YRS, OF AGE, 3 CURRENTLY WIDOWED, SEPARATED, DIVORCED OR' ANNULLED, OR SINGLE W/OWN CHILDREN; CIRCLE R'S PERSON NUMBER ON P. 2; SKIP TO Q. 14; THEN USE [POST-MARRIED QUESTIONNAIRE] MORE THAN ONE ELIGIBLE WOMEN UNDER 45 YRS. OF AGE, Od FOLLOW STEPS 1 - 4 TO SELECT CORRECT RESPONDENT Step 1: List names of eligible Step 2: Use Sampling Table on page 1 females in Summary Box to determine which eligible --in order of age, be- female to interview. ginning with the oldest on Line #1, Step 3: Circle R's Line # in Summary Box, and write selected R's SUMMARY BOX nave heres 14 Name 15 16 (Respondent's Name) Step 4: (CHECK ONE BOX) R is currently: married, or informally married; 4 OJ ask Q. 14 and use URRENTLY-MARRIED QUEX]. R is currently: widowed, separated, divorced or annulled, 5 OJ single w/own children; ask Q. 14 and use [POST-MARRIED QUEX]. 14, ASK EVERYONE: May I have your telephone number (in case my office wants to verify this interview)? Telephone no,: Area Code: L 17 Nophonte: ow wv www ea v Roos 2 Befused . uv sv os sv +» mam wn 3 IF PHONE NO. GIVEN, CODE LOCATION OF PHONE: InBousehold + , « v sv 4 wv v5 2 vo & iis Inhome of netghbor « « + + ¢« «+ sv 3 v « 5 Lem Other (SPECIFY) . + + « « v os os 3s + + + © TIME SCREENER _________ AM Thank you very much for your help. ENDED: PM PAGE 4 IMMEDIATELY AFTER YOU LEAVE THE HOUSEHOLD, INTERVIEWER: FILL OUT A-F BELOW & SAMPLING REPORT & INTERVIEWER SIGNATURE AND NUMBER ON | B. Race of household (by observation) C. Length of time minutes Black/Megto: . 4 « + 3 « 3s #3 3» » X 18 for Screener: 20 21 White . + . ov + + 4 5 0 0 4 404% 2 Other (SPECIFY) _____ = D. Date of Screener: 22 258 3 MONTH DAY Not able to observe . . .,..... 4 E. With whom did you conduct the Screener? Code type of living quarters: a ——————— i —— a ——ra a 26 27 Detached single family house . . . . . . . 1 19 [Name (2) of screener informant (s)] Tralle¥ ou wv sv wes WWE 8 we we 2 2-4 family house/apartment building. . . . 3 F. If screener informant not household member, Row house (3 or more attached units) 4 describe relationship to selected respon- dent or to household, Apartment house (5 or more units; free access to housing unite) +. «4 v5 94 5 Apartment house (5 or more units; locked entry, or guarded by doorman, or both) , 6 Other (SPECIFY) (Relationship to Household) 7 GO TO PAGE 4 31 [4 T¥:££6-09C —8L6T 301440 ONILNIYd INFWNYIAOD 'S'N + CHECK (v) HERE IF NO MRSRACE S02 # MISSED DU OR OTHER 1 ASSIGNMENT BOX CORRECTIONS SAMPLING REPORT ON MISSED DU'S AND OTHER CORRECTIONS AT SAMPLE ADDRESS PSU # Seg. # Part # Sample Line # Case # OFFICE USE ONLY |lphone Address Description of Correction DU's Added DU's Deleted IOFFICE USE DU Line Call | Corrections, Additions, Corrections, Additions, 2 OIAdditions [Additions [Additions|l ONLY Code # or or to gf Sane .jiab Save | betwen life Reason BLOCK # Col. ; Line # Address Apt_# Lineilige # (10) (11-17) Deletions Deletions (Check ) |(Check ) | # and 4 (77-80) I 2 I ' I 2 I Jr 3 I I 1 I % i ' I 5 i ' : cd | 6 I 1 | 7 I Frid i 8 I 1 Total Additional DU's > DECK 21 SIGNATURE OF INTERVIEWER: INTERVIEWER us v2 weer: [ | [TT] IF 1 TO 4 DU'S: FILL OUT HOUSEHOLD SCREENER FOR EACH & CONDUCT SCREENER INTERVIEW. IF 5 OR MORE DU'S: CALL SAMPLING DEPT. (COLLECT AC 312/684-5600) FOR INSTRUCTIONS BEFORE YOU DO ANY ADDITIONAL SCREENER INTERVIEWS. AT TIME OF PHONE CALL, CIRCLE CODE IN "PHONE CALL COL" FOR LINE (S) AT WHICH YOU ARE. INSTRUCTED TO DO SCREENER INTERVIEW (S); THEN FILL OUT SCREENER FOR EACH OF THOSE & CONDUCT SCREENER INTERVIEW. 7 DAYS RETURN PUBLIC HEALTH LIBRARY Sew 42 Warren Hall : 642-2511 - VITAL AND HEALTH STATISTICS PUBLICATIONS SERIES Formerly Public Health Service Publication No. 1000 Series 1. Programs and Collection Procedures.—Reports which describe the general programs of the National Center for Health Statistics and its offices and divisions, data collection methods used, definitions, and other material necessary for understanding the data. Series 2. Data Evaluation and Methods Research.—Studies of new statistical methodology including experimental tests of new survey methods, studies of vital statistics collection methods, new analytical techniques, objective evaluations of reliability of collected data, contributions to statistical theory. Series 3. Analytical Studies.—Reports presenting analytical or interpretive studies based on vital and health statistics, carrying the analysis further than the expository types of reports in the other series. Series 4. Documents and Committee Reports.—Final reports of major committees concerned with vital and health statistics, and documents such as recommended model vital registration laws and revised birth > and death certificates. Series 10. Data from the Health Interview Survey.—Statistics on illness; accidental injuries; disability; use of hospital, medical, dental, and other services; and other health-related topics, based on data collected in a continuing national household interview survey. Series 11. Data from the Health Examination Survey.—Data from direct examination, testing, and measurement of national samples of the civilian, noninstitutionalized population provide the basis for two types of reports: (I) estimates of the medically defined prevalence of specific diseases in the United States and the distributions of the population with respect to physical, physiological, and psychological charac- teristics; and (2) analysis of relationships among the various measurements without reference to an explicit finite universe of persons. Series 12. Data from the Institutionalized Population Surveys.—Discontinued effective 1975. Future reports from these surveys will be in Series 13. Series 13. Data on Health Resources Utilization.—Statistics on the utilization of health manpower and facilities providing long-term care, ambulatory care, hospital care, and family planning services. Series 14. Data on Health Resources: Manpower and Facilities. Statistics on the numbers, geographic distrib- ution, and characteristics of health resources including physicians, dentists, nurses, other health occu- pations, hospitals, nursing homes, and outpatient facilities. Series 20. Data on Mortality. —Various statistics on mortality other than as included in regular annual or monthly reports. Special analyses by cause of death, age, and other demographic variables; geographic and time series analyses; and statistics on characteristics of deaths not available from the vital records, based on sample surveys of those records. Series 21. Data on Natality, Marriage, and Divorce.—Various statistics on natality, marriage, and divorce other than as included in regular annual or monthly reports. Special analyses by demographic variables; geographic and time series analyses; studies of fertility; and statistics on characteristics -of births not available from the vital records, based on sample surveys of those records. Series 22. Data from the National Mortality and Natality Surveys.—Discontinued effective 1975. Future reports from these sample surveys based on vital records will be included in Series 20 and 21, respectively. Series 23. Data from the National Survey of Family Growth.—Statistics on fertility, family formation and disso- lution, family planning, and related maternal and infant health topics derived from a biennial survey of a nationwide probability sample of ever-married women 15-44 years of age. For a list of titles of reports published in these series, write to: Scientific and Technical Information Branch National Center for Health Statistics Public Health Service Hyattsville, Md. 20782 and HEALTH STATISTICS — §- DATA Series 2 -Number 77 VALUATION AND METHODS RESEARCH TCP TE ELS CHET TT TE L Cg / NCHS NLR doh Mok) R/4 A CRIN U.S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE Public Health Service Office of the Assistant Secretary for Health Library of Congress Cataloging in Publication Data Birnbaum, Z. William. : On the mathematics of competing risks. (Vital and health statistics: Series 2, Data evaluation and methods research; no. 77) (DHEW publication; (PHS) 79-1351) Bibliography: p. 56 1. Competing risks. 2. Estimation theory. 3. Statistical hypothesis testing. I. Title. II. Series: United States. National Center for Health Statistics. Vital and health statistics: Series 2, Data evaluation and methods research; no. 77. III. Series: United States. Dept. of Health, Education, and Welfare. DHEW publication; (PHS) 79-1351. RA409.U45 no. 77 [QA273] 312.07'23s [862.1'01'82] ISBN 0-8406-0138-7 78-15122 For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 DATA EVALUATION AND METHODS RESEARCH On the Mathematics of Competing Risks This report reviews the sources and origins of competing risk theory and presents the probability theory of competing risks and sta- tistical estimation techniques and tests of hypotheses. LIBRAR ( UNIVERSITY OF CALITORN'S DHEW Publication No. (PHS) 79-1351 U.S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE Public Health Service Office of the Assistant Secretary for Health National Center for Health Statistics Hyattsville, Md. January 1979 Series 2 Number 77 NATIONAL CENTER FOR HEALTH STATISTICS DOROTHY P. RICE, Director ROBERT A. ISRAEL, Deputy Director JACOB J. FELDMAN, Ph.D., Associate Director for Analysis GAIL F. FISHER, Ph.D., Associate Director for the Cooperative Health Statistics System ELIJAH L. WHITE, Associate Director for Data Systems JAMES T. BAIRD, JR., Ph.D., Associate Director for International Statistics ROBERT C. HUBER, Associate Director for Management MONROE G. SIRKEN, Ph.D. Associate Director for Mathematical Statistics PETER L. HURLEY, Associate Director for Operations JAMES M. ROBEY, Ph.D., Associate Director for Program Development PAUL E. LEAVERTON, Ph.D., Associate Director for Research ALICE HAYWOOD, Information Officer OFFICE OF THE ASSOCIATE DIRECTOR FOR MATHEMATICAL STATISTICS MONROE G. SIRKEN, Ph.D., Associate Director Vital and Health Statistics-Series 2-No. 77 DHEW Publication No. (PHS) 79-1351 Library of Congress Catalog Card Number 78-15122 FOREWORD In view of the many potential applications of the statistical theory of com- peting risks in the analysis of health and vital statistics, the National Center for Health Statistics was responsive to Dr. Birnbaum’s proposal to prepare an intro- ductory report on the mathematics of competing risks which would clarify the concepts and unify the theory common to the several disciplines in which com- peting risk models have been applied. As a result, we have this excellent report. It has become Center policy to submit all reports in this publication series to peer review. In this regard, we should like to recognize the contributions of Pro- fessor Anthony J. Quinzi who served as technical reviewer of this report. Dr. Birnbaum joins me in thanking Dr. Quinzi for his careful review and for his many helpful suggestions and comments. Monroe G. Sirken Associate Director for Mathematical Statistics } : As Lis fe (lea Fo odd dad Hoult] of great B lp hes [7 i re Dy. EH a Mis - i ie pr EAT Ts ip pre i. Le 5 Ah A : il al i i & ) AL Wa CONTENTS Foreword 1. Introduction 1.1. Sources and Origins of Competing Risk Theory ....renmimorsrsssmsossmrsiorsonssrmressessssrsesessns 1.1.1. Work of Daniel Bernouilli....... 1.1.2. Actuarial Problems ...... 1.1.3. Clinical Experiments 1.1.4. Competing Risks in Technology 1.1.5. Other Areas 1.2. Comments on the Present State of the Theory 1.2.1. Duplication and Communication Gaps 1.2.2. Probabilistic Versus Statistical Approach 1.2.8. Choice of Topics for This Report 2. Probability Theory of Competing Risks 2.1. Life Distributions 2.2. Net (Potential) and Crude (Observable) Lives 2.3. General Theory: Net Lives 2.4. General Theory: Crude Lives 2.5. An Identity 2.6. The Problem of Identifiability 2.6.1. Formulation of Problem 2.6.2. The Case of Independent Net Lives 2.6.3. The Case of Possibly Dependent Net Lives 2.6.4. An Interpretation of the Identifiability Problem: Some Inequalities ............. rm hake 2.7. Summary and Comments on Identifiability 2.8. Multiple Decrement Tables Versus Questions About Net Lives ..ccccicvrerccessensercssnnesecccsasanee oe 3. Estimation Techniques 3.1. Case of Independent Net Lives: The Kaplan-Meier Nonparametric Technique ......c.cececeunee whee 1.1. Statement of Problem 1.2. Definitions and Notations 1.3. A General Estimation Procedure 1.4. The Kaplan-Meier Estimates .1.5. Some Properties of the Kaplan-Meier Estimates ome Actuarial Estimates and Their Relationships to Kaplan-Meier Estimates ....c.ccceeeeenenee vo 3.2.1. A Generalized Kaplan-Meier Procedure and Some Actuarial Estimates .....cccececenneaseccne 3.2.2. Conditions for 2k p Being Consistent Life Table Estimates: Proportional Hazard Rates 3.3.1. Definitions and Assumptions 3.3.2. Observable Random Variables: Maximum Likelihood Estimates of Crude and Net 3 3 3 3 3 S 3.2. 33 . Probabilities 3.3.3. Conditions for Consistency of Chiang’s Estimator of the Net Survival Probabilities .... 3.3.4. Examples of Competing Risks With Proportional Hazard Rates ........... aressvannes ress 4. Estimation for Parametric Models 4.1. The Likelihood Function: General Case 4.2. The Case of Independent Net Lives 4.3. Comments on Parametric Families of Multivariate Life Distributions ...ccccceeeescseeeeccesnaneessnns 4.4. Concomitant Variables 4.5. Estimation of the Ratio of Hazard Functions fon Be OO WWW J vi 5. Tests of Hypotheses 5.1. Formulation of a Problem 5.2. Gehan’s Statistic 5.3. Testing for Independence When Data Are Censored 5.4. Large-Sample Tests References LIST OF FIGURES 1. Introductory page of Daniel Bernoulli’s monograph on his theory of competing risks 2. Daniel Bernouilli’s original life tables 3. Probability densities used in example D 4. Regions of integration considered in equations (30) and (31) 5. Graph of Kaplan-Meier estimate obtained in table A 6. Diagram of events defined by formulas (54) A. Example of a Kaplan-Meier estimate TABLE 25 27 33 36 32 ON THE MATHEMATICS OF COMPETING RISKS Z. William Birnbaum, University of Washington, Seattle 1. INTRODUCTION 1.1. SOURCES AND ORIGINS OF COMPETING RISK THEORY 1.1.1. Work of Daniel Bernoulli Toward the middle of the 18th century, the question of mandatory vaccination against smallpox was widely discussed and attempts were made to evaluate its possible effects. In his “Mémoir” pub- lished in 1776 (figure 1), Daniel Bernoulli! gave this question the following specific formulation: Available life tables reflect the mortality of the population for which they were calculated, taking into account all causes of death including smallpox. How would these life tables change if, because of mandatory vaccination, deaths from smallpox were entirely eliminated? As empirical sources of information, Bernoulli considered existing life tables, such as those com- puted in 1693 by the astronomer E. Halley? from the records of the city of Breslau in Germany. These tables were based on data which reported age at death for each individual; in addition, it may have been possible to determine whether death was a result of smallpox or of other causes. Therefore, each individual may be considered as exposed to two “risks”: death from smallpox and death from other causes. These risks competed for his life in the sense that the risk which materialized first deter- mined his life length. Thus for an individual who died of smallpox there was no way of telling how long he would have lived had smallpox been eliminated—and it was just this missing information that Bernoulli needed to answer his question. The argument devised by Bernoulli is ingenious and rather simple. It is also open to serious criti- cisms as to assumptions made explicitly or by implication. These criticisms already point at most of the difficulties encountered later in dealing with competing risks. We shall outline Bernoulli’s argu- ment,! following closely the somewhat naive reasoning of his Mémoir and only modifying his notation. Consider a population of /; individuals of age 0, and let /, denote the number of those among the lo who are still alive at age x > 0. Assume /, known for x = 0, for example from a life table. Clearly, l,, is a decreasing function of x. Let s, be the number of those of the /; who survive to age x > 0 and who have been infected with and survived smallpox. They are immune from smallpox for the rest of their lives. Similarly, let £, be the number of those surviving to age x > 0 who did not have smallpox, hence may still contract this disease. Clearly, l, =, +t, x | filles Ha a ey pO ig co hk. LN = (TTI Mii [In SN = 5M MEMOIRES MATHEMATIQUE ET DE PHYSIQUE, TIRES DES REGCISTRES de I" Académie Royale des Sciences, De T'Année M. DCCLX. ESSAI DUNE NOUVELLE ANALYSE De la mortalité caufto par la petite Vérole, ¢r des avantages de I’ Inoculation pour la prévenir. Par M. Danier BernNovuLLlL INTRODUCTION APOLOGETIQUE™ EUX qui ont fenti tout T'avantage de I'Inoculation, ont ( : imaginé différentes fagons de repréfenter cet avantage, qui, quoique revemant au méme, ne faiffent pas de faire une * Cette Introdu®ion n’a été faite que long-temps apres le Mémoire, étant du 16 Avril 1765. Mem. 1760, : A Figure 1. Introductory page of Daniel Bernouilli’s monograph on his theory of competing risks. Assume that in a unit of time (e.g., a year) smallpox attacks 1 in n individuals alive, and causes the death of 1 in m of those attacked. Bernoulli assumed m and n to be known (he estimated both to be about 8), and independent of x. The number of those dying of all causes during a time interval (x, x + dx) is Ly =k ==] x x+dx x" Among them are t, dx = number of those who get smallpox and die of the disease (1) nm and {, dx dl, — = number of those who die of other causes. (2) nm The number ¢, decreases during the time interval (x, x + dx) by the number of those among the #, who get smallpox and by the number of those among the ¢, who die of causes other than smallpox, so that ds 1, t, dx te ~luyan = dt, = t+ (dl, — . n x nm Ly nd |log (nz) =x, lx ml, This can be rewritten which yields by integration ’ “7 TH exp [x + fn] and since t, = [;, one has exp (c/n)=m —1, so that ml, 1+ (m—1)exp (x/n) ’ xr Consider now the life table obtained from the /, by eliminating smallpox as a cause of death, and denote z, = number of those surviving to age x > 0 when smallpox is eliminated, with z, =/,. In the presence of smallpox, the numbers of those dying of each of the two causes during a time interval (x, x +dx) were given by equations (1) and (2). Without smallpox only equation (2) applies, but at x there are z, alive instead of /,, hence the number of those dying in a time interval (x, x + dx) without smallpox is z, t, dx -—dz, = —7 dal, — . x nm Substituting ¢,, from equation (3), one obtains dz, ‘di, dx z, TL n[1+ (m —1) exp (x/n)]’ a differential equation with the solution z m LT om— 1+ exp (—x/n)’ @) x This ratio is clearly greater than 1 for x > 0, and it describes the improvement of the life table z, over the original life table /,. Asymptotically, one has for x —> eo z m mn sti L" m=] Using this mathematical model with the values m =n = 8 for which he claimed some empirical Justification, Daniel Bernoulli calculated his Tables I and II reproduced as they appear in his original paper (figure 2). Column headings were added for present use. In Table I the first and second columns (x and /, ) are taken from Halley’s life table; the third col- umn contains values of #, calculated from equation (3) with m =n = 8, and the fourth column lists the values s, =I, —¢,. The number of those contracting smallpox at age x appears in column 5 and is computed as follows: On the intuitive assumption that the number ¢, decreases uniformly during a year, consider (1/2)(¢, + t,,) as the number of those exposed to the risk of contracting smallpox at age x, and enter under column 5 the estimate (1/2)(¢, +t, ;)/8. Dividing this number by m = 8, one obtains the entry in column 6, an estimate of the number of those dying of smallpox in a year. Col- umn 7 accumulates the numbers of smallpox deaths from column 6, and column 8 accumulates the deaths from other causes. In Table II, the first two columns contain Halley’s life table reflecting mortality from smallpox and from all other causes; the third column contains values of z, computed according to equation (4). The fourth column lists the “gains” z, — 1. A number of criticisms were raised against certain of Bernoulli’s assumptions even before publica- tion of his paper—some he ascribed to an “eminent mathematician,” most likely d’Alembert, and he MEMOIRES DE L'ACADEMIE RoYarle DES SCIENCES. (1) (2) Xx be G Es | Survivans par felon 5 M. Halley.] pet. vérole. | pet. 1300 55 760 692 680 TABLE L (3) Ix Nayant pas cu 1300 896 685 571 8s. 16 339 311 272 (4) Bx Ayant fa Prenant (5) la pet. (6) (7) (8) MORTsS SommuE Mors de la par d des morts a pet. v maladies de |. pendant Fh pend. chaq. année. 17,1 28 12 1 97 »0 237 Figure 2. Daniel Bernouilli’s original life tables. (Column headings were added for present use.) discussed them at some length. The more obvious ones (e.g., the assumption that the probability of contracting smallpox as well as the probability of dying of smallpox are independent of age), could be replaced by more flexible and realistic assumptions without much difficulty. Other assumptions, such as the use of (1/2)(¢, + t,,,) in estimating the number of those attacked by smallpox for column 5 in Table I, have been reappearing throughout the centuries, and we will have to deal with them later on. MEMOIRES DE L'ACADEMIE RoYaLlE DES SCIENCES. TABLE 11 (1) (2) (3) (4) (1) (2) (3) (4) Xx de 2, x Ix Zx AGEs] Etat naar | ET aT | Differ. GEs| Emtnawrel | ETAT | Differ. — voiitegin non -varioliq. jou gains. ee. _, non-varioliq.| ou gains ° 1300 1300 o 13} 640 741,11 74.1 1 1000 1017.1 | 17.1 14 634 709.71 75.7 2 855s 881,8 | 26,8 13 628 03.0) 77,0 3 798 823.31 253 16 622 7oo,1 | 78,1 4 760 802.0 2,0 7 616 695.0 | 79,0 5 732 779.8 | 47.8 18 610 689,6 | 79,6 6 710 62,8 I" 53.8 19 6o4 684,0| 80,0 = 692 749,1 $7,% 20 598 678.2 | 80,2 8 680 740,9 | 60,9 21 592 672,3 | 80.3 9 670 734.4 | 64.4 22 586 666,3 | 80,3 10 661 728.4 | 67.4 273 579 659,0 | 80,0 11 653 722,9 | 69,9 2.4 572 651.7 | 70.7 12 646 18,2 | 72,2 25 565 644.3 | 79,3 Cette Table fait voir d'un coup d'eil, combien fur 1 300 enfans, fuppofCs nés en méme temps, il cn refleroit de vivans d'année en année jufqu’a lage de vingt-cing ans, en les fuppofant tous fujets a ‘la petite vérole; & combien il en refteroit s'ils étoient tous exempts de cette maladie, avec la companaifon & la différence des deux Cats. [¢1) k's Za Figure 2. Daniel Bernouilli's original life tables. (Column headings were added for present use.)—Con. Two features of Bernoulli’s approach are worth noting. One is the deterministic interpretation of all processes: The quantities /,, s,, t,, z, are functions of age x. A probabilistic approach could hardly have been expected at that time. The other feature is the nonparametric treatment: Bernoulli made no assumptions about the functional form of /, and, consequently, of the other functions of age. It is only with the arrival of the life-table models introduced by Gompertz in 18253 and Makeham in 1860% that specific functional forms of /, were considered. 1.1.2. Actuarial Problems More than one hundred years after Bernoulli’s Mémoir,! W. M, Makeham in 18745 developed a theory of “multiple decremental forces,” and thereby gave a systematic foundation to the actuarial treatment of competing risk problems. At Makeham’s time, the theory of probability had already been developed and actuaries were formulating their statements in probabilistic terms. Their earlier work was what, in discussing Bernoulli’s approach, we referred to as nonparametric: They started out with life tables obtained from experience without ascribing to them a specific functional form and estimated all the probabilities and actuarial values required. In 1860, Makeham,* expanding on earlier work by B. Gompertz in 1825,3 introduced the important parametric model known as the Gompertz- Makeham law of mortality which appeared to be particularly suitable as an approximation to many empirical life tables. Actuarial theory has traditionally used both approaches: nonparametric as well as applying the Gompertz-Makeham law. In classical works such as E. F. Spurgeon’s in 1932 (pp. 223-3206) both treat- ments are discussed in great detail, and it is pointed out that, if a life table follows Makeham’s law, the mathematical arguments become more elegant and manageable. The competing risks problems considered by actuaries were usually of a different kind and simpler than the question asked by Bernoulli. Such problems arose mostly when insurance policies had to be written on several lives, e.g., a policy for husband and wife that assured the payment of a benefit (such as a lump sum, or life annuity) after the death of one of them, to the surviving spouse. Here the premium to be charged is determined by the probability distribution of the time to the earlier death, hence could be computed if the joint probability distribution of both lives were available. Since life tables for pairs of lives, which would yield such joint probability distributions, are difficult to obtain, actuarial discussions of competing risks proceed on the assumption that the lives involved are inde- pendent in the sense of probability theory. This assumption has been recognized as unrealistic under many circumstances. For example, two people living together are likely to be exposed to the same environment, including a number of hazards, which affects their lives in a similar manner. Neverthe- less, little, if anything, has been done in actuarial theory to account for this kind of stochastic dependence. When life tables are used to estimate various probabilities, without the benefit of parametric models such as the Gompertz-Makeham law, actuaries have been facing the problem which Bernoulli had to deal with in calculating column 5 of Table I: If life-table-type data are available only at end- points of fixed time intervals, how does one use them when they appear in the denominator of a formula for a probability? The following procedure, quite analogous to Bernoulli’s, was recommended by Spurgeon in 1932 (p. 3826). Denoting by E, the number of individuals alive at age x, and by 0, the number of the E, who die between ages x and x + 1, he states: “If a number of the E, persons aged x, say w, , withdrew from observation during the year, it would not be known whether they survived to age x + 1 or died between the date of withdrawal and the attainment of that age.... Assuming that the withdrawals were equally distributed throughout the year. . ., the rate of mortality will be obtained by taking 0, : TE, — (12m, 5) 1.1.3. Clinical Experiments A large number of clinical experimental studies have been carried out in a manner which, possibly somewhat oversimplified, can be described by the following scheme. Included in an experiment are N subjects (patients, animals). At the beginning of the experiment each of them is exposed to a treatment that is conjectured to be somehow related to an event referred to as “failure.” For each individual subject, the experiment can terminate in one of two ways: Either failure is observed or the individual is lost from observation before failure occurs. Observable is the time W from the beginning of the experiment to its termination. This time W is clearly the smaller of two quantities: T = time to failure L = time to loss from observation. Typical experiments of this kind deal with the effect of potentially carcinogenic agents. Experi- mental animals are treated with such an agent and some develop cancer; others are lost from observa- tion either by death from other causes or by developing conditions that would invalidate the experi- ment. An aim of the experiment is to gather information on the time from the beginning of the treatment to the onset of cancer. This information could then be used, e.g., for comparisons with similar data for animals who have not been exposed to the agent under study; or it could be used to assess the effect of age or sex or some other factors on the time to the occurrence of cancer. The crucial difficulty in using data obtained from such experiments is that one does not know the time to the occurrence of cancer in those experimental subjects whose observation is terminated by the com- peting risk, i.e., loss from observation. Many studies overlooked this difficulty and arrived at conclu- sions that could be show: . to have no validity (for an example, see the 1939 article by Bernstein, Birn- baum, and Achs?). Another class of experimental studies in which loss from observation and, possibly, other com- peting risks make it difficult to evaluate the results, consists of experiments in which a treatment is used to delay the occurrence of some event. Research on various prophylactic treatments falls into this class, as do studies on the effectiveness of birth-control procedures. Lack of familarity with even the classical actuarial theory has often affected the validity of clinical research. It was only in the mid-1950’s that papers by statisticians such as Cornfield® began to remedy this situation by clearly pointing out the problem and by presenting actuarial techniques to these engaged in medical research. A model that is substantially more complex than that of competing risks, and yet quite realistic, was introduced in 1951 by Fix and Neyman.? They considered the study of a population of healthy "individuals who may leave that population either by becoming sick or by dying; but by becoming healthy, the sick may return to the population. Treating such health-sickness-death sequences as a stochastic process, they stimulated a succession of publications that go beyond the competing-risks concept. A survey of work in this direction may be found in Chiang’s book!? published in 1960 and in his report! published in 1974. The stochastic process approach has been particularly useful in constructing models for human reproduction. First systematically presented in 1963 by Shepps and Perrin!? and followed by a sequence of papers developing the mathematical theory and, as an alternative, proposing computer simulation (see Perrin’s 1967 study!3), these models have led to a wide range of approaches. In 1973, Shepps and Menken!# surveyed these developments. 1.1.4. Competing Risks in Technology If a technological system, such as an electronic network or a mechanical device, consists of n com- ponents cy, Cg, ..., C, in series, and each component has a random life length, then the life of the entire system will end with the failure of the shortest lived component. If one agrees to say that system failure is a result of the kth risk when c, is the shortest lived component, then the n different risks are competing in the sense that one usually can observe only the life length of the system and the component whose failure coincides with the failure of the system; in most practical situations, however, one cannot tell how long the remaining n — 1 components would have lasted. And yet such knowledge is essential if one wishes to make some statements on the extent to which the life of the system can be prolonged or maintained by one of various patterns of replacing or servicing com- ponents. For example, components can be replaced at fixed time intervals; or there is a finite supply of spare components that are used to replace a working component immediately when it fails, so that system failure can be postponed until all spares have been used and then a component fails; or a par- ticular component can be “beefed up” to increase its life length. Such problems have become particularly important since the advent of systems with large numbers of components, such as computers, contemporary aircraft, or the total equipment involved in the successful launching of a space rocket. Such advanced systems gave rise to a new discipline, the mathematical theory of reliability which has been developed mainly within the last two decades, most of it in the United States and the Soviet Union. Fortunately, those actively involved in this develop- ment represented a wide range of backgrounds and combined technological insight, knowledge of actuarial concepts and ability to use mathematical abstraction, so that much of the learning-by- mistake phase mentioned in section 1.1.3 could be avoided. 1.1.5. Other Areas The sources of competing-risk problems mentioned previously do not constitute an exhaustive list. They provide representative examples, but many others can be added. In the area of population dynamics, birth and immigration and death and emigration exemplify various modes of increment or of decrement of a population, and lead to the posing of problems in demography or in the study of biological populations. 1.2. COMMENTS ON THE PRESENT STATE OF THE THEORY 1.2.1. Duplication and Communication Gaps In surveying the literature, one encounters instances in which researchers in some fields have been unaware of progress made in other areas, and either had to duplicate work already done or else did not use that work. Consequently, their conclusions were often weaker then they could have been, or sometimes were invalid. One of the main aims of this report is to focus on basic concepts common to many areas in which competing risks have been considered and to present the mathematical theory dealing with these concepts. 1.2.2. Probabilistic Versus Statistical Approach In publications dealing with competing risks, much space has been devoted to the study of prob- abilistic models and their properties. Most of the traditional results are such that, when either a life table or some parameters of an underlying process are given, one can compute probabilities of various events, or expectations of times to failure or of other random variables, their variances and covari- ances, and so forth. How to use empirical data to arrive at conclusions about the underlying probabilities was a question which for a long time was dealt with by rather primitive methods. Actuaries used smoothing (gradua- tion) techniques to obtain life tables from raw mortality data, then estimated probabilities by expres- sions such as equation (5), and their practices were largely accepted and used by workers in such fields as vital statistics and clinical research. Only recently has the corresponding statistical theory begun to develop, and with this development came, among others, a critical investigation of the role of inde- pendence of the “lives” involved, a systematic discussion of the question of what information can be extracted from empirical data (problems of identifiability), of the advantages and disadvantages of traditional and of some newly proposed estimates, and of problems that can be stated in terms of tests of hypotheses. Part of this report will be devoted to such developments in statistical theory and to the resulting practical techniques. 1.2.3. Choice of Topics for This Report This presentation does not aim at completeness in any sense of the word. Our chief aim is to formulate the mathematical concepts and the theory of competing risks common to various fields of practical application. Having done that, we state a number of problems and describe techniques for dealing with them. There is a large literature on such problems, and subjective choices had to be made in selecting those which appeared typical, illustrative, and of practical interest. In presenting details of mathematical derivations, too, some choices had to be made. As a rule, mathematical arguments are completely included when they are reasonably simple and representative of a method of approach. For derivations that require long and complicated arguments or the use of esoteric mathematical tools, the reader is most frequently referred to original sources. In many cases, the theory available at present is inadequate, mainly because it requires assump- tions that are not satisfied in real situations, such as the assumption of independence of random quan- tities that in practice are likely to be dependent. In other cases, the theory deals with statistical estimates that are biased or not consistent. In still other cases, such as in dealing with problems of identifiability (see section 2.6), the theory leads to the negative result that the data, as they are usually available, cannot yield the information one would like to obtain. In such situations, where there seem to be no satisfactory answers, we at least try to formulate the problems and point out the difficulties. 2. PROBABILITY THEORY OF COMPETING RISKS 2.1 LIFE DISTRIBUTIONS In studying living organisms, one often considers their life length—the length of time from birth to death. Similarly, for technological devices, one may be interested in the length of time from the instant when the device was put into use to the instant when it failed. In either case one deals with a random variable capable of assuming only nonnegative values. Random variables of this kind are encountered in many other situations, such as incubation periods of infectious diseases, hospital stays, and the time an individual remains under observation or participates in an experiment. In the material that follows, we shall use the terms “life” or “life length” or “time to failure” quite generally to mean a nonnegative random variable, i.e., a random variable X such that P(X<0)=0. When a value x of a life X is observed, we shall say that the individual failed (or died) at a time (or age) x, that is, that it was alive (functioning or “‘up”) at all times ¢: 0 <¢ x) - [ nora will be called the “survival function,’ and the function A(x) =~ = log Fi (x) = fig (x)/F (x) (6) is known as the ‘hazard function” for life X. The intuitive meaning of Ax (x) becomes clear when one writes the last equality as an equation between probability elements x) dx Ax (x) dx = pl and interprets the right-hand expression as the conditional probability that an individual, having sur- vived to age x, fails in the time interval (x, x + dx). 1" The relationships Fx(x)=1-Fx (x) = exp - k Ae (5) | (7) are easily verified and one observes that each of the functions fx (x), Fx (x), Fx (x), Ax (x) determines all the others, hence any one of them describes the probability distribution of X. 2.2 NET (POTENTIAL) AND CRUDE (OBSERVABLE) LIVES Example A.—We consider an electrical circuit described by the diagram i Y in which the only components subject to failure are the contacts Cy, Cy, C5. We assume that each of these contacts deteriorates with time until failure occurs, and we denote the corresponding compo- nent lives by T,, Ty, Ty, with probability densities Fr, Oh Fr 0 rl We furthermore assume that T;, Ty, Tg are independent. Let W denote the time to failure of the cir- cuit. Clearly the circuit fails when either C; fails, or Co and Cs both fail, whichever occurs first. We shall refer to the failure of C; as “risk Ry,” and to. the failure of both C9 and Cs as “risk Rg,” and define X; = time to failure of C; = 7 Xo = time to failure of C; and Cy =max (Tg, T3) Then the time to failure of the circuit is W = min (X1,X29) = min [T}, max (Tg, T3)] 12 and its survival function can be computed as Fy (w) =P[T > w, max (Tg, Ts) > w] -[ fr, (t) if fr, (t2)fr, (ts) dts dts | dt; max (tp ,t3)>w - | " foated) | td) | fir (eg) ty iy w w tg co oo t3 -f frit) [ frat) [ fr, (t2) dtp dts dt. w w 0 Following an accepted terminology, we shall call X; and Xg the “net” lives for risks R; and Rg, respectively. In practice, only the ‘“‘actual’ life W is observed, together with the fact that the circuit fails due to risk R; or risk Rg, so that the random variable observed is two-dimensional (Ww, J) where W is the actual life and J = 1 or 2, according to which of the two risks “caused” the failure. The actually observed time to circuit failure due to risk R; is a random variable that has the condi- tional probability distribution of circuit life, given that failure is due to Rj. The random variable Y with this probability distribution is referred to as the ‘“‘crude” life for R;. It has the survival function Fy (y1)=P(W>y1l]=1) _PW>y1,/=1) r P(J=1) One similarly defines the “crude” life Y,, due to R,. Example B.—A cohort of patients is under observation during a fixed period of time 0 <¢ <7. For each individual, observation may end due to either of the two “risks”: The individual develops a specified condition C, or the individual drops out of observation. We consider the random variables: X; = time until condition C occurs X9 = time to dropping out from observation. These two random variables will be referred to as the “net” lives for the first or second risk. We assume that X; and Xo are independent, and that X; has a probability density that increases with time according to the formula 2x1 [12 for0 w) = P(X, > uw, Yo > w) * [7 [2% fey a. i dxg dx 72 T w w _ (1-w)(r2 -w2) 73 foro0 7. Since, for practical purposes, only the actual duration of observation W and the “cause” of termi- nation (condition C or dropping out) can be observed, we consider the two-dimensional random varia- ble (WJ) where J = 1 when C occurs first, i.e., if Xj < Xj, and J = 2 when the patient drops out before C occurs, i.e., if Xg w,]=1)=Pww,]=2)=Pw w,]=1)= QO} = PW>w,]=2)= WIN and for w > 7 one has PW>w,J=1)=PW>w,]=2) = 0. The marginal probabilities of termination due to either of the two risks are, therefore: P(termination due to C) =P(J = 1) P(termination due to dropout) = P(J = 2) 15 The conditional probability distribution of the time to termination, given that it occurs due to condition C, can be stated in form of the survival function Pr uiy= 1) = HSL 2 3 - -s(¥) r2(¥) for0€ww, J =2) P(]=2) 2-146) and the random variable Yo that has this probability distribution, i.e., has the survival function PW>w|]=2)= Fy,(y2)=P(Yg > yg) 3 3fy2 1fVvs — ts Te eon ane ls vere £ KC 1 3-13 forO0 x;) =Fx(0,++,0, Xr 0,---,0), with x; in either case at the 7th place in the lower expression. In view of equation (8), the survival function for the system life W is Fy (w) =P(W > w) = Fx (w,w, "+, w). (8) 17 From now on it will be assumed that, whenever the system fails, one can observe only its actual life and the mode of failure, i.e., the value of the two-dimensional random variable (Ww. J) where W is the system life and J = j when W = min (Xy,X29,- we +X) =X J=1,2, nk. Since, under our assumptions, PX; =X)=0 fori #j, so that the probability of two or more net lives being equal is zero, the value of J is uniquely deter- mined with probability one. The joint probability distribution of (W, J) can be expressed as Fy, j(w,j) =P(W1t,] =) =X; >t, and X; 1) =P(J=j)-Fu(t.j) forj=1,"-. (13) This is the probability of survival beyond age ¢ and then failure due to R;. It should be noted that Qr,(0)=P(J =] and ¥;> 0) tand X, t) = Pelt, ++); we see that A(x) = A, (x), and we note this fact as follows: Lemma.—If the net lives are independent, then the hazard rate of the actual life W is k Aw (%) = A(x) = 32 Ax, (x). (19) j=1 Together with equation (17) this yields =z Qy,(t) = - Ax, (t) exp - f A(s) i fori=1,2 = Fk, (20) : 0 Now, when the P(] = j) and Fy,(y;) are known for j = 1, - - +, k, then by equations (12) and (13) Qy;(t) are known, and relationship (20) is a system of k equations with £ unknown functions Ax (t). To solve it, we sum equations (20) over ¢ 2 Smart) =A exp - I As) | i=1 0 hence, 2 Q(t) =exp I | A(s) q +e. i=1 . 0 In view of 2_ Qv(0) -3. P(I=i)=1 i=1 22 we have ¢ = 0, and from equation (20) d Ir + Q (2) Ax, (t) = - (@) en fori=1,--,k, (21) -- Q(t) so that, knowing the Qy,(t) for i=1,- ++, k, we can compute all hazard rates Ax,(¢), and by equation (7) all Fx (1) and Fx (2). To summarize, if the net lives are independent, then the probabilities P(W < w, J = j), or the prob- abilities P(J =j) and Fy (¢) for j=1,---,k, determine all Fy (¢) and all Fy_(t), hence, also the joint probability distribution of all net lives Xi» 4%, This result’is due to Berman, 16 2.6.3. The Case of Possibly Dependent Net Lives The assumption of independence of the net lives was used to obtain equations (16) and (17), and to derive formulas (21) which show how, given the probabilities Qy,(¢) for the crude lives (or, equiv- alently, the probabilities P(]) and Fy (Y})), one can compute the probability distributions of the net lives. This suggests two questions: (a) Can formula (21) be used to obtain the distributions of net lives from those of crude lives if it is not known that the net lives are independent? (b) If it is not assumed that X;, ---, X, are independent, do the P(J) and Fy, v), f=1,:»": k determine the joint distribution of X;, ++, X,? The following example, given by Tsiatis,!> shows that the answer to question (a) is negative. Example C.—Let the joint survival function of (X;, Xy) be of the form Fx (x1,x2) = exp (= Axy - xg = yx1X2) (22) where A > 0, u > 0, 0 <+y < Au. Clearly, X;, Xp are independent if and only if y = 0. The marginal sur- vival functions for the net lives are Fx, (x1) =exp (- Ax) oe (23) Fxg (x2) = exp (- ux) and do not depend on 7. By equation (14) 2 Quy (6) = -(\ + 71) exp (- Me - ut - 722) : Qy, (t) = (1 + vt) exp (= At - pt - 7t2). Integrating each of these identities one obtains for Qy, (¢) and Qy, (¢) expressions that depend on all three parameters A, u, v in such a manner that, substituted in the right-hand side of equation (21), 23 they would lead to hazard rates Ax, (¢), Ax, (t) which depend on all three parameters and hence on 7. These hazard rates would, therefore, differ from the correct ones which correspond to equations (23) and which are independent of vy. Thus, it is shown that equation (21) cannot be used in the case of dependent net lives. The next example, due to Rose,!7 answers question (b), also in the negative. Example D.—Let k = 2 and f ( 1 for0 0 these net lives are not independent, for in the en- tire square 0 X. al2 a 2 Figure 3. Probability densities used in example D. The joint survival function of the net lives is aFxy x, (%1,%2) = (1 -x1)(1 - x2) for 0 < xq Sx; tas, (25) and is equal to other expressions in other parts of the unit square. However, to use equation (14) for computing Quy) and = Qy, (0), it is enough to know the joint survival function in an open set containing the diagonal x; = xo and equation (25) provides this information. Hence, by equations (14) and (25), we have 2 Quy) =-(1-1) 25 and 2 Qr,()= 5 ~t+Qr, (0) pe =F ~t+2()=1) for0< t<1. Since P(J = 1) = P(X; < X3) = 1/2 independently of a, we have by equations (12) and (13) for the crude life Y; Fy,1)=21 -y3 for01,7=1,2. In example D, Fy, (y,) and Fy,(yy) as well as P(J = 1), P(J = 2) are the same for all values 0 x1,X9 > x9) . (28) and Qi (x1) =P(X; >x; and X; x9 and Xy x1) = Fx, (x1) = F(x, 0), P(X9 > xg) = Fx, (x2) = F(0, x9)? 26 As indicated on figure 4, F(x; , xg) is the integral of the joint probability density f(x, xg) over the region contained in the right angle between bold lines: F(x1, xg) of Jing) dx dxg, while Qj (x1) is the integral over the interior of the 45° angle bounded by broken lines SIs fry ,%9) ) dx dxo and Qs (x2) is the integral over the interior of the 45° angle bounded by dotted lines xg) = J J fxr, x2) dxy dxg. —r———f mmm mm mmm = = = » iy 1 Xi Figure 4. Regions of integration considered in equations (30) and (31). 27 By inspection one has F(x1,x2) = Qi (x1) + Q2 (x2) - P(A) (30) where P(A) is the probability of (X;, Xg) falling into the triangle denoted by A in figure 4 or, more explicitly, Fxg, x9) = Q1(x1) + Qa(xg) - Px x) of W, the actual life, without the assumption of independence. 28 2.7. SUMMARY AND COMMENTS ON IDENTIFIABILITY We have seen that the joint probability distribution of the net lives Xj, ..., Xj, as given by the survival function Fx (x1, . . . , X ), determines the probabilities of the crude lives, i.e., all P(J =j) and Fy,(y;) forj=1,...,% or, equivalently, all P(Wt). (38) into models with independent variables. As one of the applications, they obtained a set of assumptions which are dif- ferent from assuming either independence or a parametric model, and are sufficient for a positive answer to the prob- lem of identifiability. 30 The recorded observations determine the nonnegative, decreasing, integer-valued function defined by n(t) = number of individuals alive and in observation at time ¢, (39) with the convention that a death occurring at ¢ is already subtracted in computing n(t), while a loss at. t is not yet subtracted. In other words, deaths at ¢ are treated as if they occurred slightly before ¢, and losses from observation at ¢ are counted as if they occurred slightly after ¢. Some consequences of this convention are these properties of n(t): n(t) is continuous at ¢ if neither death nor loss occurs at ¢, n(t - 0) - n(¢) = number of deaths occurring at ¢, (40) n(t) - n(t + 0) = number of losses occurring at ¢. 3.1.3. A General Estimation Procedure A number of estimation techniques for F(¢) can be obtained as special cases of the following general scheme. Step (a).—The time axis is divided in some disjoint intervals 0, u1]), (1,42), ..., (W-1,%]),--.. We introduce the notations P; = P(T> u;) = F(u;), (41) and pj = ne - (42) Pi. Step (b).—We decide to use some estimates p; for pi1=12,.... Step (c).—For any t > 0, we use as an estimate for F(t) the statistic He) =T"15; (43) uj 12.1. Had the last recorded event been a death, then we would have had H(t) = 0 from then on. When the data are large, some grouping may be desirable before carrying out the calculations lead- ing to H(t )- Several ways of doing this were suggested by Kaplan and Meier. It may be important for some practical applications to note that the K-M procedure permits one to consider individuals entering into observation after the beginning of their lives. This is done by counting each such entrance as a negative loss, i.e., one records the time of entrance, increases the number of individuals in observation by 1, and otherwise treats the event as a loss. Such entering Table A. Example of a Kaplan-Meier estimate 1 A 4 j uj Events ni | pj Hiuj) 0 0.0 --- 8 1 1 1 0.8 A 7 7/8 7/8 2 1.0 A 6 1 7/8 3 2.7 A 5 1 7/8 4 3.4 A 4 | 4/5 7/10 5 5.4 A 3 | 3/4 21/40 6 7.0 A 2 1 21/40 7 9.2 A 1 1/2 21/80 8 12.1 A 0 1 21/80 1A death is indicated by A, a loss from observation by A. 32 0 2 4 6 8 10 12 Figure 5. Graph of Kaplan-Meier estimate obtained in table A. individuals can later on disappear from observation and will then be counted as ordinary losses. It should be stressed, however, that the assumption of independence of life length and time to loss is being used whether the loss is positive (individual drops out from observation) or negative (individual enters into observation). . Under the assumption of independence of T and L, Kaplan and Meier showed that H(t) is that member of the class of all survival functions which maximizes the likelihood function for the recorded values and that it is consistent. They also derived several approximate expressions for the variance of H(t). For these derivations, the reader is referred to the original paper. Much further theoretical research has been done on the asymptotic properties of the K-M estimates (Breslow and Crowley?3 in 1974, Crowley?* in 1975, and Aalen?5 in 1976). A generalization to the case of more than two com- peting risks was introduced in 1972 by Hoel.26 3.2. SOME ACTUARIAL ESTIMATES AND THEIR RELATIONSHIPS TO KAPLAN-MEIER ESTIMATES 3.2.1. A Generalized K-M Procedure and Some Actuarial Estimates The procedure described in section 3.1.4 can be obtained as a special case of the following more general way of carrying out the steps listed in section 3.1.3. Step (a).—Given a recorded sequence of deaths and losses and the corresponding actual lives, we choose uy t)=1-Fr(t) FL(t)=P(L>t)=1-Fg(2). For any given interval (a, b], we wish to estimate the conditional probability Fr(b) Pap = 5 by using estimate (53). CThe reader may compare this with Bernoulli’s estimates for column (5) in his Table I (figure 2) which we men- tioned in section 1.1.1, and Spurgeon’s recommendation of formula (5). 35 Instead of intervals (a, b] we may, without loss of generality, consider the intervals I, = (0,£],£>0 with arbitrary £. We now define the following events (see figure 6): 8; ={0 £} (individual dies in J, not due to be lost in I), 5: ={0 £} (individual is not due for loss in I), vo = {0 7 £ Figure 6. Diagram of events defined by formulas in (55). 36 Not all of these events are observable; however, the event u is observable and so are the following unions 6=208, Udy (individual dies in I; before getting lost) . Y=v1 Ure (individual is alive and present, hence under risk, at 0). Consider now the random variables. Ni = number of individuals for which vy; occurs Ny = number of individuals for which v9 occurs Dj; = number of individuals for which §; occurs (56) Dy = number of individuals for which 89 occurs M = number of individuals for which x occurs. One clearly has N = N; + No = number of individuals for which vy occurs, i.e., number under risk at 0 D = Dj + Dy = number of individuals for which § occurs, i.e., whose deaths occur in I¢, before they are lost. The random variables M, N, and D are observable. The probabilities of the events in (55) are P51) =Fri)i1 - £1. (8) £ P52) = [ Fris) dri (s) 0 £ Pn) =f [1 -Fr(s)] dFy (5) (57) Bly1Y=1 Fri) Plva)y=Fr(5) and, assuming the number N known, each of the random variables in (56) has binomial probability distribution with parameters N and the corresponding probability in (57). The statistic (53) can now be written Poy = N-M/2 =1-q5, 37 where eg og iN Db, Na-up Dy To" N_M/2 N-M2 N; N-M/2 Ny-M/2 (58) As N => oo, each of the quantities Nj /N, D;/N, Dy [N, M/N tends in probability to the corresponding probability in (57) hence the right side of equation (58) tends to 1- Fp (8) , Fr@l - Fr (8)] 1- Fr (8) 1-2) f (-Fr)ar; ‘ £ £ FL®-2) f (-Fr)dr, [ Fran + 4 X ! : : (59) Co 1-(2) f a-Frydn Fo®)-(112) [ (1-Fr)dF, We assume Fp (§) < 1, which must be true if there are any individuals left in observation after £. Expression (59) then reduces to a weighted mean of the form £ / Fr df, 0 A-Fr)+(1-4)- : (60) FL®- 2) [ (-Fr) dF with 0 <4 <1. Since Po is consistent if do.¢ tends in probability to Fi (§), i.e., when the expression (60) is equal to Fr (&), we obtain £ / Fr dF}, 0 Fr(§) = : forall §>0 (61) Fu®-2) [ (-Fr)dr, 0 as a necessary and sufficient condition for py £ being consistent for every /,. Abbreviating E Fr dFy G(§) = aT ; (62) we rewrite equation (61) as Fr(§) = fo : (63) 38 From equation (62) one verifies that 1+g FE 1-G Fr’ G' G a differential equation which has the solution G —_— =F for c > 0. (64) (1-6)? Solving equation (64) for G in terms of I; and substituting in equation (63) one has Frif}=l <= (65) V1+cFL(§) We see, therefore, that relationship (65) between the probability distribution functions Fr and Fr, is necessary and sufficient for the statistic (53) being a consistent estimate of p,; for all intervals (a, b]. In practical situations, it appears quite unrealistic to assume that 7 and L are not only independent but even have probability distributions related by the very stringent condition (65). One arrives, therefore, at the disappointing conclusion that the “adjusted observed” estimates of the probabilities Pap are in general not consistent. It would be interesting to obtain bounds on the asymptotic bias of these estimates, but such bounds do not appear to be known. 3.3. LIFE-TABLE ESTIMATES: PROPORTIONAL HAZARD RATES 3.3.1. Definitions and Assumptions We consider risks Ry, Rg, +--+, R,, ++, Ry. The time axis is divided by points chosen once for all (e.g., the last days of consecutive calendar years) into fixed time intervals 5 = (wy, wy) forj=1,2,.... One starts out with a cohort of N individuals, and observes the numbers 8,; = number of failures due to R, in I;. (66) We make the assumption that the net lives X;, Xo, ---, X};, corresponding to the k risks, are independent random variables, and wish to estimate the “net probabilities” Let A, (t) denote the hazard rate for the net life X,,7=1,2, -- -, k and A\(¢) the hazard rate for the actual life W = min (X,---, X}). Since the X, are independent, we have according to equation (19) k Ae) =2_ Ar (2)- (68) r=1 39 The probability that in the presence of all competing risks an individual, alive at u;_; , will survive to uj can be written pj = P(W > uy | W> %.1) =P(W > uj) [P(W > Wi) Hy = exp, -f As) ds|=1-g;. (69) uj-1 The “crude” probability that an individual, alive at u;_; , will fail of risk R, during /; is 2;=2PX, EL, md X, u,_,) and can be written Uj-1 UY jm] =f ew - [ s] M(t) dt. (70) We now make, in addition to the assumption of independent net lives, the following assumption of proportional hazard rates (PHR): For each interval I; there are constants cyj, €gj,* + +, Crj, = * +, Ckj such that A(t) DO) = 0 fort Er, (71) Under this assumption, the crude probabilities of equation (70) can be expressed as uj t Qi = Cry / exp -f A(s) ds | \(¢) dt Uj..1 Uji “i =gy91 ~exp| - f A(s) ds |), Uji hence Qs = criqj forr=1,---,k;j=1,2,.-., (72) where g; is defined by equation (69) as the probability that an individual, alive at u;_1, will fail in I;. From equations (71) and (72) one has = = Cp for t in I;. 73 NY) og i (73) 40 Summing over r and using equation (68) one sees that k 2 Qji=gj. (74) r=] Equation (74) follows directly from the definition of the Q,; and does not require the PHR assump- tion. Using the PHR assumption, the net probability g,; defined by equation (67) can be written gri=1-exp - / Ar (s) | Le] uy =1-exp| - cy f A(s) ds Uj-1 = 1 of ki and by equation (72) ary = 1p (75 which expresses the net probability g,; in terms of the probabilities p; and g; = 1 - pj, and the crude probability Q;. 3.3.2. Observable Random Variables: Maximum Likelihood Estimates of Crude and Net Probabilities We assume that, as is most often the case in life-table-type studies, the records contain only the numbers ; = number of those alive immediately after ;_; forj=1,2,...;7=1,...,k (76) drj= number of those failing in I; due to R, Clearly, k L=2>_ dpj + liv 1.- (77) r=1 Given that an individual survived u;_1, the probabilities that it will fail duetoRy,...,R,,..., Rg are, respectively, Qy;,..., Qj, . , Qrj, and the probability that it will survive beyond u; is p;. There- fore, the conditional joint probability distribution of dy, ere» drjy «oo » dijy b+ 1, given fj, is the multi- nomial expression A 1 Afi... %ipki+1 dy! djl! Qu’ Qh (78) 41 When for an interval I; the observed frequencies /;, dy, . . ., dij and [+1 are available from obser- vation, then it is well known that the maximum likelihood estimates for the probabilities appearing in expression (78) are the relative frequencies eid The ary k =F Orr=1,2, 0000 ~ lim (79) 8; =7" * and expressions for variances and covariances can be explicitly obtained (p. 25319). Thus far, the arguments have been straightforward and fairly simple, but they yielded only the estimates (79) of the crude probabilities. To estimate the net probabilities ¢,;, Chiang recommends that the values (79) can be substituted in equation (75), so that one obtains the estimates , & fee qr . -— i, 7 ; dypild; / L rjl@j op 5] (80) 3 where dj = I; - [;+1 = total number of failures in ;. Since in most practical situations one is mainly interested in the net probabilities, the question arises whether the estimates (80) have the usual desirable properties and in particular whether they are consistent. 3.3.3. Conditions for Consistency of Chiang’s Estimator of the Net Survival Probabilities As in section 3.2.2, we consider the case of & = 2 competing risks, call the corresponding lives T= time to failure and L = time to loss from observation, assume that 7" and L are independent random variables, and denote their survival probabilities by Fr (t) and Fy (t) and their probability densities by fr(t) and fi (t). Again, without loss of generality, we fix our attention on an interval I; = (0, £],£ > 0, and for given initial size N of the cohort use the estimator (80). Using the events defined by equations (55) and the random variables in (56) we rewrite (80) in the form 3 N-D-M D|(D+M) qT, ¢ = 1 le ——————— N 21 ( Diy Dy A (D1/N+D2[N)/(D1[N+D2/N+M|N) TENT RTROR (81) Again, as in section 3.2.2 we conclude that with N => oo each of the quotients in this expression tends in probability to the corresponding probability in (57), hence re tends in probability to g*=1-[1-P(,)-P(53) -P(u)] [P(81)+P(52)]/[P(61)+P(52)+P(u)] (82) 42 As can be seen from figure 6, the sets § = §;U8y and u correspond to the symmetric, observable events “failure before £ and before loss’’ and “loss before £ and before failure,” and their probabilities P(8), P(u) satisfy the equation P(8) + P(u) + P(L > §,T >) =P(8) + P(u) + FL (§)Fr(§) = 1, so that equation (82) can be written g* = 1 - [Fy (5)Fr(8)] [P(6)]/[1-F (5)Fp(8)] (83) Therefore, for gr, ¢ to be consistent, it is necessary and sufficient that [FL (8) * Fr(§)] [P(8)1/[1 Fp ()Fp(8)] _ Fr(t) which reduces to [Fr (£)]70) = [Fr(§)]*®. (84) If the PHR assumption (71) is satisfied, which in our case of two independent competing risks means Ar (s) = cA(s), AL (s) = (1 = c)A(s), then and £ — —— Pl) = - [ Prin) dF, (a) =0 £ =(1-¢) h - exp Nl A(s) «| 0 £ P(5) a | Fy tn) dFr (2) 0 eal fod and one verifies that condition (84) is satisfied. We conclude that under the PHR assumption, estimate (80) proposed by Chiang is consistent. 43 3.3.4. Examples of Competing Risks With Proportional Hazard Rates We have seen that for data of the life-table type, under the assumptions of independence and proportional hazard rates, Chiang’s estimate (80) is consistent. Leaving aside the question of how realistic these assumptions may be in specific practical situations, one may still wish to see nontrivial examples of independent competing risks which satisfy the PHR assumption. Following H. A. David in 1970,27 we present a further discussion of the PHR property (71), which leads to the construction of such examples. Writing equation (71) as A(t) = cj N(2) foruj; ty, 6) = F(t; 0, 6) = exp [- at”] (89) which has the well known property that the minimum of independent identically distributed random variables of this family has again a Weibull distribution (his discussion goes further, to consider all three known classes of extreme-value distributions of the minimum). Choosing cy, cg, ..., ¢; so that forr = 2, ... , k the ratios p, are positive integers, and assuming for X; a Weibull distribution (89), one obtains an example of independent net lives, each with a Weibull distribution, which satisfy condi- tion (87), i.e., have proportional hazard rates on the entire time axis. For suggestions of further examples the reader may wish to consult David’s 1970 paper.?’ 4.ESTIMATION FOR PARAMETRIC MODELS 4.1. THE LIKELIHOOD FUNCTION: GENERAL CASE We shall now assume that the joint probability distribution of the net lives belongs to a specified parametric family. Let the joint probability density of these net lives Xj, ..., X; be fro @)Y= Axis ova 8p30y ovo 30m) (90) For fixed j, let mr; = P(min X; = X;) forj=1,...,k, (91) be the probability that failure due to risk R; is observed. Writing in equation (11) fx (x; 8) instead of f(x1,...,x;), one obtains Xj=0 X=; Xj-1=Xj JX Jr1=Xj Xp =Xj i#] and the probability density of the “crude” life Y}, as defined in section 2.4, can be written fr; {yi:8)= = =f I Axissen, Xi1s Vis Xia ls eves Xe300, 0. 0m)] | ax;. (93) i#]J When 7 individuals are observed to failure, and n; of them fail due to R;, j = 1, , k, then the joint probability density of the observed (crude) life lengths Y,.,»=1,... n contitinan on the n, jr? 4b is k ny ni: I I Ym] wf L fxysess > Xj Ls Yrs XL» 3% 30 0) | | dx;. j=1 r=1 Vir #7] 45 Since the n; have a multinomial probability distribution k k gly, «ov otz) (fr nt) (F 7) j=1 j=1 the likelihood function of the observed (crude) life lengths is etn LTA Def Rus «vin y Rpts Vins Ripa sv + sp Zn 300 a 54 Om YA I dye (94) iF] This expression, given in 1971 by Moeschberger and David,?® does not require the assumption that the net lives are independent, but only the assumption of a specified parametric form of the joint prob- ability density (equation 90) of the net lives. Whenever such a parametric family is specified and the values of the crude lives yj, are available, the likelihood function (94) may be used to obtain maxi- mum likelihood estimates of the parameters 6;, ... 0, by the usual procedure of computing the partial derivatives OL dln L 30, \°" Tee, )° equating them to zero, and solving the resulting system of m equations for 64, ..., 6,, . However, even if the density (90) is of a reasonably simple form, one would expect in carrying out these steps to encounter difficulties which, at best, may be overcome by using computers. 4.2. THE CASE OF INDEPENDENT NET LIVES If one assumes that the net lives Xj, ..., Xj are independent, with probability densities f;(x;; 6) and survival functions Fj(x;; 8), then equation (93) becomes fii 0) (vj: 0) = fy; (vj ) mF; F533 6) : 0) rl Fy; 9) (95) and the likelihood function (94) takes the form ee(mfr I Tw) 1] ; irs O)1/[F5( Vir; 8 i 1 Fy(y;35 0) (96) j=1 r=1 This expression is much less complicated than (94). Moreover, for simple parametric models, it lends itself to manageable treatment for obtaining maximum likelihood estimates of the parameters 0=(01,...,0m). 46 4.3. COMMENTS ON PARAMETRIC FAMILIES OF MULTIVARIATE LIFE DISTRIBUTIONS The maximum likelihood estimation procedure under the assumption of independent net lives, as just described, has been actually used. The reader may find technical details as well as completely worked out numerical examples in the 1971 paper by Herman and Patell?® or in Moeschberger and David?® for the cases when the net lives are assumed to have independent exponential or Weibull distributions. Moeschberger and David consider also the multivariate exponential distribution intro- duced in 1967 by Marshall and Olkin,3® which deals with dependent net lives, and suggest a way of proceeding in this case.4 The Marshall-Olkin multivariate exponential distribution is one of the few multivariate life distri- butions admitting dependence. A multivariate Weibull distribution has been proposed by several authors, and a rather general method for obtaining new multivariate life distributions was outlined by Lee and Thompson.®! To this writer’s knowledge, little work has been done on the use of such dis- tributions. It would seem desirable to construct more parametric families of multivariate life distribu- tions, justify their use either by deriving them from some plausible assumptions, or by at least showing that they agree reasonably well with empirical data, and to develop in detail the maximum likelihood estimation techniques for their parameters. 4.4. CONCOMITANT VARIABLES In some practical situations, the available empirical data contain more information than just the observed crude lives (i.e., actual lives and the risk recorded at failure), and it appears desirable to use this additional information. An important example is the situation when values of ‘“‘concomitant variables” have been observed. Considerable advances have been made recently in developing tech- niques for using concomitant variables and, while a systematic presentation of this area of research would require a separate monograph, it may be useful to give here an example of the concepts in- volved and mention some of the pertinent papers. In 1965 Feigl and Zelen®? considered the study of data on leukemia patients which, for each patient, contain the observed time from diagnosis to death (life length) and the white blood cell count at diagnosis (concomitant variable). They assumed that the probability distribution of life length T" at diagnosis depends on the white cell count x in such a way that the probability density of T is - Nt fort =0 F(t) = exp(- At) or 0 fort <0 where E(T) = 5 =a + bx. : ’ : : ‘ The problem was to estimate the parameters a, b which determine the dependence of T on x; knowing these parameters would clearly help in estimating the life expectancy of a patient for whom a value of 4The Marshall-Olkin distribution is also discussed in Langberg, Proschan, and Quinzi’s 1978 paper.20 47 x was observed. Feigl and Zelen derived the maximum likelihood procedure for this problem, com- puted the asymptotic variance-covariance matrix, and applied the theory to numerical data. In 1966 Zippin and Armitage33 extended the Feigl-Zelen model to the case in which not all patients had died at the time when the study was concluded, thus introducing a competing risk. The important paper of 1972 by Cox3* considered a very general model dealing with both censor- ing (competing risks) and concomitant variables. This paper was followed by a number of studies, such as Kalbfleisch and Prentice3? in 1973, Lagakos®® in 1976, and Holford?’ also in 1976. 4.5. ESTIMATION OF THE RATIO OF HAZARD FUNCTIONS As an example of a problem which requires estimating a parameter from data with competing risks, we refer to a 1975 paper by Crowley? in which he discussed the following situation. Survival data were obtained independently for two different populations, each affected by com- peting risks. There is reason to assume that the two net life distributions are of the same type and that the difference between them is due only to the fact that their hazard rates differ by a constant factor. How can one estimate that factor? Let X; denote the net life in the first population, and 7; the competing life, so that only the actual life Wy = min (Xi, Ty) and an indicator variable {; when X;| T; can be observed, and let Xo, To, Wo, 62 be similarly defined for the second population. We shall say that W; is an uncensored value when 8; = 1, and a censored value when 6; = 0, and use similar terms for Woy . Available are the samples of (Wy, 81) (Wij, S1:)i= 142, vu sm (97) and of (Wg, 89) Wzp: 822), =1,2,...,5:. (98) We assume that (1) Xj, 7}, Xs, and Ty are independent and (2) the hazard rates of X; and X, differ only by a constant factor, i.e., Axy (2) = 0A, (2) fot = 0. (99) Assumption (99) is equivalent to the relationship between survival functions Fx, (t) = [Fx, (1)]°. (100) If these assumptions are satisfied, then 6 > 1 implies that Xo is stochastically smaller than X . 48 Crowley considered several possibilities of presenting the data (individual sample values are avail- able, or data are grouped in time intervals, etc.) and discussed several estimators. We shall describe one of them, for the case when the exact individual values (97) and (98) are available. Let ni nip = 2_ 81; = number of uncensored values of W; i=1 ny => (1- 81j) = number of censored values of W; j=1 nig so that ny; + n19 =n; and, similarly, %y Bq nor = 2 8g ngg = 2 _ (1-8g), kr=1 k=1 with ng; + ngg = ny. We denote the uncensored values of Wy by Wy 1, Wy a, ..., Wyn, ; the cen- sored values of Wy by Wy, 41, Wi ny+25-++5 Wing +n, the uncensored values of Wy by Wa 1sWa sen ns Wo ny, 5 and the censored values of Wy by Wang, +1s eens Wang, +ngy- The likelihood function (96) becomes now ny! ni1 3 ni1+nig BN gy] l fx,(Wir)Pr,(W,) T 1 fri(Wu)Fx, (Wy) 11°27 renyq+1 ! 11 ng! n21 - ng1+nag 2 X vee Homa] I 1 fx, (Waos)Fr, (Wes) | [| fro (Wos)Fx, (Was). (101) es s§s=noj+ To carry out the procedure leading to a solution of the likelihood equation for 6, one must assume a specific functional expression for Fy (t). Following Crowley, we illustrate this procedure by choos- ing Fx, (¢) = exp (- At) (102) hence Fx, (t) = exp (- Oz). (103) Writing expression (101) for these specific survival functions and differentiating log L with respect to A and to 6, one arrives at the likelihood equations nip +n "1 =? So = 3 Wi -0 3 Wy =0 r=1 s=1 nai vr 5 = > Was =0, s=1 49 and the estimators for A and 6 obtained by solving these equations are nj A=n11/ 2 Wy, r=1 ny ng 0 = (na1fnin) 2° Wy / 3° Wa (104) r=1 s=1 Estimate (104) is consistent, since it can be written: ny ng 2_ Wi J 27 Wa b= ng [ N11 r=1 s=1 LE nm ny LL and this tends in probability to oo P(X, T). (111) For every observed four values X; , §;, Y;, €;, we define a scoring function Q(X; + Dis Y; , €) by assigning to it the value 1 when the four values establish unequivocally that X; 2 Y}, the value 0 when the four values establish unequivocally that X; < Yj, and the value 1/2 in all other cases. More for- mally 1 when €; = 1 and X; > Y; Q(X7,8;,Y ,6)=10 when 8; = 1 and X; oo, n—=>0co, so that [m/(m +1)] = X\ where 0 < A < 1, then under H, the probability distribution function of Vm Fn [W-(1/2)] tends to No, (1/12) (1)o? ol ] X 2} (118) where ' of = P(F,F2 > F3), (119) 03 =P(F2F, > F?), that is, the random variabley/m +n (W - 1/2) is asymptotically normal with expectation 0 and vari- ance 1{ , 1 9 (1/12) X (os & EY 3). Furthermore, Efron suggests consistent estimates for 0? and v3 , but does not elaborate on the way to compute them. Under the additional assumption Fy = Fy, i.e., of the same probability distribution for the two censoring variables, Gehan®® proposed in 1965 the use of W for a conditional test of Hy of a combina- torial nature. Mantel*® offers a simple combinatorial formulation of Gehan’s conditional test statistic," and discusses its properties under the assumption Fy = Fy and also under less restrictive assumptions. 5.3. TESTING FOR INDEPENDENCE WHEN DATA ARE CENSORED An important problem of hypothesis testing, treated extensively in 1974 by Brown, Hollander, and Korwar,** may be stated as follows. Consider the random variables X, Y with a bivariate life distribution, i.e., such that PX=0,y=20)=1. If a sample (X1,Y1), (X2,Y2),..., (Xu, Va) (120) is available, then there are a number of well known tests of the hypothesis that X and Y are indepen- dent or, more generally, uncorrelated. A new problem arises when to one or both of the two lives X, ¥ corresponds a competing life (censoring variable), U in competition with X, and V in competition with Y, so that one can only observe (X71 1, ol £1) cee (x3, 8, Y:, €)s Te Wy x, Bus Y:, €n) (121) where X} , §;, Y; , €; are defined in equations (105)-(108). Brown, Hollander, and Korwar** considered data from a heart transplant program, and explored hypotheses such as that sex (X) and survival time after transplant (Y) are independent, where Y is censored by V = time to closing date of the research program. To test the hypothesis of independence of X and Y when only Y is censored (a generalization to the case of X and Y both censored is straightforward), the authors modified Kendall’s rank correla- tion statistic which for a complete sample (120) is defined as §S=2_2_ aby (122) i=1 j=1 where 1 ifX > X; aj; = 0 if X; = X; (123) -1 EX ; bi; = 0 if Y; = Y; (124) -1 if; Y; ande;=1,0rY; =Y; and¢; =0 bjj=<-1 if Y7 >" a;jbi;. (127) i=1 j=1 55 If X and Y are independent, then S$’ has a conditional probability distribution of a purely combina- torial nature, hence is nonparametric and can be used to test the hypothesis of independence of X and Y, provided the following additional assumption is satisfied: Assumption A: When X and Y are independent, then X and (Y™*,€) are independent. If assumption A holds, critical values of S' can be calculated by a combinatorial argument when n is small. For large n, again under assumption A and when the hypothesis is true, the statistic S' is con- ditionally asymptotically normal with conditional expectation E(S’) = 0 and a conditional variance that is given by Brown, Hollander, and Korwar** and is a function of the a;j and bij. A further statistic for testing independence of X, Y when one or both variables are censored, based on Kaplan-Meier extimates of the survival functions for the net lives X and Y, is proposed in their paper. The reader is referred to the original paper for a description of this test, as well as of still another “pseudocondi- tional’ test. 5.4. LARGE-SAMPLE TESTS In preceding sections we gave examples of tests of hypotheses about net lives which are observed in the presence of competing risks. These examples dealt with tests designed for specific problems, and the sampling distributions of the test statistics could in some cases be computed exactly for small sample sizes, and in all cases can be obtained for large samples from the asymptotic normality of the test statistics. Clearly, additional large sample tests can be obtained in those competing risk situations for which estimates of parameters are available and are known to be asymptotically normal. 000 56 REFERENCES IBernoulli, Daniel: Essai d’une nouvelle analyse de la mortalité causée par la petite verole, & des avantages de inoculation pour la prévenir. Académie des Sciences, Paris. Historie avec les Mémoires, 1760. pp. 1-45. 2Halley, E.: An estimate of the degrees of the mortality of mankind, drawn from curious tables of the births and funerals at the city of Breslau. Philos. Trans. Roy. Soc. (London) 17:569-610, 1693. 3Gompertz, B.: On the nature of the function expressive of the law of human mortality, Philos. Trans. Roy. Soc. (London) 115:513-583, 1825. 4Makeham, W. M.: On the law of mortality and the construction of annuity tables. J. Inst. Actuaries 8:1860. 5Makeham, W. M.: On an application of the theory of the composition of decremental forces. J. Inst. Actuaries 18:317-322, 1874. 6Spurgeon, E. F.: Life Contingencies, 3rd ed. London. Cambridge University Press, 1932. "Bernstein, F., Birnbaum, Z. W., and Achs, S.: Is or is not cancer dependent on age? Am. J. Cancer 37:298-311, 1939. 8Cornfield, J.: The estimation of the probability of developing a disease in the presence of competing risks. Am. J. Public Health 47:601-607, 1957. 9Fix, E., and Neyman, J.: A simple stochastic model of recovery, relapse, death and loss of patients. Hum. Biol. 23:205-241, 1951. 10Chiang, C. L.: Introduction to Stochastic Processes in Biostatistics. New York. Wiley, 1968. I1Chiang, C. L.: Neyman’s Contribution to the Theory of Competing Risks, a Fix-Neyman Mode. Long Term Care Report. No. 2. School of Public Health, University of California, Berkeley, 1974. 12Shepps, M. C., and Perrin, E. B.: Changes in birth rates as a function of contraceptive effectiveness: Some appli- cations of a stochastic model. Am. J. Pub. Health 53:1031-1046, 1963. 13 Perrin, E. B.: Uses of stochastic models in the evaluation of population policies. II. Extensions of the results by computer simulation. Proc. Fifth Berkeley Symp. Math. Stat. Probab. 4:137-146, 1967. 14Shepps, M. C., and Menken, J. A.: Mathematical Models of Conception and Birth. Chicago. University of Chicago Press, 1973. 15Tsiatis, A.: A nonidentifiability aspect of the problem of competing risks. Proc. Nat. Acad. Sci. USA 72:20-22, 1975. 16 Berman, S. M.: Note on extreme values, competing risks and semi-Markov processes. Ann. Math. Stat. 34:1104- 1106, 1963. 17Rose, D. M.: An Investigation of Dependent Competing Risks. Unpublished doctoral thesis, University of Wash- ington, 1973. 18Peterson, A. V., Jr.: Bounds for a Joint Distribution Function With Fixed Sub-Distribution Functions; Application to Competing Risks. Tech. Rep. No. 7. Stanford University, Division of Biostatistics, 1975. 19Langberg, N., Proschan, F., and Quinzi, A. J.: Transformations yielding reliability models based on independent random variables: A survey, P. R. Krishnaiah, ed., in Applications of Statistics. Amsterdam. North Holland Publishing Co., 1977. pp. 323-337. 20Langberg, N., Proschan, F., and Quinzi, A. J.: Estimating dependent life lengths, with applications to the theory of competing risks. To be published. 21Langberg, N., Proschan, F., and Quinzi, A. J.: Converting dependent models into independent ones, preserving essential features. Ann. Probab. 6: 1978. In press. 22Kaplan, E. L., and Meier, P.: Nonparametric estimation from incomplete observations. J. Am. Stat. Assoc. 53:457- 481, 1958. 23 Breslow, N., and Crowley, J.: A large sample study of the life table and product limit estimates under random censorship. Ann. Stat. 2:437-453, 1974. 57 24Crowley, J.: Estimation of Relative Risk in Survival Studies. Tech. Rep. No. 423. Department of Statistics, Uni- versity of Wisconsin, Madison, 1975. 25 Aalen, O.: Nonparametric inference in connection with multiple decrement models. Scand. J. Stat. 3:15-27, 1976. 26Hoel, D. G.: A representation of mortality data by competing risks. Biometrics 28:475-488, 1972. 27David, H. A.: On Chiang’s proportionality assumption in the theory of competing risks. Biometrics 26:336-339, 1970, 28Moeschberger, M. L., and David, H. A.: Life tests under competing causes of failure and the theory of competing risks. Biometrics 27:909-933, 1971. 29Herman, R. J., and Patell, R. K. N.: Maximum likelihood estimation for multi-risk model. Technometrics 13:385- 396, 1971. 30Marshall, A. W., and Olkin, I.: A multivariate exponential distribution. J. Am. Stat. Assoc. 62:30-44, 1967. 31 Lee, L., and Thompson, W. A., Jr.: Results on failure time and pattern for the series system, in Frank Proschan and R. J. Serfling, eds. Reliability and Biometry. Philadelphia. Society for Industrial and Applied Mathematics, 1974. pp- 291-302. 32Feigl, P., and Zelen, M.: Estimation of exponential survival probabilities with concomitant information. Biometrics 21:826-838, 1965. 33 Zippin, C., and Armitage, P.: Use of concomitant variables and incomplete survival information in the estimation of an exponential survival parameter. Biometrics 22:665-672, 1966. 34Cox, D. R.: Regression models and life tables (with discussion). J. Roy. Stat. Soc. B 34:187-220, 1972. 35Kalbfleisch, F. O., and Prentice, R. L.: Marginal likelihood based on Cox’s regression and life model. Biometrika 60:267-278, 1973. 861.agakos, S. W.: A stochastic model for censored survival data in the presence of an auxiliary variable. Biometrics 32:551-559, 1976. 37Holford, T. R.: Life tables with concomitant information. Biometrics 32:587-597, 1976. 38Gehan, E. A.: A generalized Wilcoxon test for comparing arbitrarily single-censored samples. Biometrika 52:203- 223, 1965. 39Gilbert, J. P.: Random Censorship. Unpublished doctoral thesis, University of Chicago, 1962. 40Gehan, E. A.: A generalized two-sample Wilcoxon test for doubly censored data. Biometrika 52:650-653, 1965. 41Efron, B.: The two-sample problem with censored data. Proc. Fifth Berkeley Symp. Math. Stat. Probab. 4:831- 853, 1967. 42Breslow, N.: A generalized Kruskal-Wallis test for comparing K samples subject to unequal patterns of censorship. Biometrika 57:579-594, 1970. 43Mantel, N.: Ranking procedures for arbitrarily restricted observation. Biometrics 23:65-78, 1967. 44Brown, B. W., Hollander, M., and Korwar, R. M.: Nonparametric tests for censored data, with application to heart transplant studies, in Frank Proschan and R. J. Serfling, eds. Reliability and Biometry. Philadelphia, Society for Indus- trial and Applied Mathematics, 1974. pp. 327-354. 58 *U.S. GOVERNMENT PRINTING OFFICE : 1979 0-281-259/1 Series 1, Series 2. Series 3. Series 4. Series 10, Series 11. Series 12. Series 13. Series 14. Series 20. Series 21, Series 22, Series 23. 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