3. general considerations for the analysis of case-control ... - IARC

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Factor C+ Exposure E + - BRESLOW & DAY Factor C- Exposure E + - Pooled levels of C Exposure E + - Case Control Odds ratio From these tables it can be seen that the cell entries when C is positive differ markedly from the cell entries when C is negative. This lack of balance has- two consequences. First, the unequal ratio of cases to controls and the unequal proportion of those exposed to E, in the two post-stratification tables, lead to strong positive confounding. Second, as a reflection of the confounding the minimum cell entries in the two tables obtained after stratification are both much smaller (both equal to one, in fact) than half the minimum cell entry in the pooled table (equal to 19). Thus one can expect the estimate of the odds ratio to be considerably less precise than an estimate obtained from more balanced tables. Both effects can be mitigated by equalizing the ratio of cases to controls in those exposed and those not exposed to a confounder C, in which case we say the design is balanced for Factor C. The results could be represented as follows: Factor C+ Exposure E + - Factor C- Exposure E Pooled levels of C Exposure E + - + - Case Control Odds ratio II, II, Balancing or even equalizing cases and controls in each stratum does not eliminate confounding, as the following example illustrates: Factor C+ Exposure E + - Factor C- Exposure E + - Pooled levels of C Exposure E + - Case Control Odds ratio
GENERAL CONSIDERATIONS 103 However, using expression (3.1) and the balance in the design one can show that the odds ratio in the pooled table, p,, lies between unity and p, that is we have: Thus, in contrast to the unbalanced situation, where the confounding effects can be either positive or negative and where the pooled odds ratio can be the opposite side of unity from the within-stratum odds ratio, with a balanced design the expected pooled odds ratio is both on the same side of and closer to unity than the expected withinstratum odds ratio. An unstratified analysis will bias the odds ratio towards unity, unless the confounding and exposure variables are (conditional on disease status) independent, but not change the side of unity on which the odds ratio lies. Obviously the odds ratio of C with disease bears no relation to the true association. If a factor has been balanced, the data so generated give no information on-the association of that factor with disease. Interaction can still be estimated, however, as is discussed in 5 3.5. Balance, as described above, where the control series is chosen to ensure equal frequency of cases and controls in different strata, is sometimes referred to as frequency matching. On other occasions, where for each case a set of controls is chosen to have the same, or nearly the same, values of prescribed covariates, we speak of individual matching. In later chapters matching refers specifically to individual matching. Incorporation of matching factors in the analysis The purpose of matching, as we have just seen, is to control confounding and increase the lnformation per observation in the post-stratification analysis. Most studies, and certainly those of cancer, would match for age and sex, since both could confound the effect of most other factors. A large number of studies match on additional variables, often to the point where each case may be associated with a set of controls in an individual stratum. One purpose of this matching, as we have mentioned, is to improve the precision of the estimates of the relevant relative risks obtained from a stratified analysis. Some matching factors, such as place of residence or membership of a sibship, represent a complex of factors. Then, the purpose of the matching is to eliminate the confounding effect of a range of only vaguely specified variables, since the matching provides a stratification by these variables which would otherwise be difficult to perform because of their indeterminate nature. In these circumstances, matching can be an important way of eliminating bias in the risk estimate. The result given for a dichotomous matching variable can be extended without difficulty to any complexity of matching variables. The expected odds ratio resulting from an analysis incorporating the matching is always more extreme than the expected odds ratio obtained ignoring the matching (Seigel & Greenhouse, 1973). Now, the purpose of matching implies that the matching factors must a priori be considered as ones for which stratification would be necessary, that is, as confounding variables. It would follow that variables which have been used for matching in the design should be incorporated in the analysis as confounding variables. Until recently,
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WORLD HEALTH ORGANIZATION INTERNATI
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N.E. Breslow & N. E. Day (1980) Sta
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CONTENTS Foreword .................
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PREFACE Twenty years have elapsed s
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ACKNOWLEDGEMENTS Since the initial
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LIST OF PARTICIPANTS AT IARC WORKSH
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1.1 The case-control study in cance
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INTRODUCTION 15 a specific disease
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History INTRODUCTION 17 In 1926 Lan
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INTRODUCTION 19 day human affairs c
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INTRODUCTION 21 cording to age, sex
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INTRODUCTION 1.5 Planning The case
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INTRODUCTION 25 determinants of sur
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INTRODUCTION 27 like exposed subjec
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INTRODUCTION 29 warrants careful co
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INTRODUCTION 31 strata, and formati
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INTRODUCTION 33 in which at least 1
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INTRODUCTION 35 analytical techniqu
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INTRODUCTION 37 ity; is it understo
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INTRODUCTION 39 Hutchison, G. B. (1
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2. FUNDAMENTAL MEASURES OF DISEASE
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MEASURES OF DISEASE 43 operate prio
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MEASURES OF DISEASE 4 5 change is r
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MEASURES OF DISEASE 4 7 veillance s
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MEASURES OF DISEASE 49 Fig. 2.3 Age
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Page 54 and 55: MEASURES OF DISEASE Table 2.4 Cumul
Page 56 and 57: MEASURES OF DISEASE 55 exposed vers
Page 58 and 59: MEASURES OF DISEASE 57 Example: Fig
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Page 70 and 71: 2.7 Logical properties of the relat
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Page 82 and 83: MEASURES OF DISEASE 8 1 Plk P2 k R
Page 84 and 85: CHAPTER I11 GENERAL CONSIDERATIONS
Page 86 and 87: 86 BRESLOW & DAY 3.2 Criteria for a
Page 88 and 89: 88 BRESLOW & DAY Fig. 3.1 Relative
Page 90 and 91: 90 BRESLOW & DAY Considerations ext
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Page 94 and 95: 94 BRESLOW & DAY decreases breast c
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Page 98 and 99: 98 BRESLOW & DAY The confounding ef
Page 100 and 101: BRESLOW & DAY Comparison of w* with
Page 104 and 105: 104 BRESLOW & DAY there were limita
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Page 108 and 109: 1 08 BRESLOW & DAY 3. If a factor i
Page 110 and 111: 110 BRESLOW & DAY Table 3.6 Risk fo
Page 112 and 113: 112 BRESLOW & DAY risk for some fac
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Page 116 and 117: 116 BRESLOW & DAY Boice, J.D. & Mon
Page 118 and 119: 118 BRESLOW & DAY Report of the Sur
Page 120 and 121: 4. CLASSICAL METHODS OF ANALYSIS OF
Page 122 and 123: ANALYSIS OF GROUPED DATA Table 4.1
Page 124 and 125: ANALYSIS OF GROUPED DATA 125 such a
Page 126 and 127: Estimation of q ANALYSIS OF GROUPED
Page 128 and 129: ANALYSIS OF GROUPED DATA 129 for th
Page 130 and 131: ANALYSIS OF GROUPED DATA 131 analog
Page 132 and 133: ANALYSIS OF GROUPED DATA 133 Referr
Page 134 and 135: ANALYSIS OF GROUPED DATA 135 Halper
Page 136 and 137: ANALYSIS OF GROUPED DATA 137 are pa
Page 138 and 139: ANALYSIS OF GROUPED DATA 1.39 signi
Page 140 and 141: ANALYSIS OF GROUPED DATA 141 strata
Page 142 and 143: ANALYSIS OF GROLIPED DATA 143 appro
Page 144 and 145: ANALYSIS OF GROLIPED DATA 145 Table
Page 146 and 147: ANALYSIS OF GROUPED DATA Exposure l
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Page 150 and 151: ANALYSIS OF GROUPED DATA 151 Alcoho
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ANALYSIS OF GROUPED DATA 153 relati
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ANALYSIS OF GROUPED DATA 155 obtain
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ANALYSIS OF GROUPED DATA 157 Gart,
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ANALYSIS OF GROUPED DATA 159 Cov(x,
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CHAPTER V CLASSICAL METHODS OF ANAL
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164 BRESLOW & DAY 5.2 Matched pairs
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166 BRESLOW & DAY Approximate confi
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168 BRESLOW & DAY where 2.42 = F.,,
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170 BRESLOW & DAY The first and las
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BRESLOW & DAY This is a special cas
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ANALYSIS OF MATCHED DATA Case Expos
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176 BRESLOW & DAY or limits of 3.8-
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BRESLOW & DAY Table 5.3 Data layout
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180 BRESLOW & DAY Case : control ra
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182 BRESLOW & DAY = 11.82, from whi
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184 BRESLOW & DAY observed and expe
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BRESLOW & DAY Their solution, obtai
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188 BRESLOW & DAY Miettinen, 0. S.
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6. UNCONDITIONAL LOGISTIC REGRESSIO
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LOGISTIC REGRESSION FOR LARGE STRAT
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LOGISPIC REGRESSION FOR LARGE STRAT
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6.8 Regression adjustment for confo
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6.9 Analysis of continuous data LOG
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7. CONDITIONAL LOGISTIC REGRESSION
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LOGISTIC REGRESSION FOR MATCHED SET
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LOGIS-I-IC REGRESSION FOR MATCHED S
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Table 7.7 Matched multivariate anal
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Table 7.9 (contd) C. Dose, duration
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LOGIS'TIC REGRESSION FOR MATCHED SE
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Table 7.12 Coefficients (f standard
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APPENDIX I AGE (YRS) ALCOHOL (GM/DA
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APPENDIX 11: GROUPED DATA FROM THE
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APPENDIX II YEAR OF DEATH AGE AT DE
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APPENDIX II YEAR OF DEATH AGE AT DE
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APPENDIX 111: MATCHED DATA FROM THE
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292 APPENDIX Ill CASE OR CONTROL AG
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294 APPENDIX Ill CASE OR CONTROL AG
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296 APPENDIX Ill CASE OR CONTROL CA
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APPENDIX IV MAIN PROGRAM .C MASTER
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300 APPENDIX IV 103 FORMAT(1H ,'NUM
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302 APPENDIX IV C UPON CONVERGENCE
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APPENDIX IV MODEL WITH 2 VARIABLES:
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APPENDIX IV MODEL WITH 4 VARIABLES:
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APPENDIX V MAIN PROGRAM DIMENSION N
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31 0 APPENDIX V C REFERENCES : C N.
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APPENDIX V CALL SYMINV~COVI,NP,COV,
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APPENDIX V SUBROUTINE SYMINVCA, N,
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APPENDIX V SUBROUTINE TWIDL(X, Y, Z
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APPENDIX V MODEL WITH SINGLE VARIAB
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APPENDIX V MODEL WITH 3 VARIABLES:
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APPENDIX VI LISTING OF PROGRAM LOGO
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C C C C C C APPENDIX VI SUBPROGRAM
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APPENDIX VI SUBROUTINE CALC(NTAB,P,
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328 APPENDIX VI SUBROUTINE MYSTCT,
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APPENDIX VI DOUBLE PRECISION FUNCTI
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332 APPENDIX VI C C C C C C REDUCE
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MODEL WITH LINEAR EFFECT OF YEAR RE
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TABLE A 0 E 31 12 10.64 32 4 5.12 3
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0 03 TABLE A B 0 E 0 E 9 1 6 7.06 6
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340 SUBJECT INDEX Biological monito
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342 SUBJECT INDEX Confounding risk
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344 SUBJECT INDEX Grouped data anal
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346 SUBJECT INDEX Matched case-cont
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348 SUB.IECT INDEX Poisson variabil
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350 SUB-IECT INDEX Tobacco consumpt
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