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

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LOGISTIC REGRESSION FOR MATCHED SETS 265 factors which are possibly linked to endometrial cancer. Given that a woman is already at elevated risk from her history of gall-bladder disease, obesity, or non-oestrogen drug use, the further increase in risk from use of oestrogens is not nearly as important as when she is not exposed to other risk factors. This same observation, that oestrogen use interacts negatively with traditional risk factors for endometrial cancer, such as hypertension and obesity, has been made in other case-control studies (Smith et al., 1975). It suggests that the effects of oestrogen use are more likely to combine additively rather than multiplicatively with those of other factors. Another interesting feature of the relationship, which could not be investigated in the Los Angeles study, is that the excess risk is much smaller among ex-users compared with continuing users of oestrogen (Jick et al., 1979). So far our analysis has accounted only for the fact of oestrogen use and not of dose or duration. Unfortunately, information about one or both of these items was lacking for nine cancer cases, leading to the exclusion of the corresponding matched sets from the analysis, and for one control in each of seven of the remaining 54 sets. Moreover, the drug tended to be administered at one of a few standard doses, which precluded analysis of this variable as a true continuous variable. Instead both dose and duration were treated as ordered categorical variables, and arbitrary scale values were assigned to the increasing levels for regression analysis of trends (see Tables 7.2 and 7.6). A series of analyses which investigate the effect of dose and/or duration of conjugated oestrogen exposure on risk is presented in Table 7.9. In part A of the table we first fit the main effect for oestrogen exposure followed by a single variable DOS representing the trend in risk with coded dose level. Since women with EST = 1 but DOS = 0 use oestrogens but not the conjugated variety, the coefficient of EST determines the relative risk for women taking only non-conjugated oestrogens, exp(1.451) = 4.3. Estimated relative risks for the three dose levels of conjugated oestrogen are exp(1.451+ 0.402) = 6.4, exp(1.451+ 2 x 0.402) = 9.5 and exp(1.451+ 3 x 0.402) = 14.3, respectively. The third model is a generalization of the second in that the effects of the individual dose levels are allowed to vary independently rather than being determined by the trend. While the estimated relative risks for dose levels 1 and 2 are rather similar, there is no strong evidence for a deviation from the fitted trend (y$ = 2.41, p = 0.30). As shown in Model 4, there is a significant trend with duration, even after accounting for the dose effects. Part B of the table considers in a similar way the effect of duration of exposure. Here there is a smooth progression in risk, and the fit of the linear trend in coded duration level seems quite adequate 012 = 1.11, p = 0.78). The trend in dose continues to be significant even after adjustment for duration (Model 3, Part B). In Part C of the table we simultaneously fit separate effects for both dose and duration. Since the sums of both DOSl + DOS2 + DOS3 and DUR1 + DUR2 + DUR3 + DUR4 equal the variable CEST defined above, it was necessary to drop one of these indicator variables from the equation in order to avoid linear dependence among the variables and to obtain unique estimates of all coefficients; this explains the absence of DOSl from the list of variables. Comparing Model 2 with Model 1 shows that the effects of dose and duration are reasonably multiplicative; addition of the linear interaction term results in only a slight improvement in goodness of fit(yi = 0.59, p = 0.44). In Models 3-6 we consider the effects of some of the other risk factors after
Table 7.9 Multivariate analysis of effects of dose and duration of conjugated oestrogens: Los Angeles study of endometrial cancer - Model NO. of Goodness Score Regression coefficients for each variable in the equation (standardized coefficients in parentheses) a para- of fit testb m (I, meters G 6 z A. Effect of dose Po EST DOS DOS1 DOS2 DOS3 DUR 1 1 139.86 27.22 2.088 (4.60) 2 2 135.63 4.19 1.451 0.402 (2.59) (2.01) 3 4 133.20 2.41 1.856 0.029 0.023 1.141 (2.74) (0.05) (0.04) (1.80) 4 5 128.32 4.82 1.987 -1 .I01 -1.116 4.013 0.420 (2.86) (-1.33) (-1.32) (-0.02) (2.15) B. Effect of duration EST DUR DUR1 DUR2 DUR3 DUR4 DOS 1 .2 134.84 4.91" 1.431 0.309 (2.58) (2.17) 2 5 133.76 1.11 1.868 -0.418 0.122 0.596 0.899 (2.73) (-0.58) (0.19) (0.88) (1.43) 3 6 129.52 4.22 1.946 -1.655 4.876 4.586 4.296 0.578 (2.83) (-1.70) (-1.08) (-0.65) (4.34) (2.01)
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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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MEASURES OF DISEASE t A (t) = 2 l(n
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MEASURES OF DISEASE Table 2.4 Cumul
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MEASURES OF DISEASE 55 exposed vers
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MEASURES OF DISEASE 57 Example: Fig
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MEASURES OF DISEASE 59 explore thes
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31 5 42.5 47.5 52.5 57.5 62.5 67.5
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MEASURES OF DISEASE 63 Fig. 2.8 Rat
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MEASURES OF DISEASE 65 Fig. 2.9 Age
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MEASURES OF DISEASE 67 Table 2.8 Jo
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2.7 Logical properties of the relat
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MEASURES OF DISEASE 71 Example: Sup
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MEASURES OF DISEASE 73 or similar b
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MEASURES OF DISEASE 75 categories i
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MEASURES OF DISEASE 77 RAR = AR2-AR
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MEASURES OF DISEASE 79 Court Brown,
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MEASURES OF DISEASE 8 1 Plk P2 k R
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CHAPTER I11 GENERAL CONSIDERATIONS
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86 BRESLOW & DAY 3.2 Criteria for a
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88 BRESLOW & DAY Fig. 3.1 Relative
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90 BRESLOW & DAY Considerations ext
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92 BRESLOW & DAY of this type can b
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94 BRESLOW & DAY decreases breast c
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96 BRESLOW & DAY E and those not ex
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98 BRESLOW & DAY The confounding ef
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BRESLOW & DAY Comparison of w* with
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Factor C+ Exposure E + - BRESLOW &
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104 BRESLOW & DAY there were limita
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106 BRESLOW & DAY to have a strong
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1 08 BRESLOW & DAY 3. If a factor i
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110 BRESLOW & DAY Table 3.6 Risk fo
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112 BRESLOW & DAY risk for some fac
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114 BRESLOW & DAY an additional cat
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116 BRESLOW & DAY Boice, J.D. & Mon
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118 BRESLOW & DAY Report of the Sur
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4. CLASSICAL METHODS OF ANALYSIS OF
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ANALYSIS OF GROUPED DATA Table 4.1
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ANALYSIS OF GROUPED DATA 125 such a
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Estimation of q ANALYSIS OF GROUPED
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ANALYSIS OF GROUPED DATA 129 for th
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ANALYSIS OF GROUPED DATA 131 analog
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ANALYSIS OF GROUPED DATA 133 Referr
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ANALYSIS OF GROUPED DATA 135 Halper
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ANALYSIS OF GROUPED DATA 137 are pa
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ANALYSIS OF GROUPED DATA 1.39 signi
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ANALYSIS OF GROUPED DATA 141 strata
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ANALYSIS OF GROLIPED DATA 143 appro
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ANALYSIS OF GROLIPED DATA 145 Table
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ANALYSIS OF GROUPED DATA Exposure l
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ANALYSIS OF GROUPED DATA 149 Nor wi
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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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Page 212 and 213: LOGISTIC REGRESSION FOR LARGE STRAT
Page 222 and 223: 6.8 Regression adjustment for confo
Page 224 and 225: 6.9 Analysis of continuous data LOG
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Page 246 and 247: LOGISTIC REGRESSION FOR MATCHED SET
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Page 260 and 261: Table 7.7 Matched multivariate anal
Page 264 and 265: Table 7.9 (contd) C. Dose, duration
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Page 272 and 273: Table 7.12 Coefficients (f standard
Page 278 and 279: APPENDIX I AGE (YRS) ALCOHOL (GM/DA
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Page 282 and 283: APPENDIX II YEAR OF DEATH AGE AT DE
Page 284 and 285: APPENDIX II YEAR OF DEATH AGE AT DE
Page 286 and 287: APPENDIX 111: MATCHED DATA FROM THE
Page 288 and 289: 292 APPENDIX Ill CASE OR CONTROL AG
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Page 292 and 293: 296 APPENDIX Ill CASE OR CONTROL CA
Page 294 and 295: APPENDIX IV MAIN PROGRAM .C MASTER
Page 296 and 297: 300 APPENDIX IV 103 FORMAT(1H ,'NUM
Page 298 and 299: 302 APPENDIX IV C UPON CONVERGENCE
Page 300 and 301: APPENDIX IV MODEL WITH 2 VARIABLES:
Page 302 and 303: APPENDIX IV MODEL WITH 4 VARIABLES:
Page 304 and 305: APPENDIX V MAIN PROGRAM DIMENSION N
Page 306 and 307: 31 0 APPENDIX V C REFERENCES : C N.
Page 308 and 309: APPENDIX V CALL SYMINV~COVI,NP,COV,
Page 310 and 311: 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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