Biostatistical Methods: The Assessment of Relative Risks, Second Edition (Wiley Series in Probability and Statistics)

Cover......Page 1
S Title: Biostatistical Methods......Page 2
Series Editors......Page 3
Title: Biostatistical Methods: The Assessment of Relative Risks......Page 4
ISBN 978-0-470-50822-0......Page 5
Dedication......Page 6
Contents......Page 7
Preface......Page 18
PREFACE TO FIRST EDITION......Page 20
1.1 STATISTICS AND THE SCIENTIFIC METHOD......Page 23
1.2 BIOSTATISTICS......Page 24
1.3 NATURAL HISTORY OF DISEASE PROGRESSION......Page 25
1.4 TYPES OF BIOMEDICAL STUDIES......Page 27
1.5 STUDIES OF DIABETIC NEPHROPATHY......Page 29
2 Relative Risk Estimates and Tests for Independent Groups......Page 35
2.1.2 Binomial Distribution and Large Sample Approximations......Page 36
2.1.3.2 Logit Confidence Limits......Page 38
2.1.3.3 Complementary log-log Confidence Limits......Page 39
2.1.3.4 Test-inverted Confidence Limits......Page 40
2.2 MEASURES OF DIFFERENTIAL OR RELATIVE RISK......Page 41
2.3.1 Risk Difference......Page 45
2.3.2 Relative Risk......Page 46
2.3.3 Odds Ratio......Page 48
2.4.2 Conditional Hypergeometric Likelihood......Page 50
2.4.4 Asymptotically Unbiased Estimates......Page 52
2.5.1 Confidence Limits......Page 54
2.5.2 Fisher-Irwin Exact Test......Page 55
2.6.1 General Considerations......Page 58
2.6.2 Unconditional Test......Page 60
2.6.3 Conditional Mantel-Haenszel Test......Page 61
2.6.4 Cochran\'s Test......Page 62
2.6.6 Test-Based Confidence Limits......Page 64
2.6.7 Continuity Correction......Page 65
2.6.8.1 Equivalence......Page 67
2.6.8.2 Noninferiority......Page 68
2.7 SAS PROC FRECM......Page 70
2.8.1 Attributable Risk Fraction......Page 74
2.8.2 Population Attributable Risk......Page 75
2.9.1 Multinomial Distribution and Large Sample Approximation......Page 78
2.9.2 Pearson Chi-Square Test......Page 79
2.9.3 Pearson Goodness-of-Fit Test......Page 81
2.9.4 Logits......Page 82
2.10.1 Large Sample Test of Proportions......Page 83
2.10.2 The Pearson Contingency Chi-Square Test......Page 84
2.10.4 Rank Tests: Cochran-Mantel-Haenszel Mean Scores Test......Page 85
2.11.1 The Pearson Test......Page 89
2.11.4 Multiple Tests......Page 91
2.11.5 Rank and Correlation Tests......Page 95
2.11.6 The Cochran-Armitage Test for Trend......Page 96
2.12 PROBLEMS......Page 98
3 Sample Size, Power, and Efficiency......Page 107
3.1 ESTIMATION PRECISION......Page 108
3.2.1 Type I and II Errors and Power......Page 109
3.2.2 Power and Sample Size......Page 112
3.3 TEST FOR TWO PROPORTIONS......Page 114
3.3.1 Power of the Z-Test......Page 115
3.3.2 Relative Risk and Odds Ratio......Page 117
3.3.3 Equivalence......Page 118
3.3.4 Noninferiority......Page 120
3.4.1 Noncentral Chi-Square Distribution......Page 121
3.4.2.1 A Multinomial Distribution......Page 122
3.4.2.2 R x C Contingency Table......Page 123
3.4.3 The Mean Score (Rank) Test......Page 124
3.4.4 The Cochran-Armitage Test of Trend......Page 126
3.5.1 Test for Two Proportio......Page 128
3.5.2 Wilcoxon Mann-Whitney Test......Page 129
3.6.1 Pitman Efficiency......Page 130
3.6.2 Asymptotic Relative Efficiency......Page 132
3.6.3 Estimation Efficiency......Page 133
3.6.4 Stratified Versus Unstratified Analysis of Risk Differences......Page 134
3.7 PROBLEMS......Page 137
4.1 INTRODUCTION......Page 141
4.2.2 Marginal Unadjusted Analysis......Page 143
4.2.3 Mantel-Haenszel Test......Page 145
4.2.4 Cochran\'s Test......Page 147
4.3.1 Mantel-Haenszel Estimates......Page 148
4.3.2 Test-Based Confidence Limits......Page 149
4.3.3 Large Sample Variance of the Log Odds Ratio......Page 150
4.3.4 Maximum Likelihood Estimate of the Common Odds Ratio......Page 152
4.3.5 Minimum Variance Linear Estimators......Page 153
4.3.6 MVLE Versus Mantel-Haenszel Estimates......Page 156
4.3.7 SAS PRQC FREQ......Page 157
4.4 NATURE OF COVARIATE ADJUSTMENT......Page 158
4.4.1 Confounding and Effect Modification......Page 159
4.4.2 Stratification Adjustment and Regression Adjustment......Page 160
4.4.3 When Does Adjustment Matter?......Page 162
4.5.1 Multivariate Null Hypothesis......Page 167
4.5.2 Omnibus Test......Page 168
4.5.3 Multiple Tests......Page 170
4.5.4 Partitioning of the Omnibus Alternative Hypothesis......Page 171
4.6 TESTS OF HOMOGENEITY......Page 172
4.6.1 Contrast Test of Homogeneity......Page 173
4.6.2 Cochran\"s Test of Homogeneity......Page 175
4.6.3 Zelen\'s Test......Page 176
4.6.4 Breslow-Day Test for Odds Ratios......Page 177
4.7.1 Restricted Alternative Hypothesis of Association......Page 178
4.7.2 Radhakrishna Family of Efficient Tests of Association......Page 180
4.8.1 Family of Tests......Page 185
4.8.2 Asymptotic Relative Efficiency......Page 187
4.9.1 Maximin Efficiency......Page 191
4.9.2 Gastwirth Scale Robust Test......Page 192
4.9.3 Wei-Lachin Test of Stochastic Ordering......Page 193
4.9.4 Comparison of Weighted Tests......Page 196
4.10.1 Measurement Error Model......Page 197
4.10.2 Stratified-Adjusted Estimates from Multiple 2 X 2 Tables......Page 199
4.11 POWER AND SAMPLE SIZE FOR TESTS OF ASSOCIATION......Page 205
4.11.1 Power Function of the Radhakrishna Family......Page 206
4.11.2 Power and Sample Size for Cochran\'s Test......Page 208
4.12.1 Cochran-Mantel-Haenszel Tests......Page 210
4.12.2 Stratified-Adjusted Estimate......Page 211
4.12.4 Stratified Mean Scores Estimate and Test......Page 213
4.12.5 Stratified Cochran-Armitage Test of Trend......Page 214
4.13 PROBLEMS......Page 215
5.1 UNMATCHED CASE-CONTROL (RETROSPECTIVE) SAMPLING......Page 223
5.1.1 Odds Ratio......Page 224
5.1.2 Relative Risk......Page 226
5.1.3 Attributable Risk......Page 227
5.2 MATCHING......Page 228
5.2.1 Frequency Matching......Page 229
5.2.2 Matched Pairs Design: Cross-Sectional or Prospective......Page 230
5.3.1 Exact Test......Page 233
5.3.2 McNemar\'s Large Sample Test......Page 234
5.3.3 SAS PROC FREQ......Page 235
5.4.1 Conditional Odds Ratio......Page 236
5.4.2.1 Exact Limits......Page 237
5.4.2.2 Large Sample Limits......Page 238
5.4.4 Mantel-Haenszel Analysis......Page 239
5.4.5 Relative Risk for Matched Pairs......Page 240
5.4.6 Attributable Risk for Matched Pairs......Page 241
5.5 PAIR-MATCHED RETROSPECTIVE STUDY......Page 242
5.5.1 Conditional Odds Ratio......Page 243
5.5.2 Relative Risks from Matched Retrospective Studies......Page 244
5.6.1 Unconditional Power Function......Page 245
5.6.2 Conditional Power Function......Page 246
5.6.3 Other Approaches......Page 247
5.6.4 Matching Efficiency......Page 248
5.7.1 Pair and Member Stratification......Page 249
5.7.2 Stratified Mantel-Haenszel Analysis......Page 250
5.7.4.1 Conditional Odds Ratio......Page 251
5.7.4.2 Marginal Relative Risk......Page 252
5.7.4.3 Robust Tests......Page 253
5.8 MULTIPLE MATCHING: MANTEL-HAENSZEL ANALYSIS......Page 254
5.9.2 Bowker\'s Test of Symmetry......Page 256
5.10.1 Duplicate Gradings, Binary Characteristic......Page 257
5.10.2 Duplicate Gradings, Polychotomous or ordinal Characteristic......Page 259
5.11 PROBLEMS......Page 261
6.1 BINOMIAL......Page 268
6.2.1 MLEs And Their Asymptotic Distribution......Page 270
6.2.2 Logit Model......Page 271
6.2.3 Tests of Significance......Page 275
6.2.3.2 Likelihood Ratio Test......Page 276
6.2.3.3 Efficient Score Test......Page 277
6.3 2x2 TABLE, CONDITIONALLY......Page 278
6.4 SCORE-BASED ESTIMATE......Page 279
6.5.1 Conditional Mantel-Haenszel Test and the Score Estimate......Page 281
6.5.2 Unconditional Cochran Test as a C(a) Test......Page 282
6.6.1 Unconditional Logit Model......Page 284
6.6.2 Conditional Logit Model......Page 286
6.6.5 Matched Case-Control Study......Page 289
6.7.1 Newton-Raphson (or Newton\'s Method)......Page 290
6.7.2 Fisher Scoring (Method of Scoring)......Page 291
6.8 PROBLEMS......Page 296
7.1.1 General Logistic Regression Model......Page 304
7.1.2 Logistic Regression and Binomial Logit Regression......Page 307
7.1.3 SAS Procedures......Page 309
7.1.4 Stratified 2 X 2 Tables......Page 312
7.1.5 Family of Binomial Regression Models......Page 314
7.2.1 Model Coefficients and Odds Ratios......Page 315
7.2.2 Class Effects in PROC LOGISTIC......Page 321
7.2.3 Partial Regression Coefficients......Page 323
7.2.4 Model Building: Stepwise Procedu......Page 325
7.2.5 Disproportionate Sampling......Page 328
7.2.6 Unmatched Case-Control Study......Page 329
7.3.1.2 Test of Model Components......Page 330
7.3.2.1 Model Test......Page 331
7.3.3 Wald Tests......Page 333
7.3.4 SAS PROC GENMOD......Page 335
7.3.5 Robust Inferences......Page 338
7.3.6.1 Univariate Effects......Page 342
7.3.6.2 Multiple Categorical Effects......Page 343
7.3.6.3 Models Adjusted for Multiple Factors......Page 345
7.4 INTERACTIONS......Page 346
7.4.1 Qualitative-Qualitative Covariate Interaction......Page 347
7.4.2 Interactions with a Quantitative Covariate......Page 351
7.5.1 Squared Error Loss......Page 354
7.5.2 Entropy Loss......Page 355
7.6.1 Conditional Logistic Model......Page 358
7.6.2 Matched Retrospective Study......Page 361
7.6.4 Allowing for Clinic Effects in a Randomized Trial......Page 362
7.6.5 Robust Inference......Page 366
7.6.7 Power and Sample Size......Page 369
7.6.7.1 Quantitative Covariate......Page 371
7.6.7.3 Multivariate Model......Page 372
7.7.1 Multinomial Logistic Model......Page 373
7.7.2 Proportional Odds Model......Page 378
7.8.1 Random Intercept Model......Page 380
7.8.2 Random Treatment Effect......Page 382
7.9 MODELS FOR MULTIVARIATE OR REPEATED MEASURES......Page 384
7.9.1 GEE Repeated Measures Models......Page 385
7.9.2 GEE Multivariate Models......Page 389
7.9.3 Random Coefficient Models......Page 390
7.10 PROBLEMS......Page 391
8 Analysis of Count Data......Page 402
8.1.2 Doubly Homogeneous Poisson Model......Page 403
8.1.3 Relative Risks......Page 405
8.1.4 Violations of the Homogeneous Poisson Assumptions......Page 409
8.2.1 Two-Stage Random Effects Model......Page 410
8.2.2 Relative Risks......Page 413
8.3.1 Homogeneous Poisson Regression Model......Page 414
8.3.3 Applications of Poisson Regression......Page 422
8.4.1 Quasi-likelihood Overdispersed Poisson Regression......Page 423
8.4.2 Robust Inference Using the Information Sandwich......Page 425
8.4.3 Zeros-inflated Poisson Regression Model......Page 428
8.5 CONDITIONAL POISSON REGRESSION FOR MATCHED SETS......Page 431
8.6.1 The Negative Binomial Distribution......Page 433
8.6.2 Negative Binomial Regression Model......Page 435
8.7.1 Poisson Models......Page 437
8.7.2 Negative Binomial Models......Page 439
8.8 MULTIPLE OUTCOMES......Page 440
8.9 PROBLEMS......Page 441
9 Analysis of Event-Time Data......Page 449
9.1.1 Hazard and Survival Function......Page 450
9.1.2 Censoring at Random......Page 451
9.1.3 Kaplan-Meier Estimator......Page 452
9.1.4 Estimation of the Hazard Function......Page 455
9.1.5 Comparison of Survival Probabilities for Two Groups......Page 456
9.2 LIFETABLE CONSTRUCTION......Page 461
9.2.1 Discrete Distributions: Actuarial Lifetable......Page 463
9.2.2 Modified Kaplan-Meier Estimator......Page 464
9.2.3 SAS PROC LIFETEST: Survival Estimation......Page 466
9.3.1 Weighted Mantel-Haenszel Test......Page 469
9.3.2 Mantel-Logrank Test......Page 470
9.3.3 Modified Wilcoxon Test......Page 471
9.3.4 G^p Family of Tests......Page 472
9.3.5 Measures of Association......Page 473
9.3.6 SAS PROC LIFETEST: Tests of Significance......Page 475
9.4.1 Cox\'s Proportional Hazards Model......Page 476
9.4.2 Stratified Models......Page 480
9.4.4 Fitting the Model......Page 481
9.4.5 Robust Inference......Page 483
9.4.6 Adjustments for Tied Observations......Page 484
9.4.6.1 Discrete and Grouped Failure Time Data......Page 485
9.4.6.2 Cox\'s Adjustment for Ties......Page 486
9.4.6.4 Peto-Breslow Adjustment for Ties......Page 487
9.4.7 Survival Function Estimation......Page 488
9.4.8 Model Assumptions......Page 489
9.4.9 Explained Variation......Page 491
9.4.10 SAS PROC PHREG......Page 493
9.5.1 Exponential Survival......Page 503
9.5.2 Cox\'s Proportional Hazards Model......Page 506
9.5.2.1 Qualitative Covariate......Page 507
9.5.2.2 Quantitative Covariate......Page 508
9.5.2.4 Maximum Information Design......Page 509
9.6 ADDITIONAL MODELS......Page 511
9.6.1 Competing Risks......Page 512
9.6.2 Interval Censoring......Page 515
9.6.3 Parametric Models......Page 516
9.6.4 Multiple Event Times......Page 517
9.7 ANALYSIS OF RECURRENT EVENTS......Page 519
9.7.1 Counting Process Formulation......Page 520
9.7.2 Nelson-Aalen Estimator, Kernel Smoothed Esti......Page 522
9.7.3 Aalen-Gi11 Test Statistics......Page 524
9.7.4 Multiplicative Intensity Model......Page 527
9.7.5 Robust Estimation: Proportional Rate Models......Page 531
9.7.6 Stratified Recurrence Models......Page 532
9.8 PROBLEMS......Page 533
A.1.1 Notation......Page 554
A.1.2 Matrices......Page 555
A.2.1 Univariate Case......Page 556
A.2.2 Multivariate Case......Page 559
A.3.1 Univariate Case......Page 560
A.3.2 Multivariate Case......Page 561
A.4.1 Convergence in Distribution......Page 562
A.4.3 Convergence in Distribution of Transformations......Page 563
A.5.1 Ordinary Least Squares......Page 565
A.5.3 Weighted Least Squares......Page 567
A.5.4 Iteratively Reweighted Least Squares......Page 569
A.6.1 Estimating Equation......Page 570
A.6.2 Efficient Score......Page 571
A.6.3 Fisher\'s Information Function......Page 572
A.6.4 Cramer-Rao Inequality: Efficient Estimators......Page 574
A.6.5 Asymptotic Distribution of the Efficient Score and the MLE......Page 575
A.6.6 Consistency and Asymptotic Efficiency of the MLE......Page 576
A.6.8 Invariance Under Transformations......Page 577
A.6.9 Independent But Not Identically Distributed Observations......Page 579
A.7.1 Wald Tests......Page 580
A.7.1.3 Test of a Linear Hypothesis......Page 581
A. 7.2.1 Composite Test......Page 582
X4.7.2.2 Test of a Subhypothesis......Page 583
A.7.3.2 Test of a Subhypothesis: C(a) Tests......Page 584
A. 7.3.3 Relative Efficiency Versus the Likelihood Ratio Test......Page 586
A.8 EXPLAINED VARIATION......Page 588
A.8.1 Squared Error Loss......Page 589
A.8.2 Residual Variation......Page 591
A.8.4 Madalla\'s RLR......Page 592
A.9.1 Information Sandwich......Page 593
A.9.1.1 Correct Model Specification......Page 594
A.9.1.2 Incorrect Model Specification......Page 595
A.10 GENERALIZED LINEAR MODELS AND QUASI-LIKELIHOOD......Page 598
A.10.1 Generalized Linear Models......Page 599
A.10.2 Exponential Family of Models......Page 600
A-10.3 Deviance and the Chi-Square Goodness of Fit......Page 603
A.10.4 Quasi-likelihood......Page 604
A.11 GENERALIZED ESTIMATING EQUATIONS (GEE)......Page 607
1. Independence......Page 608
4. Unstructured......Page 609
References......Page 611
Author Index......Page 635
Index......Page 641
List of Publications of WILEY SERIES IN PROBABILITY AND STATISTICS......Page 654