Preface vii
1 Introduction 1
1.1 Survival data . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Longitudinal data . . . . . . . . . . . . . . . . . . . . . . . . 14
2 Probabilistic background 17
2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Martingales . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 Counting processes . . . . . . . . . . . . . . . . . . . . . . . 23
2.4 Marked point processes . . . . . . . . . . . . . . . . . . . . 30
2.5 Large-sample results . . . . . . . . . . . . . . . . . . . . . . 34
2.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3 Estimation for filtered counting process data 49
3.1 Filtered counting process data . . . . . . . . . . . . . . . . . 49
3.2 Likelihood constructions . . . . . . . . . . . . . . . . . . . . 62
3.3 Estimating equations . . . . . . . . . . . . . . . . . . . . . . 70
3.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4 Nonparametric procedures for survival data 81
4.1 The Kaplan-Meier estimator . . . . . . . . . . . . . . . . . . 81
4.2 Hypothesis testing . . . . . . . . . . . . . . . . . . . . . . . 86
4.2.1 Comparisons of groups of survival data . . . . . . . 86
xii Contents
4.2.2 Stratified tests . . . . . . . . . . . . . . . . . . . . . 93
4.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5 Additive Hazards Models 103
5.1 Additive hazardsmodels . . . . . . . . . . . . . . . . . . . . 108
5.2 Inference for additive hazardsmodels . . . . . . . . . . . . . 116
5.3 Semiparametric additive hazardsmodels . . . . . . . . . . . 126
5.4 Inference for the semiparametric hazards model . . . . . . . 135
5.5 Estimating the survival function . . . . . . . . . . . . . . . 146
5.6 Additive ratemodels . . . . . . . . . . . . . . . . . . . . . . 149
5.7 Goodness-of-fit procedures . . . . . . . . . . . . . . . . . . . 151
5.8 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
5.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
6 Multiplicative hazards models 175
6.1 The Coxmodel . . . . . . . . . . . . . . . . . . . . . . . . . 181
6.2 Goodness-of-fit procedures for the Cox model . . . . . . . . 193
6.3 Extended Cox model with time-varying regression effects . . 205
6.4 Inference for the extended Coxmodel . . . . . . . . . . . . 213
6.5 A semiparametric multiplicative hazards model . . . . . . . 218
6.6 Inference for the semiparametric multiplicative model . . . 224
6.7 Estimating the survival function . . . . . . . . . . . . . . . 226
6.8 Multiplicative ratemodels . . . . . . . . . . . . . . . . . . . 227
6.9 Goodness-of-fit procedures . . . . . . . . . . . . . . . . . . . 228
6.10 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
6.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
7 Multiplicative-Additive hazards models 249
7.1 The Cox-Aalen hazardsmodel . . . . . . . . . . . . . . . . . 251
7.1.1 Model and estimation . . . . . . . . . . . . . . . . . 252
7.1.2 Inference and large sample properties . . . . . . . . 255
7.1.3 Goodness-of-fit procedures . . . . . . . . . . . . . . . 260
7.1.4 Estimating the survival function . . . . . . . . . . . 266
7.1.5 Example . . . . . . . . . . . . . . . . . . . . . . . . . 270
7.2 Proportional excess hazardsmodel . . . . . . . . . . . . . . 273
7.2.1 Model and score equations . . . . . . . . . . . . . . . 274
7.2.2 Estimation and inference . . . . . . . . . . . . . . . 276
7.2.3 Efficient estimation . . . . . . . . . . . . . . . . . . . 280
7.2.4 Goodness-of-fit procedures . . . . . . . . . . . . . . . 283
7.2.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . 284
7.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
8 Accelerated failure time and transformation models 293
8.1 The accelerated failure time model . . . . . . . . . . . . . . 294
8.2 The semiparametric transformationmodel . . . . . . . . . . 298
Contents xiii
8.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
9 Clustered failure time data 313
9.1 Marginal regression models for clustered failure time data . 314
9.1.1 Working independence assumption . . . . . . . . . . 315
9.1.2 Two-stage estimation of correlation . . . . . . . . . . 327
9.1.3 One-stage estimation of correlation . . . . . . . . . . 330
9.2 Frailtymodels . . . . . . . . . . . . . . . . . . . . . . . . . . 334
9.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338
10 Competing Risks Model 347
10.1 Product limit estimator . . . . . . . . . . . . . . . . . . . . 351
10.2 Cause specific hazardsmodeling . . . . . . . . . . . . . . . . 356
10.3 Subdistribution approach . . . . . . . . . . . . . . . . . . . 361
10.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370
11 Marked point process models 375
11.1 Nonparametric additive model for longitudinal data . . . . 380
11.2 Semiparametric additive model for longitudinal data . . . . 389
11.3 Efficient estimation . . . . . . . . . . . . . . . . . . . . . . . 393
11.4 Marginalmodels . . . . . . . . . . . . . . . . . . . . . . . . 397
11.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408
A Khmaladze’s transformation 411
B Matrix derivatives 415
C The Timereg survival package for R 417
Bibliography 453
Index 467

 

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