Dynamic Regression Models for Survival Data (eBook)

Preface 7
Contents 10
Introduction 13
1.1 Survival data 13
1.2 Longitudinal data 26
Probabilistic background 29
2.1 Preliminaries 29
2.2 Martingales 32
2.3 Counting processes 35
2.4 Marked point processes 42
2.5 Large-sample results 46
2.6 Exercises 56
Estimation for filtered counting process data 61
3.1 Filtered counting process data 61
3.2 Likelihood constructions 74
3.3 Estimating equations 82
3.4 Exercises 86
Nonparametric procedures for survival data 92
4.1 The Kaplan-Meier estimator 92
4.2 Hypothesis testing 97
4.3 Exercises 106
Additive Hazards Models 113
5.1 Additive hazards models 118
5.2 Inference for additive hazards models 126
5.3 Semiparametric additive hazards models 136
5.4 Inference for the semiparametric hazards model 145
5.5 Estimating the survival function 156
5.6 Additive rate models 159
5.7 Goodness-of-fit procedures 161
5.8 Example 169
5.9 Exercises 175
Multiplicative hazards models 184
6.1 The Cox model 190
6.2 Goodness-of-fit procedures for the Cox model 202
6.3 Extended Cox model with time-varying regression effects 214
6.4 Inference for the extended Cox model 222
6.5 A semiparametric multiplicative hazards model 227
6.6 Inference for the semiparametric multiplicative model 233
6.7 Estimating the survival function 235
6.8 Multiplicative rate models 236
6.9 Goodness-of-fit procedures 237
6.10 Examples 243
6.11 Exercises 249
Multiplicative-Additive hazards models 257
7.1 The Cox-Aalen hazards model 259
7.2 Proportional excess hazards model 281
7.3 Exercises 298
Accelerated failure time and transformation models 301
8.1 The accelerated failure time model 302
8.2 The semiparametric transformation model 306
8.3 Exercises 317
Clustered failure time data 320
9.1 Marginal regression models for clustered failure time data 321
9.2 Frailty models 341
9.3 Exercises 345
Competing Risks Model 353
10.1 Product limit estimator 357
10.2 Cause specific hazards modeling 362
10.3 Subdistribution approach 367
10.4 Exercises 376
Marked point process models 380
11.1 Nonparametric additive model for longitudinal data 385
11.2 Semiparametric additive model for longitudinal data 394
11.3 Efficient estimation 398
11.4 Marginal models 402
11.5 Exercises 413
Khmaladze’s transformation 415
Matrix derivatives 418
The Timereg survival package for R 419
Bibliography 454
Index 468