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Dynamic Regression Models for Survival Data
Torben Martinussen, Thomas H. Scheike
Verlag Springer-Verlag, 2007
ISBN 9780387339603 , 470 Seiten
Format PDF
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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
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