Dynamic Regression Models for Survival Data (eBook)

Torben Martinussen, Thomas H. Scheike (Autoren)

eBook Download: PDF

2007 | 2006
XIV, 470 Seiten
Springer New York (Verlag)
978-0-387-33960-3 (ISBN)

Infos

This book studies and applies modern flexible regression models for survival data with a special focus on extensions of the Cox model and alternative models with the aim of describing time-varying effects of explanatory variables. Use of the suggested models and methods is illustrated on real data examples, using the R-package timereg developed by the authors, which is applied throughout the book with worked examples for the data sets.

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In survival analysis there has long been a need for models that goes beyond the Cox model as the proportional hazards assumption often fails in practice. This book studies and applies modern flexible regression models for survival data with a special focus on extensions of the Cox model and alternative models with the specific aim of describing time-varying effects of explanatory variables. One model that receives special attention is Aalen's additive hazards model that is particularly well suited for dealing with time-varying effects. The book covers the use of residuals and resampling techniques to assess the fit of the models and also points out how the suggested models can be utilised for clustered survival data. The authors demonstrate the practically important aspect of how to do hypothesis testing of time-varying effects making backwards model selection strategies possible for the flexible models considered.The use of the suggested models and methods is illustrated on real data examples. The methods are available in the R-package timereg developed by the authors, which is applied throughout the book with worked examples for the data sets. This gives the reader a unique chance of obtaining hands-on experience.This book is well suited for statistical consultants as well as for those who would like to see more about the theoretical justification of the suggested procedures. It can be used as a textbook for a graduate/master course in survival analysis, and students will appreciate the exercises included after each chapter. The applied side of the book with many worked examples accompanied with R-code shows in detail how one can analyse real data and at the same time gives a deeper understanding of the underlying theory.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 24.11.2007
• Reihe/Serie: Statistics for Biology and Health
• Reihe/Serie: Statistics for Biology and Health
• Zusatzinfo: XIV, 470 p. 75 illus.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Medizin / Pharmazie ► Allgemeines / Lexika
• Themenwelt: Medizin / Pharmazie ► Pflege
• Schlagworte: Cluster • Counting • counting process • Permutation Tests • Point Process • resampling • selection • Sets • Statistica • Survival Analysis • techniques • Testing • Time • Transformation • Variable
• ISBN-10: 0-387-33960-4 / 0387339604
• ISBN-13: 978-0-387-33960-3 / 9780387339603