Martinussen / Scheike Dynamic Regression Models for Survival Data

1. Auflage 2007
ISBN: 978-0-387-33960-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 470 Seiten

Reihe: Mathematics and Statistics (R0)

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.

Autoren/Hrsg.

Martinussen, Torben

Scheike, Thomas H.

Inhaltsverzeichnis

1;Preface;7
2;Contents;10
3;Introduction;13
3.1;1.1 Survival data;13
3.2;1.2 Longitudinal data;26
4;Probabilistic background;29
4.1;2.1 Preliminaries;29
4.2;2.2 Martingales;32
4.3;2.3 Counting processes;35
4.4;2.4 Marked point processes;42
4.5;2.5 Large-sample results;46
4.6;2.6 Exercises;56
5;Estimation for filtered counting process data;61
5.1;3.1 Filtered counting process data;61
5.2;3.2 Likelihood constructions;74
5.3;3.3 Estimating equations;82
5.4;3.4 Exercises;86
6;Nonparametric procedures for survival data;92
6.1;4.1 The Kaplan-Meier estimator;92
6.2;4.2 Hypothesis testing;97
6.3;4.3 Exercises;106
7;Additive Hazards Models;113
7.1;5.1 Additive hazards models;118
7.2;5.2 Inference for additive hazards models;126
7.3;5.3 Semiparametric additive hazards models;136
7.4;5.4 Inference for the semiparametric hazards model;145
7.5;5.5 Estimating the survival function;156
7.6;5.6 Additive rate models;159
7.7;5.7 Goodness-of-fit procedures;161
7.8;5.8 Example;169
7.9;5.9 Exercises;175
8;Multiplicative hazards models;184
8.1;6.1 The Cox model;190
8.2;6.2 Goodness-of-fit procedures for the Cox model;202
8.3;6.3 Extended Cox model with time-varying regression effects;214
8.4;6.4 Inference for the extended Cox model;222
8.5;6.5 A semiparametric multiplicative hazards model;227
8.6;6.6 Inference for the semiparametric multiplicative model;233
8.7;6.7 Estimating the survival function;235
8.8;6.8 Multiplicative rate models;236
8.9;6.9 Goodness-of-fit procedures;237
8.10;6.10 Examples;243
8.11;6.11 Exercises;249
9;Multiplicative-Additive hazards models;257
9.1;7.1 The Cox-Aalen hazards model;259
9.2;7.2 Proportional excess hazards model;281
9.3;7.3 Exercises;298
10;Accelerated failure time and transformation models;301
10.1;8.1 The accelerated failure time model;302
10.2;8.2 The semiparametric transformation model;306
10.3;8.3 Exercises;317
11;Clustered failure time data;320
11.1;9.1 Marginal regression models for clustered failure time data;321
11.2;9.2 Frailty models;341
11.3;9.3 Exercises;345
12;Competing Risks Model;353
12.1;10.1 Product limit estimator;357
12.2;10.2 Cause specific hazards modeling;362
12.3;10.3 Subdistribution approach;367
12.4;10.4 Exercises;376
13;Marked point process models;380
13.1;11.1 Nonparametric additive model for longitudinal data;385
13.2;11.2 Semiparametric additive model for longitudinal data;394
13.3;11.3 Efficient estimation;398
13.4;11.4 Marginal models;402
13.5;11.5 Exercises;413
14;Khmaladze’s transformation;415
15;Matrix derivatives;418
16;The Timereg survival package for R;419
17;Bibliography;454
18;Index;468