Duchateau / Janssen The Frailty Model

2008
ISBN: 978-0-387-72835-3
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 316 Seiten

Reihe: Statistics for Biology and Health

Clustered survival data are encountered in many scientific disciplines including human and veterinary medicine, biology, epidemiology, public health and demography. Frailty models provide a powerful tool to analyse clustered survival data. In contrast to the large number of research publications on frailty models, relatively few statistical software packages contain frailty models.

It is demanding for statistical practitioners and graduate students to grasp a good knowledge on frailty models from the existing literature. This book provides an in-depth discussion and explanation of the basics of frailty model methodology for such readers. The discussion includes parametric and semiparametric frailty models and accelerated failure time models. Common techniques to fit frailty models include the EM-algorithm, penalised likelihood techniques, Laplacian integration and Bayesian techniques. More advanced frailty models for hierarchical data are also included.

Real-lifeexamples are used to demonstrate how particular frailty models can be fitted and how the results should be interpreted. The programs to fit all the worked-out examples in the book are available from the Springer website with most of the programs developed in the freeware packages R and Winbugs. The book starts with a brief overview of some basic concepts in classical survival analysis, collecting what is needed for the reading on the more complex frailty models.

Autoren/Hrsg.

Duchateau, Luc

Janssen, Paul

Inhaltsverzeichnis

1;Preface;7
2;Contents;10
3;Glossary of Definitions and Notation;14
4;1 Introduction;17
4.1;1.1 Goals;17
4.2;1.2 Outline;18
4.3;1.3 Examples;19
4.4;1.4 Survival analysis;33
4.5;1.5 Semantics and history of the term frailty;48
5;2 Parametric proportional hazards models with gamma frailty;58
5.1;2.1 The parametric proportional hazards model with frailty term;59
5.2;2.2 Maximising the marginal likelihood: the frequentist approach;60
5.3;2.3 Extension of the marginal likelihood approach to interval- censored data;76
5.4;2.4 Posterior densities: the Bayesian approach;80
5.5;2.5 Further extensions and references;90
6;3 Alternatives for the frailty model;91
6.1;3.1 The fixed effects model;92
6.2;3.2 The stratified model;101
6.3;3.3 The copula model;107
6.4;3.4 The marginal model;118
6.5;3.5 Population hazards from conditional models;125
6.6;3.6 Further extensions and references;130
7;4 Frailty distributions;131
7.1;4.1 General characteristics of frailty distributions;132
7.2;4.2 The gamma distribution;144
7.3;4.3 The inverse Gaussian distribution;164
7.4;4.4 The positive stable distribution;178
7.5;4.5 The power variance function distribution;191
7.6;4.6 The compound Poisson distribution;204
7.7;4.7 The lognormal distribution;209
7.8;4.8 Further extensions and references;210
8;5 The semiparametric frailty model;212
8.1;5.1 The EM algorithm approach;212
8.2;5.2 The penalised partial likelihood approach;223
8.3;5.3 Bayesian analysis for the semiparametric gamma frailty model through Gibbs sampling;246
8.4;5.4 Further extensions and references;271
9;6 Multifrailty and multilevel models;272
9.1;6.1 Multifrailty models with one clustering level;273
9.2;6.2 Multilevel frailty models;290
9.3;6.3 Further extensions and references;299
10;7 Extensions of the frailty model;300
10.1;7.1 Censoring and truncation;300
10.2;7.2 Correlated frailty models;301
10.3;7.3 Joint modelling;303
10.4;7.4 The accelerated failure time model;305
11;References;307
12;Applications and Examples Index;320
13;Author Index;321
14;Subject Index;326