The Frailty Model (eBook)

Luc Duchateau, Paul Janssen (Autoren)

eBook Download: PDF

2007 | 2008
XVII, 316 Seiten
Springer New York (Verlag)
978-0-387-72835-3 (ISBN)

Infos

Readers will find in the pages of this book a treatment of the statistical analysis of clustered survival data. Such data are encountered in many scientific disciplines including human and veterinary medicine, biology, epidemiology, public health and demography. A typical example is the time to death in cancer patients, with patients clustered in hospitals. Frailty models provide a powerful tool to analyze clustered survival data. In this book different methods based on the frailty model are described and it is demonstrated how they can be used to analyze clustered survival data. All programs used for these examples are available on the Springer website.

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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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 23.10.2007
• Reihe/Serie: Statistics for Biology and Health
• Reihe/Serie: Statistics for Biology and Health
• Zusatzinfo: XVII, 316 p.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Medizin / Pharmazie ► Allgemeines / Lexika
• Themenwelt: Medizin / Pharmazie ► Medizinische Fachgebiete ► Onkologie
• Themenwelt: Medizin / Pharmazie ► Pflege
• Themenwelt: Technik
• Schlagworte: Biology • clustered survival data • Copula • frailty model • Infectious Diseases • Laplace transform • likelihood • recurrent analysis • statistical software • Survival Analysis
• ISBN-10: 0-387-72835-X / 038772835X
• ISBN-13: 978-0-387-72835-3 / 9780387728353