The Frailty Model (eBook)

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