The Frailty Model

Front Cover
Springer Science & Business Media, Oct 23, 2007 - Mathematics - 316 pages

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-life examples 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.

 

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Contents

Introduction
1
12 Outline
2
13 Examples
3
14 Survival analysis
17
141 Survival likelihood
18
142 Proportional hazards models
20
143 Accelerated failure time models
26
144 The loglinear model representation
30
435 Dependence measures
161
436 Diagnostics
164
442 Joint and population survival function
167
443 Updating
171
445 Dependence measures
173
446 Diagnostics
176
45 The power variance function distribution
177
452 Joint and population survival function
181

15 Semantics and history of the term frailty
32
Parametric proportional hazards models with gamma frailty
43
21 The parametric proportional hazards model with frailty term
44
the frequentist approach
45
23 Extension of the marginal likelihood approach to intervalcensored data
61
the Bayesian approach
65
242 Theoretical foundations of the Metropolis algorithm
74
25 Further extensions and references
75
Alternatives for the frailty model
77
31 The fixed effects model
78
312 Asymptotic efficiency of fixed effects model parameter estimates
84
32 The stratified model
87
33 The copula model
93
332 Definition of the copula model
95
333 The Clayton copula
97
334 The Clayton copula versus the gamma frailty model
99
34 The marginal model
104
342 Consistency of parameter estimates from marginal model
105
343 Variance of parameter estimates adjusted for correlation structure
107
35 Population hazards from conditional models
111
352 Population versus conditional hazard ratio from frailty models
114
36 Further extensions and references
116
Frailty distributions
117
41 General characteristics of frailty distributions
118
411 Joint survival function and the Laplace transform
119
412 Population survival function and the copula
120
413 Conditional frailty density changes over time
122
414 Measures of dependence
123
42 The gamma distribution
130
422 Joint and population survival function
131
423 Updating
134
424 Copula form representation
137
425 Dependence measures
138
426 Diagnostics
141
some theoretical considerations
147
43 The inverse Gaussian distribution
150
432 Joint and population survival function
152
433 Updating
158
453 Updating
184
454 Copula form representation
185
455 Dependence measures
186
456 Diagnostics
189
46 The compound Poisson distribution
190
462 Joint and population survival functions
192
463 Updating
193
47 The lognormal distribution
195
48 Further extensions and references
196
The semiparametric frailty model
199
512 Expectation and maximisation for the gamma frailty model
200
513 Why the EM algorithm works for the gamma frailty model
207
52 The penalised partial likelihood approach
210
522 The penalised partial likelihood for the gamma frailty distribution
214
523 Performance of the penalised partial likelihood estimates
221
524 Robustness of the frailty distribution assumption
228
53 Bayesian analysis for the semiparametric gamma frailty model through Gibbs sampling
233
531 The frailty model with a gamma process prior for the cumulative baseline hazard for grouped data
234
532 The frailty model with a gamma process prior for the cumulative baseline hazard for observed event times
239
533 The normal frailty model based on Poisson likelihood
244
534 Sampling techniques used for semiparametric frailty models
250
535 Gibbs sampling a special case of the MetropolisHastings algorithm
257
54 Further extensions and references
258
Multifrailty and multilevel models
259
61 Multifrailty models with one clustering level
260
612 Frequentist approach using Laplacian integration
268
62 Multilevel frailty models
277
622 The Bayesian approach for multilevel frailty models using Gibbs sampling
279
63 Further extensions and references
286
Extensions of the frailty model
287
72 Correlated frailty models
288
73 Joint modelling
290
74 The accelerated failure time model
292
References
295
Applications and Examples Index
308
Author Index
309
Subject Index
314
Copyright

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