The Frailty Model / Edition 1

The Frailty Model / Edition 1

by Luc Duchateau, Paul Janssen
     
 

ISBN-10: 144192499X

ISBN-13: 9781441924995

Pub. Date: 11/19/2010

Publisher: Springer New York

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

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Overview

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.

Product Details

ISBN-13:
9781441924995
Publisher:
Springer New York
Publication date:
11/19/2010
Series:
Statistics for Biology and Health Series
Edition description:
Softcover reprint of hardcover 1st ed. 2008
Pages:
316
Product dimensions:
0.70(w) x 6.14(h) x 9.21(d)

Related Subjects

Table of Contents

Preface     vii
Glossary of Definitions and Notation     xv
Introduction     1
Goals     1
Outline     2
Examples     3
Survival analysis     17
Survival likelihood     18
Proportional hazards models     20
Accelerated failure time models     26
The loglinear model representation     30
Semantics and history of the term frailty     32
Parametric proportional hazards models with gamma frailty     43
The parametric proportional hazards model with frailty term     44
Maximising the marginal likelihood: the frequentist approach     45
Extension of the marginal likelihood approach to interval-censored data     61
Posterior densities: the Bayesian approach     65
The Metropolis algorithm in practice for the parametric gamma frailty model     65
Theoretical foundations of the Metropolis algorithm     74
Further extensions and references     75
Alternatives for the frailty model     77
The fixed effects model     78
The model specification     78
Asymptotic efficiency of fixed effects model parameter estimates     84
The stratifiedmodel     87
The copula model     93
Notation and definitions for the conditional, joint, and population survival functions     93
Definition of the copula model     95
The Clayton copula     97
The Clayton copula versus the gamma frailty model     99
The marginal model     104
Defining the marginal model     104
Consistency of parameter estimates from marginal model     105
Variance of parameter estimates adjusted for correlation structure     107
Population hazards from conditional models     111
Population versus conditional hazard from frailty models     111
Population versus conditional hazard ratio from frailty models     114
Further extensions and references     116
Frailty distributions     117
General characteristics of frailty distributions     118
Joint survival function and the Laplace transform     119
Population survival function and the coupla     120
Conditional frailty density changes over time     122
Measures of dependence     123
The gamma distribution     130
Definitions and basic properties     130
Joint and population survival function      131
Updating     134
Copula form representation     137
Dependence measures     138
Diagnostics     141
Estimation of the cross ratio function: some theoretical considerations     147
The inverse Gaussian distribution     150
Definitions and basic properties     150
Joint and population survival function     152
Updating     158
Copula form representation     158
Dependence measures     161
Diagnostics     164
The positive stable distribution     164
Definitions and basic properties     164
Joint and population survival function     167
Updating     171
Copula form representation     171
Dependence measures     173
Diagnostics     176
The power variance function distribution     177
Definitions and basic properties     177
Joint and population survival function     181
Updating     184
Copula form representation     185
Dependence measures     186
Diagnostics     189
The compound Poisson distribution     190
Definitions and basic properties      190
Joint and population survival functions     192
Updating     193
The lognormal distribution     195
Further extensions and references     196
The semiparametric frailty model     199
The EM algorithm approach     199
Description of the EM algorithm     199
Expectation and maximisation for the gamma frailty model     200
Why the EM algorithm works for the gamma frailty model     207
The penalised partial likelihood approach     210
The penalised partial likelihood for the normal random effects density     210
The penalised partial likelihood for the gamma frailty distribution     214
Performance of the penalised partial likelihood estimates     221
Robustness of the frailty distribution assumption     228
Bayesian analysis for the semiparametric gamma frailty model through Gibbs sampling     233
The frailty model with a gamma process prior for the cumulative baseline hazard for grouped data     234
The frailty model with a gamma process prior for the cumulative baseline hazard for observed event times     239
The normal frailty model based on Poisson likelihood     244
Sampling techniques used for semiparametric frailty models     250
Gibbs sampling, a special case of the Metropolis-Hastings algorithm     257
Further extensions and references     258
Multifrailty and multilevel models     259
Multifrailty models with one clustering level     260
Bayesian analysis based on Laplacian integration     260
Frequentist approach using Laplacian integration     268
Multilevel frailty models     277
Maximising the marginal likelihood with penalised splines for the baseline hazard     277
The Bayesian approach for multilevel frailty models using Gibbs sampling     279
Further extensions and references     286
Extensions of the frailty model     287
Censoring and truncation     287
Correlated frailty models     288
Joint modelling     290
The accelerated failure time model     292
References     295
Applications and Examples Index     308
Author Index     309
Subject Index     314

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