The frailty model:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2008
|
| Series: | Statistics for biology and health
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XVII, 316 S. graph. Darst. |
| ISBN: | 9780387728346 0387728341 9780387728353 |
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| 245 | 1 | 0 | |a The frailty model |c Luc Duchateau ; Paul Janssen |
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| 300 | |a XVII, 316 S. |b graph. Darst. | ||
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| 650 | 7 | |a Análise de sobrevivência |2 larpcal | |
| 650 | 7 | |a Processos estocásticos |2 larpcal | |
| 650 | 7 | |a Statistiques médicales |2 ram | |
| 650 | 7 | |a Survie (médecine) |2 ram | |
| 650 | 4 | |a Statistik | |
| 650 | 4 | |a Proportional Hazards Models | |
| 650 | 4 | |a Statistics | |
| 650 | 4 | |a Survival Analysis | |
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Record in the Search Index
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Contents
Preface. vii
Glossary of Definitions and Notation . xv
1 Introduction. 1
1.1 Goals. 1
1.2 Outline . 2
1.3 Examples. 3
1.4 Survival analysis . 17
1.4.1 Survival likelihood. 18
1.4.2 Proportional hazards models. 20
1.4.3 Accelerated failure time models. 26
1.4.4 The loglinear model representation. 30
1.5 Semantics and history of the term frailty. 32
2 Parametric proportional hazards models with gamma
frailty . 43
2.1 The parametric proportional hazards model with frailty term . 44
2.2 Maximising the marginal likelihood: the frequentist approach . 45
2.3 Extension of the marginal likelihood approach to
interval-censored data. 61
2.4 Posterior densities: the Bayesian approach. 65
2.4.1 The Metropolis algorithm in practice for the
parametric gamma frailty model. 65
2.4.2 * Theoretical foundations of the Metropolis algorithm . 74
2.5 Further extensions and references. 75
3 Alternatives for the frailty model. 77
3.1 The fixed effects model. 78
3.1.1 The model specification. 78
Contents
3.1.2 * Asymptotic efficiency of fixed effects model parameter
estimates. 84
3.2 The stratified model. 87
3.3 The copula model. 93
3.3.1 Notation and definitions for the conditional, joint, and
population survival functions . 93
3.3.2 Definition of the copula model. 95
3.3.3 The Clayton copula. 97
3.3.4 The Clayton copula versus the gamma frailty model . 99
3.4 The marginal model.104
3.4.1 Defining the marginal model.104
3.4.2 * Consistency of parameter estimates from marginal
model.105
3.4.3 Variance of parameter estimates adjusted for
correlation structure.107
3.5 Population hazards from conditional models .Ill
3.5.1 Population versus conditional hazard from frailty
models.Ill
3.5.2 Population versus conditional hazard ratio from frailty
models.114
3.6 Further extensions and references.116
Frailty distributions .117
4.1 General characteristics of frailty distributions.118
4.1.1 Joint survival function and the Laplace transform.119
4.1.2 Population survival function and the copula .120
4.1.3 Conditional frailty density changes over time.122
4.1.4 Measures of dependence.123
4.2 The gamma distribution.130
4.2.1 Definitions and basic properties.130
4.2.2 Joint and population survival function.131
4.2.3 Updating.134
4.2.4 Copula form representation.137
4.2.5 Dependence measures.138
4.2.6 Diagnostics.141
4.2.7* Estimation of the cross ratio function: some theoretical
considerations.147
4.3 The inverse Gaussian distribution .150
4.3.1 Definitions and basic properties.150
4.3.2 Joint and population survival function.152
4.3.3 Updating.158
4.3.4 Copula form representation.158
4.3.5 Dependence measures.161
4.3.6 Diagnostics.164
Contents xiii
4.4 The positive stable distribution .164
4.4.1 Definitions and basic properties.164
4.4.2 Joint and population survival function.167
4.4.3 Updating.171
4.4.4 Copula form representation.171
4.4.5 Dependence measures.173
4.4.6 Diagnostics.176
4.5 The power variance function distribution.177
4.5.1 Definitions and basic properties.177
4.5.2 Joint and population survival function.181
4.5.3 Updating.184
4.5.4 Copula form representation.185
4.5.5 Dependence measures.186
4.5.6 Diagnostics.189
4.6 The compound Poisson distribution.190
4.6.1 Definitions and basic properties.190
4.6.2 Joint and population survival functions .192
4.6.3 Updating.193
4.7 The lognormal distribution.195
4.8 Further extensions and references.196
The semiparametric frailty model.199
5.1 The EM algorithm approach.199
5.1.1 Description of the EM algorithm.199
5.1.2 Expectation and maximisation for the gamma frailty
model.200
5.1.3 Why the EM algorithm works for the gamma frailty
model.207
5.2 The penalised partial likelihood approach.210
5.2.1 The penalised partial likelihood for the normal
random effects density.210
5.2.2 The penalised partial likelihood for the gamma frailty
distribution.214
5.2.3 Performance of the penalised partial likelihood
estimates.221
5.2.4 Robustness of the frailty distribution assumption.228
5.3 Bayesian analysis for the semiparametric gamma frailty
model through Gibbs sampling.233
5.3.1 The frailty model with a gamma process prior for the
cumulative baseline hazard for grouped data.234
5.3.2 The frailty model with a gamma process prior for the
cumulative baseline hazard for observed event times . . . 239
5.3.3 The normal frailty model based on Poisson likelihood . . 244
5.3.4 Sampling techniques used for semiparametric frailty
models.250
xiv Contents
5.3.5 Gibbs sampling, a special case of the Metropolis-
Hastings algorithm.257
5.4 Further extensions and references.258
6 Multifrailty and multilevel models.259
6.1 Multifrailty models with one clustering level.260
6.1.1 Bayesian analysis based on Laplacian integration.260
6.1.2 Frequentist approach using Laplacian integration.268
6.2 Multilevel frailty models.277
6.2.1 Maximising the marginal likelihood with penalised
splines for the baseline hazard .277
6.2.2 The Bayesian approach for multilevel frailty models
using Gibbs sampling.279
6.3 Further extensions and references.286
7 Extensions of the frailty model .287
7.1 Censoring and truncation.287
7.2 Correlated frailty models.288
7.3 Joint modelling .290
7.4 The accelerated failure time model.292
References.295
Applications and Examples Index.308
Author Index.309
Subject Index .314 |
| adam_txt |
Contents
Preface. vii
Glossary of Definitions and Notation . xv
1 Introduction. 1
1.1 Goals. 1
1.2 Outline . 2
1.3 Examples. 3
1.4 Survival analysis . 17
1.4.1 Survival likelihood. 18
1.4.2 Proportional hazards models. 20
1.4.3 Accelerated failure time models. 26
1.4.4 The loglinear model representation. 30
1.5 Semantics and history of the term frailty. 32
2 Parametric proportional hazards models with gamma
frailty . 43
2.1 The parametric proportional hazards model with frailty term . 44
2.2 Maximising the marginal likelihood: the frequentist approach . 45
2.3 Extension of the marginal likelihood approach to
interval-censored data. 61
2.4 Posterior densities: the Bayesian approach. 65
2.4.1 The Metropolis algorithm in practice for the
parametric gamma frailty model. 65
2.4.2 * Theoretical foundations of the Metropolis algorithm . 74
2.5 Further extensions and references. 75
3 Alternatives for the frailty model. 77
3.1 The fixed effects model. 78
3.1.1 The model specification. 78
Contents
3.1.2 * Asymptotic efficiency of fixed effects model parameter
estimates. 84
3.2 The stratified model. 87
3.3 The copula model. 93
3.3.1 Notation and definitions for the conditional, joint, and
population survival functions . 93
3.3.2 Definition of the copula model. 95
3.3.3 The Clayton copula. 97
3.3.4 The Clayton copula versus the gamma frailty model . 99
3.4 The marginal model.104
3.4.1 Defining the marginal model.104
3.4.2 * Consistency of parameter estimates from marginal
model.105
3.4.3 Variance of parameter estimates adjusted for
correlation structure.107
3.5 Population hazards from conditional models .Ill
3.5.1 Population versus conditional hazard from frailty
models.Ill
3.5.2 Population versus conditional hazard ratio from frailty
models.114
3.6 Further extensions and references.116
Frailty distributions .117
4.1 General characteristics of frailty distributions.118
4.1.1 Joint survival function and the Laplace transform.119
4.1.2 Population survival function and the copula .120
4.1.3 Conditional frailty density changes over time.122
4.1.4 Measures of dependence.123
4.2 The gamma distribution.130
4.2.1 Definitions and basic properties.130
4.2.2 Joint and population survival function.131
4.2.3 Updating.134
4.2.4 Copula form representation.137
4.2.5 Dependence measures.138
4.2.6 Diagnostics.141
4.2.7* Estimation of the cross ratio function: some theoretical
considerations.147
4.3 The inverse Gaussian distribution .150
4.3.1 Definitions and basic properties.150
4.3.2 Joint and population survival function.152
4.3.3 Updating.158
4.3.4 Copula form representation.158
4.3.5 Dependence measures.161
4.3.6 Diagnostics.164
Contents xiii
4.4 The positive stable distribution .164
4.4.1 Definitions and basic properties.164
4.4.2 Joint and population survival function.167
4.4.3 Updating.171
4.4.4 Copula form representation.171
4.4.5 Dependence measures.173
4.4.6 Diagnostics.176
4.5 The power variance function distribution.177
4.5.1 Definitions and basic properties.177
4.5.2 Joint and population survival function.181
4.5.3 Updating.184
4.5.4 Copula form representation.185
4.5.5 Dependence measures.186
4.5.6 Diagnostics.189
4.6 The compound Poisson distribution.190
4.6.1 Definitions and basic properties.190
4.6.2 Joint and population survival functions .192
4.6.3 Updating.193
4.7 The lognormal distribution.195
4.8 Further extensions and references.196
The semiparametric frailty model.199
5.1 The EM algorithm approach.199
5.1.1 Description of the EM algorithm.199
5.1.2 Expectation and maximisation for the gamma frailty
model.200
5.1.3 Why the EM algorithm works for the gamma frailty
model.207
5.2 The penalised partial likelihood approach.210
5.2.1 The penalised partial likelihood for the normal
random effects density.210
5.2.2 The penalised partial likelihood for the gamma frailty
distribution.214
5.2.3 Performance of the penalised partial likelihood
estimates.221
5.2.4 Robustness of the frailty distribution assumption.228
5.3 Bayesian analysis for the semiparametric gamma frailty
model through Gibbs sampling.233
5.3.1 The frailty model with a gamma process prior for the
cumulative baseline hazard for grouped data.234
5.3.2 The frailty model with a gamma process prior for the
cumulative baseline hazard for observed event times . . . 239
5.3.3 The normal frailty model based on Poisson likelihood . . 244
5.3.4 Sampling techniques used for semiparametric frailty
models.250
xiv Contents
5.3.5 Gibbs sampling, a special case of the Metropolis-
Hastings algorithm.257
5.4 Further extensions and references.258
6 Multifrailty and multilevel models.259
6.1 Multifrailty models with one clustering level.260
6.1.1 Bayesian analysis based on Laplacian integration.260
6.1.2 Frequentist approach using Laplacian integration.268
6.2 Multilevel frailty models.277
6.2.1 Maximising the marginal likelihood with penalised
splines for the baseline hazard .277
6.2.2 The Bayesian approach for multilevel frailty models
using Gibbs sampling.279
6.3 Further extensions and references.286
7 Extensions of the frailty model .287
7.1 Censoring and truncation.287
7.2 Correlated frailty models.288
7.3 Joint modelling .290
7.4 The accelerated failure time model.292
References.295
Applications and Examples Index.308
Author Index.309
Subject Index .314 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T21:01:58Z |
| indexdate | 2024-07-20T09:41:56Z |
| institution | BVB |
| isbn | 9780387728346 0387728341 9780387728353 |
| language | English |
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| spelling | Duchateau, Luc Verfasser aut The frailty model Luc Duchateau ; Paul Janssen New York, NY Springer 2008 XVII, 316 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistics for biology and health Analyse de survie Análise de sobrevivência larpcal Processos estocásticos larpcal Statistiques médicales ram Survie (médecine) ram Statistik Proportional Hazards Models Statistics Survival Analysis Ereignisdatenanalyse (DE-588)4132103-0 gnd rswk-swf Ereignisdatenanalyse (DE-588)4132103-0 s DE-604 Janssen, Paul Verfasser (DE-588)139999280 aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2951105&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016525940&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Duchateau, Luc Janssen, Paul The frailty model Analyse de survie Análise de sobrevivência larpcal Processos estocásticos larpcal Statistiques médicales ram Survie (médecine) ram Statistik Proportional Hazards Models Statistics Survival Analysis Ereignisdatenanalyse (DE-588)4132103-0 gnd |
| subject_GND | (DE-588)4132103-0 |
| title | The frailty model |
| title_auth | The frailty model |
| title_exact_search | The frailty model |
| title_exact_search_txtP | The frailty model |
| title_full | The frailty model Luc Duchateau ; Paul Janssen |
| title_fullStr | The frailty model Luc Duchateau ; Paul Janssen |
| title_full_unstemmed | The frailty model Luc Duchateau ; Paul Janssen |
| title_short | The frailty model |
| title_sort | the frailty model |
| topic | Analyse de survie Análise de sobrevivência larpcal Processos estocásticos larpcal Statistiques médicales ram Survie (médecine) ram Statistik Proportional Hazards Models Statistics Survival Analysis Ereignisdatenanalyse (DE-588)4132103-0 gnd |
| topic_facet | Analyse de survie Análise de sobrevivência Processos estocásticos Statistiques médicales Survie (médecine) Statistik Proportional Hazards Models Statistics Survival Analysis Ereignisdatenanalyse |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2951105&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016525940&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT duchateauluc thefrailtymodel AT janssenpaul thefrailtymodel |