Preface |
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vii | |
Glossary of Definitions and Notation |
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xv | |
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1 | (42) |
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1 | (1) |
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2 | (1) |
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3 | (14) |
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17 | (15) |
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18 | (2) |
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Proportional hazards models |
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20 | (6) |
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Accelerated failure time models |
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26 | (4) |
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The loglinear model representation |
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30 | (2) |
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Semantics and history of the term frailty |
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32 | (11) |
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Parametric proportional hazards models with gamma frailty |
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43 | (34) |
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The parametric proportional hazards model with frailty term |
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44 | (1) |
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Maximising the marginal likelihood: the frequentist approach |
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45 | (16) |
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Extension of the marginal likelihood approach to interval-censored data |
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61 | (4) |
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Posterior densities: the Bayesian approach |
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65 | (10) |
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The Metropolis algorithm in practice for the parametric gamma frailty model |
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65 | (9) |
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Theoretical foundations of the Metropolis algorithm |
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74 | (1) |
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Further extensions and references |
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75 | (2) |
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Alternatives for the frailty model |
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77 | (40) |
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78 | (9) |
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78 | (6) |
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Asymptotic efficiency of fixed effects model parameter estimates |
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84 | (3) |
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87 | (6) |
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93 | (11) |
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Notation and definitions for the conditional, joint, and population survival functions |
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93 | (2) |
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Definition of the copula model |
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95 | (2) |
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97 | (2) |
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The Clayton copula versus the gamma frailty model |
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99 | (5) |
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104 | (7) |
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Defining the marginal model |
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104 | (1) |
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Consistency of parameter estimates from marginal model |
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105 | (2) |
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Variance of parameter estimates adjusted for correlation structure |
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107 | (4) |
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Population hazards from conditional models |
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111 | (5) |
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Population versus conditional hazard from frailty models |
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111 | (3) |
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Population versus conditional hazard ratio from frailty models |
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114 | (2) |
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Further extensions and references |
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116 | (1) |
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117 | (82) |
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General characteristics of frailty distributions |
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118 | (12) |
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Joint survival function and the Laplace transform |
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119 | (1) |
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Population survival function and the copula |
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120 | (2) |
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Conditional frailty density changes over time |
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122 | (1) |
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123 | (7) |
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130 | (20) |
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Definitions and basic properties |
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130 | (1) |
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Joint and population survival function |
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131 | (3) |
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134 | (3) |
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Copula form representation |
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137 | (1) |
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138 | (3) |
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141 | (6) |
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Estimation of the cross ratio function: some theoretical considerations |
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147 | (3) |
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The inverse Gaussian distribution |
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150 | (14) |
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Definitions and basic properties |
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150 | (2) |
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Joint and population survival function |
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152 | (6) |
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158 | (1) |
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Copula form representation |
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158 | (3) |
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161 | (3) |
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164 | (1) |
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The positive stable distribution |
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164 | (13) |
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Definitions and basic properties |
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164 | (3) |
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Joint and population survival function |
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167 | (4) |
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171 | (1) |
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Copula form representation |
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171 | (2) |
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173 | (3) |
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176 | (1) |
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The power variance function distribution |
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177 | (13) |
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Definitions and basic properties |
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177 | (4) |
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Joint and population survival function |
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181 | (3) |
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184 | (1) |
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Copula form representation |
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185 | (1) |
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186 | (3) |
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189 | (1) |
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The compound Poisson distribution |
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190 | (5) |
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Definitions and basic properties |
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190 | (2) |
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Joint and population survival functions |
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192 | (1) |
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193 | (2) |
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The lognormal distribution |
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195 | (1) |
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Further extensions and references |
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196 | (3) |
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The semiparametric frailty model |
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199 | (60) |
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The EM algorithm approach |
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199 | (11) |
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Description of the EM algorithm |
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199 | (1) |
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Expectation and maximisation for the gamma frailty model |
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200 | (7) |
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Why the EM algorithm works for the gamma frailty model |
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207 | (3) |
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The penalised partial likelihood approach |
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210 | (23) |
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The penalised partial likelihood for the normal random effects density |
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210 | (4) |
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The penalised partial likelihood for the gamma frailty distribution |
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214 | (7) |
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Performance of the penalised partial likelihood estimates |
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221 | (7) |
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Robustness of the frailty distribution assumption |
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228 | (5) |
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Bayesian analysis for the semiparametric gamma frailty model through Gibbs sampling |
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233 | (25) |
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The frailty model with a gamma process prior for the cumulative baseline hazard for grouped data |
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234 | (5) |
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The frailty model with a gamma process prior for the cumulative baseline hazard for observed event times |
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239 | (5) |
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The normal frailty model based on Poisson likelihood |
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244 | (6) |
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Sampling techniques used for semiparametric frailty models |
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250 | (7) |
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Gibbs sampling, a special case of the Metropolis-Hastings algorithm |
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257 | (1) |
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Further extensions and references |
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258 | (1) |
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Multifrailty and multilevel models |
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259 | (28) |
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Multifrailty models with one clustering level |
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260 | (17) |
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Bayesian analysis based on Laplacian integration |
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260 | (8) |
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Frequentist approach using Laplacian integration |
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268 | (9) |
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Multilevel frailty models |
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277 | (9) |
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Maximising the marginal likelihood with penalised splines for the baseline hazard |
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277 | (2) |
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The Bayesian approach for multilevel frailty models using Gibbs sampling |
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279 | (7) |
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Further extensions and references |
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286 | (1) |
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Extensions of the frailty model |
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287 | (8) |
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287 | (1) |
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Correlated frailty models |
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288 | (2) |
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290 | (2) |
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The accelerated failure time model |
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292 | (3) |
References |
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295 | (13) |
Applications and Examples Index |
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308 | (1) |
Author Index |
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309 | (5) |
Subject Index |
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314 | |