In Section 1.4.2 we briefly reviewed some ideas on parametric and semiparametric proportional hazards modelling in univariate survival analysis. The extension of the parametric proportional hazards model to the parametric proportional hazards model with a gamma frailty term, a model that can be used to fit multivariate survival data, is discussed at length in Chapter 2. In this chapter we study in detail the extension of the semiparametric proportional hazards model to the semiparametric frailty model. This model is a standard statistical tool to analyse multivariate or clustered survival data. A detailed discussion will be given on the different techniques that are available to fit these models. Section 5.1 deals with the EM algorithm approach for semiparametric gamma frailty models. In Section 5.2 an alternative approach to fit semiparametric gamma frailty models based on penalised partial likelihood maximisation is introduced. It is shown that this technique leads to the same estimates as the EM algorithm. This technique, however, can be extended to a semiparametric model with normal distributed random effects. In Section 5.3 we show how Bayesian techniques based on Gibbs sampling can be used to fit semiparametric frailty models.
KeywordsGibbs Sampling Outer Loop Posterior Density Baseline Hazard Marginal Likelihood
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