ABSTRACT
In Bayesian inference, prior information about a set of unknown parameters in a model is combined with the likelihood function for sample data to give a posterior distribution, and this distribution is used to make inferences about the parameters. The Bayesian approach to the analysis of survival data is described and illustrated in this chapter. The chapter includes sections on quantifying prior knowledge, choice of prior distribution, methods for summarising posterior information, and Bayesian hypothesis tests. Computational methods for obtaining a posterior distribution using Markov Chain Monte Carlo simulation methods are described, with an emphasis on Gibbs sampling. The use of these methods is illustrated in practical examples. It is also shown how predictive distributions can be used to obtain the posterior distribution of functions of unknown parameters. Their use in predicting hazard and survivor functions is described. Bayesian methods for comparing alternative models using the DIC and WAIC statistics are also summarised. The chapter concludes with a brief discussion of the relative merits of the Bayesian approach to modelling survival data.
