Nonparametric and semiparametric Bayesian methods in survival analysis have recently become quite popular due to recent advances in computing technology and the development of efficient computational algorithms for implementing these methods. Nonparametric Bayesian methods have now become quite common and well accepted in practice, since they offer a more general modeling strategy that contains fewer assumptions. The literature on nonparametric Bayesian methods has been recently surging, and all of the references are far too enormous to list here. In this chapter, we discuss several types of nonparametric prior processes for the baseline hazard or cumulative hazard, and focus our discussion primarily on the Cox proportional hazards model. Specifically, we examine piecewise constant hazard models, the gamma process, beta process, correlated prior processes, and the Dirichlet process. In each case, we give a development of the prior process, construct the likelihood function, derive the posterior distributions, and discuss MCMC sampling techniques for inference. Several applications involving case studies are given to demonstrate the various methods.
KeywordsPosterior Distribution Baseline Hazard Dirichlet Process Dirichlet Distribution Semiparametric Model
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