Abstract:
Non- and semi-parametric Bayesian inference of the gap-time survivor function governing the time to occurrence of a recurrent event in the presence of censoring is considered.  In our nonparametric Bayesian approach, gap-time distribution, F has a Dirichlet process prior with parameter α.  We derive nonparametric Bayes (NPB) and empirical Bayes (NPEB) estimators of the survivor function   = 1 - F and construct point-wise credible intervals. The resulting Bayes estimator of   extends that based on single-event right-censored data, and the PL-type estimator is a limiting case of this Bayes estimator. We also consider semi-parametric Bayesian inference of the gap-time survivor function with the effect of covariates of a correlated recurrent event.  A frailty model is considered   to allow the association between inter-occurrence gap-times.  We assume that for a subject or unit  given the unobserved frailty variable  Z=z , the inter-occurrence gap-time  { ,  j1 }  are IID with some distribution function  F(.|Z=z). We employ the Gibbs sampler techniques to obtain samples from the joint posterior distribution. Simulation studies demonstrate the effectiveness of the proposed methods. We illustrate our method by an application to a gastroenterology data.

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