Bayesian estimators for conditional hazard functions

This article introduces a new Bayesian approach to the analysis of right-censored survival data. The hazard rate of interest is modeled as a product of conditionally independent stochastic processes corresponding to (1) a baseline hazard function and (2) a regression function representing the temporal influence of the covariates. These processes jump at times that form a time-homogeneous Poisson process and have a pairwise dependency structure for adjacent values. The two processes are assumed to be conditionally independent given their jump times. Features of the posterior distribution, such as the mean covariate effects and survival probabilities (conditional on the covariate), are evaluated using the Metropolis-Hastings-Green algorithm. We illustrate our methodology by an application to nasopharynx cancer survival data.