Bayesian Estimators for Conditional Hazard Functions

by Ian W. McKeague and Mourad Tighiouart

Abstract

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 time-homogeneous Poisson processes, 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.