Bayesian Estimation Based on Beta Prior in Cure Model

This paper is to study nonparametric Bayesian estimation for a proportional hazards model with "long-term survivors". The cumulative hazards function is modeled by a beta process, and the priors of the cure rate and coefficient of covariates can be improper distributions under the proposed model. The posterior estimators of the cure rate, the coefficient for covariates and the survival function are estimated from the cases of discrete-time, continuous-time and grouped survival data. A set of leukemia data are re-analyzed to illustrate the proposed model and statistical inference via a Markov chain Monte Carlo (MCMC) algorithm with Gibbs sampling.