Using WinBUGS to Cox Model with Changing from the Baseline Hazard Function

The proportional hazards model (PHM) in the context survival data analysis, take in the famous Cox model as it is also called, was introduced by Cox (1972) in order to estimate the effects of different covariates influencing the times-to-event data. It's well known that Bayesian analysis has the advantage in dealing with censored data and small sample over frequentist methods. Therefore in this paper we discuss the PHM for right-censored death times from Bayesian perspective, and then compute the Bayesian estimator based on the Markov Chain Monte Carlo (MCMC) method. Survival model can be conveniently inspected with the help of hazard function. A common approach to handling the prior probability for the baseline hazard function in PHM is a Gamma process prior. However, this can lead to biased and misleading results (Spiegelhalter et al., 1996). The Gibbs sampling is proposed to simulate the Markov chain of parameters' posterior distribution dynamically, which avoids the calculation of complex integrals of the posterior using WinBUGS package. For the problem, we adopt the idea behind the polygonal baseline hazard approach proposed in Beamonte and Bermúdez (2003) to develop the estimation for the survival curves. The proposed methodology is illustrated by re examining two textbook data examples