Abstract
In survival data analysis, the aim of fitting a Cox's proportional hazards (Cox's PH) model is to estimate the effect of covariates on the baseline hazard function. However, Cox's PH model makes a number of assumptions, which may be violated in many applications. Applying Cox's PH model without ensuring that its underlying assumptions are validated can lead to negative consequences on the resulting estimates. In this article, a generalization of the Cox's PH model in terms of the increment in cumulative hazard function taking a form similar to the Cox's PH model, with the extension that the increment in baseline cumulative hazard function is raised to a power function. The problem of parameter estimation for the parameters in that generalization of Cox's PH model will be solved using Bayesian inference. When the increment in cumulative hazard function is a gamma process, the likelihood has a semi-closed form, which allows posterior sampling to be carried out for the parameters, hence achieving model using Markov chain Monte Carlo (MCMC) methods which became very popular within the last decade. An innovative simulation algorithm via Bayesian inference using Gibbs sampling (BUGS) is developed to sample event times in the presence of arbitrary covariates, which provides a tool to assess the precision of inference. A common application is the relative hazard between patients given a treatment and patients given a placebo, therefore, real-life data is used to illustrate the applicability of our methodology in that applications.