Estimating Proportional Hazards Model Using Frequentist and Bayesian Approaches

In statistics, the proportional hazards model (PHM) is one of a class of survival models. This model estimates the effects of different covariates influencing the time-to-event data in which the hazard function has been assumed to be the product of the baseline hazard function and a non-negative function of covariates. In this study, we investigate the hazard function, also known as the risk function or intensity function, which is employed in modelling the survival data and waiting times. The model parameters can be estimated via frequentist or Bayesian approach. However, the Bayesian approach is well known to have the advantages over frequentist methods when the data are small in size and involve censored individuals. In this paper, the PHM for right-censored data from Bayesian perspective will be discussed and the Markov Chain Monte Carlo (MCMC) method will be used to estimate the posterior distributions of the model parameters using Leukemia data.