Performance of piecewise gamma baseline hazard function in Bayesian survival analysis

Abstract

Bayesian analysis can compute estimator for a wide range of models, such as hierarchical models and missing data problems. It provides a theoretical framework for combining prior information with the data to produce posterior distribution. In the context of survival analysis, Cox proportional hazards model (PHM) is popular for its unique feature in measuring the effects of covariates on survival data without making any assumptions concerning the nature and shape of the underlying baseline hazard function. In this study, different models are used as prior distribution of baseline hazard function in conducting Bayesian analysis of censored survival data. The purpose of this study is to investigate the effect of hyperparameters of gamma process prior on parameter estimation in relation to hyper distribution used in piecewise gamma model. The study intends to assess the performance of piecewise gamma model in estimating parameters for non-informative and censored survival data. The Bayesian estimator of the parameter is computed by using Markov chain Monte Carlo (MCMC) method. Gibbs sampler is applied to simulate samples from Markov chains to estimate the quantities of interest without integrating the posterior distribution analytically. OpenBUGS statistical software is employed in this study to implement Bayesian analysis of survival data. The results obtained show that by increasing values fixed for hyperparameters of gamma process prior, it will decrease the parameter estimates. In addition, piecewise gamma model is found to be adequate in estimating parameters of Cox proportional hazards model for leukemia and hepatitis data as the Monte Carlo error is less than 5% of standard deviation of parameter. Hence, piecewise gamma model can be an alternative model for baseline hazard function.