Comparison of shared gamma frailty models using the Bayesian approach

Abstract

The shared frailty models allow for the unbiased heterogeneity or statistical dependence between the observed survival data. The most common shared frailty model is a model in which hazard function is a product of a random factor (frailty) and the baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and the distribution of frailty. In this paper, we consider shared gamma frailty model with three different baseline distributions namely, the generalized Rayleigh, the weighted exponential and the extended Weibull distributions. With these three baseline distributions we propose three different shared frailty models. We also compare these models with the models where the above mentioned distributions are considered without frailty. We develop the Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in these models. We present a simulation study to compare the true values of the parameters with the estimated values. A search of the literature suggests that currently no work has been done for these three baseline distributions with a shared gamma frailty so far. We also apply these three models by using a real life bivariate survival data set of McGilchrist and Aisbett [15] related to the kidney infection data and a better model is suggested for the data.