Comparison of Shared Gamma Frailty Models for Acute Leukemia Data

There are certain assumptions about the baseline distribution and distribution of frailty. Mostly Weibull distribution is considered for baseline hazard but we consider some different baseline distributions. Mostly assumption of gamma distribution is considered for frailty distribution. In this paper also, we consider gamma distribution as frailty distribution and two different baseline distributions namely, Gompertz and log-logistic distribution. With these two baseline distributions, we propose two different gamma shared frailty models. We fit these models to a real life bivariate survival data set of leukemia remission times (Freireich et al., 1963). Analysis is performed using Markov Chain Monte Carlo methods. Model comparison is made using Bayesian model selection criterion and a better model is suggested for the data.