Analysis of Tumorigenesis Data Using Shared Gamma Frailty Models via Bayesian Approach

Many analysis in epidemiological and prognostic studies and in studies of event history data require methods that allow for unobserved covariates or “frailties”. We consider the shared frailty model in the frame work of parametric proportional hazard model. There are certain assumptions about the distribution of frailty and baseline distribution. Mostly gamma distribution is considered for frailty distribution and Weibull distribution for baseline hazard. In this paper also, we consider gamma distribution as frailty distribution but some different baseline distributions, namely, Gompertz and log-logistic distribution because it is well known that the Weibull model is not suitable for modeling survival data in all situations. With these two baseline distributions, we propose two different shared gamma frailty models. We fit these models to a real life bivariate survival data set of tumorigenesis experiment. Data from a litter matched tumorigenesis experiment are analyzed using Bayesian approach to the analysis of clustered survival data in which there is a dependence of failure time observations within the same litter. The variance component estimation provides the estimated dispersion of the random effects. We carried out a test for frailty (or heterogeneity) using Bayes factor. Model comparison is made using information criterion and Bayes factor. We observed that the shared gamma frailty model with Gompertz baseline is the better fit for the tumorigenesis data.