Modeling Heterogeneity in Bivariate Survival Data by Compound Poisson Distribution using Bayesian Approach

Shared frailty models are often used to model heterogeneity in survival analysis. There are certain assumptions about the baseline distribution and distribution of frailty. In this paper, we consider compound Poisson distribution as frailty distribution and three different baseline distributions namely, Weibull, generalized exponential and exponential power distribution. With these three baseline distributions, we propose three different compound Poisson shared frailty models. To estimate the parameters involved in these models we adopt Markov Chain Monte Carlo(MCMC) approach. We present a simulation study to compare the true values of the parameters with the estimated values. Also we fit these three models to a real life bivariate survival data set of McGilchrist and Aisbett (1991) related to kidney infection and the compound Poisson frailty with Weibull baseline is most suitable choice for kidney infection data. It is observed from the data analysis that female patients have a lower risk for infection as compared to male patients and also there is a strong evidence of high degree of heterogeneity in the population of patients.