Comparisons of frailty models for kidney infection data under Weibull baseline distribution

Abstract

Shared frailty models are often used to model heterogeneity in the survival analysis. The most common shared frailty model is a model in which hazard function is a product of 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. Mostly assumption of the gamma distribution is considered for frailty distribution. To compare the results with the gamma frailty model, we introduce three shared frailty models with the Weibull as baseline distribution. The other three shared frailty models are the inverse Gaussian shared frailty model, the compound Poisson shared frailty model and the compound negative binomial shared frailty model. We fit these models to a real life bivariate survival dataset of McGilchrist and Aisbett (1991) related to kidney infection data using the Markov chain Monte Carlo (MCMC) technique. Model comparison is made using the Bayesian model selection criteria and the inverse Gaussian frailty model model is suggested for this data.