Modeling of Inverse Gaussian Frailty Model for Bivariate Survival Data

Abstract

Shared frailty models are often used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of random factor (frailty) and baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and distribution of frailty. In this article, we consider inverse Gaussian 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 inverse Gaussian 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 apply these three models to a real life bivariate survival data set of McGilchrist and Aisbett (1991) related to kidney infection and a better model is suggested for the data.

Keywords:

• Bayesian model comparison
• Inverse Gaussian frailty
• Likelihood ratio test
• Markov Chain Monte Carlo
• Shared frailty

Mathematics Subject Classification:

• 62F15
• 62N01
• 62P10

Acknowledgments

We thank the referee for the useful suggestions and comments which improved an earlier version of this article.