Modeling Frailty Using Birnbaum Saunders Distribution for Bivariate Survival Data

Abstract

Frailty models are survival models, which are designed to explore the properties of the unobserved heterogeneity in individuals pertaining to disease and death. In this paper, we propose the new frailty model called Birnbaum–Saunders frailty model with Weibull, Pareto, and exponential power as baseline distributions. Estimation of the proposed model parameters was done using Bayesian estimation procedure under Markov chain Monte Carlo technique. A simulation study was also presented to compare the true values and the estimated parameters. We then applied these proposed models to kidney infection data. Models comparison was done using various information criteria and Bayes factor. The best model for the data related to infection occur due to insertion of catheter is suggested.

Keywords

• Bayesian model comparison
• Birnbaum–Saunders frailty
• Exponential power distribution
• Pareto distribution
• Shared frailty
• Weibull distribution