Correlated positive stable frailty models

Abstract

Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyze the bivariate data on related survival times, the shared frailty models were suggested. Shared frailty models are used despite their limitations. To overcome their disadvantages correlated frailty models may be used. In this paper, we introduce the correlated positive stable frailty models with two different baseline distributions namely, the generalized log logistic and the generalized Weibull. We introduce the Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in these models. We present a simulation study to compare the true values of the parameters with the estimated values. Also we apply these models to a real life bivariate survival data set of McGilchrist and Aisbett related to the kidney infection data and a better model is suggested for the data.

Keywords:

• Bayesian estimation
• correlated positive stable frailty
• generalized log-logistic distribution
• generalized Weibull distribution
• MCMC

Mathematical Subject Classification:

• 62F15
• 62N01
• 62P10