Modeling Australian twin data using shared positive stable frailty models based on reversed hazard rate

ABSTRACT

Unobserved heterogeneity, also called frailty, is a major concern in the application of survival analysis. The shared frailty models allow for the statistical dependence between the observed survival data. In this paper, we consider shared positive stable frailty model with the reversed hazard rate (RHR) with three different baseline distributions, namely the exponentiated Gumbel, the generalized Rayleigh, and the generalized inverse Rayleigh distributions. With these three baseline distributions we propose three different shared frailty models. We develop the Bayesian estimation procedure using Markov Chain Monte Carlo 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. A search of the literature suggests that currently no work has been done for these three baseline distributions with a shared positive stable frailty with the RHR so far. We also apply these three models by using a real-life bivariate survival data set of Australian twin data given by Duffy et a1. (1990) and a better model is suggested for the data.

KEYWORDS:

• Bayesian estimation
• exponentiated Gumbel distribution
• generalized inverse Rayleigh distribution
• generalized Rayleigh distribution
• Markov Chain Monte Carlo (MCMC)
• model selection criterion
• positive stable frailty
• reversed hazard rate.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F15
• 62N01
• 62P10

Acknowledgments

We thank both the referees for the valuable suggestions and comments which resulted in an improved version of the earlier manuscript.