Gamma shared frailty model based on reversed hazard rate

Abstract

Frailty models are used in survival analysis to account for unobserved heterogeneity in individual risks to disease and death. To analyze bivariate data on related survival times (e.g., matched pairs experiments, twin, or family data), shared frailty models were suggested. Shared frailty models are frequently 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 paper, we introduce shared gamma frailty models with reversed hazard rate. We introduce Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in the model. We present a simulation study to compare the true values of the parameters with the estimated values. Also, we apply the proposed model to the Australian twin data set.

Keywords:

• Bayesian estimation
• Gamma frailty
• Generalized exponential distribution
• Left censoring
• MCMC
• Reversed hazard rate
• Shared frailty

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F15
• 62N01
• 62P10

Acknowledgments

We thank all the referees for the valuable suggestions and comments which improved the earlier version of the manuscript.