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. In this paper, we introduce the shared inverse Gaussian frailty model based on the reversed hazard rate with the three baseline distributions, namely, log-logistic distribution, the inverse Weibull distribution and the generalized Weibull distribution. We introduce the Bayesian estimation procedure using the Markov Chain Monte Carlo technique to estimate the parameters involved in the model. We present a simulation study and show that the estimates of the parameters are very close to true values of the parameters. We apply the proposed models to the Australian twin data set and suggest a better model from the proposed eight models for Australian twin data set.