Frailty models are used in the survival analysis to account for the
unobserved heterogeneity in individual risks of disease and death. The shared frailty
models have been suggested to analyze the bivariate data on related survival times
(e.g., matched pairs experiments, twin or family data). This paper introduces the
shared Inverse Gaussian (IG) frailty model with baseline distribution as Weibull
exponential, Lomax, and Logistic exponential. 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
actual 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 [1] related to the
kidney infection data, and a better model is suggested for the data.
Keywords: Bayesian model comparison, Inverse gaussian frailty, Lomax
distribution, Logistic exponential distribution, MCMC, Shared frailty, Weibull
exponential distribution.
