Analysis of diabetic retinopathy data using shared inverse Gaussian frailty model

The dependence between individuals in a group is modeled by the group specific quantity, which can be interpreted as an unobserved covariates or “frailties” common to the individuals in the group and assumed to follow some distribution. We consider the shared frailty model in the frame work of parametric Cox proportional hazard model. The Cox regression model with the shared frailty factor allows for unobserved heterogeneity or for statistical dependence between the observed survival times. There are certain assumptions about the distribution of frailty and baseline distribution. The exponential distribution is the commonly used distribution for analyzing life time data. In this paper, we consider shared inverse Gaussian frailty model with bivariate exponential of Marshall-Olkin (1967) distribution as baseline hazard for bivariate survival times. We fit the model to the real life bivariate survival data set of diabetic retinopathy data. Data are analyzed using Bayesian approach to the analysis of clustered survival data in which there is a dependence of failure time observations within the same group. The variance component estimation provides the estimated dispersion of the random effects. The problem of analyzing and estimating parameters of shared inverse Gaussian frailty for diabetic retinopathy data is the interest of this paper. Also, we carried out a test for independence using information criteria.