Shared Gamma Frailty Models Based on Additive Hazards

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 (e.g. matched pairs experiments, twin or family data), the shared frailty models were suggested. These models are based on the assumption that frailty act multiplicatively to hazard rate. In this paper we assume that frailty acts additively to hazard rate. We introduce the shared gamma frailty models with two different baseline distributions namely, the generalized log logistic and the generalized Weibull. We introduce the Bayesian estimation procedure using Markov Chain Monte Carlo technique to estimate the parameters involved in these models. We apply these models to a real life bivariate survival data set of McGilchrist and Aisbett (Biometrics 47:461–466, 1991) related to the kidney infection data and a better model is suggested for the data.