Bayesian Estimation in Shared Compound Negative Binomial Frailty Models
Frailty models are used in survival analysis to model unobserved heterogeneity. To study such heterogeneity by the inclusion of a random term called the frailty is assumed to multiply hazards of all subjects in the shared frailty. We study compound negative binomial distribution as frailty distribution and two different baseline distributions namely Pareto and linear failure rate distribution in this paper. A simulation study is done to compare the true values of parameters with the estimated value. We develop the Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters of the proposed models. We try to fit the proposed models to a real life bivariate survival data set of McGrilchrist and Aisbett related to kidney infection. Also, we present a comparison study for the same data by using model selection criterion, and suggest a better model.
David D Hanagal* and Asmita T Kamble