In the survival analysis, when there is a cure fraction and the occurrence times of events are correlated, the cure frailty model is utilized. The main objective is to propose a method of analysis for two types of correlated frailty in the non-mixture cured model in order to separate the individual and shared heterogeneity between subjects. The cure models with correlated frailty and promotion time are considered. In both models, the likelihood function are based on piecewise exponential distribution for hazard function. To estimate the parameters, hierarchical Bayesian modeling is employed. Due to non-closed forms of the posteriors, they are estimated by MCMC algorithms. The Cox correlated frailty model is used as a benchmark and models are compared by DIC Criterion . The results show the superiority of cure models with correlated frailty.

On Hypergeometric Generalized Negative Binomial Distribution in Promotion Time Cure Model In analysis of survival data if exposes a high percentage of censoring due to termination of the study, whereas the study has lasted long enough, it is preferred to utilize cure models. These models, which are based on the latent variable distribution, has obtained much attention in the last decade. In this paper the Hypergeometric Generalized Negative Binomial distribution of the latent variable is used to model the long time survival data. The new model parameters are estimated in Bayesian approach. This model is applied for a Primary Biliary Cirrhosis clinical trial data and a simulated data set. With respect to DIC, Hypergeometric Generalized Negative Binomial model is a suitable fit to the data.