Bayesian Analysis of Frailty Models in Long-term Survivors


1 Department of Biostatistics, Alborz University of Medical Sciences, Karaj, Iran

2 Department of Statistics, Allameh Tabatabaei University, Tehran, Iran


In the survival analysis with long term survivors, there are two classes of Models: Mixture Cure Model and Non-Mixture Cure Model. Whereas using the Mixture Cure model have some disadvantage such as uncertainly in identifiability of true parameter and when we use non informative uniform prior distribution for coefficient variation, the posterior distribution would be improper the Bayesian approach, we used the non-mixture cure model. Also there are a lot of immeasurable factors have effect on the survival probability then introduced the frailty in the survival analysis. In the non-mixture cure model Yin (2005) introduced the frailty.  In this paper us insertion two definition of frailty and extend two new models. Also we show the better fitness of new models to Yin Models in the data set of leukemia.  For estimation the parameter in these models we used the hierarchical Bayesian approach. We construction the likelihood functions based on piecewise exponential distribution and log-normal distribution for frailty distribution. Since the posteriors distribution do not have close form then we use the Markov Chain Monte Carlo methods. Based on the Deviance Information Criteria (DIC) the fitness on the proposal models confirmed.