Discrete Frailty Model with Compound Poisson Distribution

Abstract

Frailty models provide an alternative to proportional hazards models where misspecified or omitted covariates are described by an unobservable random variable. These models are generally assumed a continuous frailty random variable. In some circumstances, it is appropriate to consider discrete frailty distributions. Besides, exponential, Weibull, gamma distributions and their generalizations have been used as failure time distributions in survival analysis. As an alternative to exponential distribution, Lindley distribution gains importance for the similarity of exponential distribution and allowance for the different shapes of hazard function. In this paper, frailties are assumed to be random variables drawn from a discrete compound Poisson distribution for the Lindley distributed failure time. In our study, proposed methods are applied to analyze subscription based business. The results of this study suggest that the Neyman type A frailty model for analyzing individual pension data. The results show that the Lindley is a more flexible failure time distribution than exponential since the hazard rates of the models is not constant.