A multivariate survival model induced by discrete frailty

Abstract

Frailty models are generally used to model heterogeneity and dependence between individuals. The distribution of the frailty variable is often assumed to be continuous. However, there are situations where a discretely-distributed frailty may be appropriate. On the other hand, when a cure rate is present in survival data, these continuous distributions may not be appropriate since individuals with long-term survival times encompass zero frailty. Having zero frailty can be interpreted as being immune or cured (long-term survivors). In this paper, we propose a new multivariate survival model induced by frailty for multivariate lifetime data in the presence of surviving fractions and examine some of its properties. The inferential approach exploits the Bayesian methods. We provide some simulation results to assess the performance of the proposed model. Furthermore, we illustrate the performance of the proposed model by means of a real data set.