Survival models induced by frailties

Abstract

Frailty models are used for modeling heterogeneity in survival data analysis. In analyzing these data the distribution of frailty in general is assumed continuous. In some cases it may be appropriate to consider the distribution of discrete frailty distributions. Survival data containing experimental units in the event of interest has not happened even after a long period of observation (survival data with cure fraction), this situation these experimental units have zero frailty and survival models induced by continue frailty would not be appropriate.In this study we propose new survival models induced by discrete frailty to data modeling univariate and bivariate (or multivariate) survival.Two survival models for modeling univariate data with a cure fraction are proposed, the first result when considering distribution hyper-Poission the fragility for the distribution of the frailty and the second proposal is obtained when considering the inflated power series distribution of zeros. The bivariate model is constructed considering the Poisson bivariate (or multivariate) to frailty. For the models proposed we intend to develop inferential procedures from classical and Bayesian perspective. In the context of classical inference (or frequentist) we intend to use the method of maximum likelihood and Bayesian methods approach Monte Carlo Markov Chain (MCMC). (AU)