Name: Vicente Garibay
Institution: Instituto de Ciencias Matematicas e de Computação, Universidade de São Paulo, São Carlos, SP, Brazil
Co-authors:  Adriano K. Suzuki, Edwin M. M. Ortega, Gauss M. Cordeiro


In this paper, we extend the proportional hazards frailty model to allow a discrete distribution for the frailty variable. Frailty zero can be interpreted as being immune or cured. We develop a class of survival models induced by a discrete frailty having a mixed Poisson distribution, which can account for unobserved dispersion. We construct a regression model to evaluate the effects of covariates in the cure fraction. Several former cure survival models are special cases of our modeling framework. The inferential approach exploits the Bayesian methods. Finally, the modelling is fully illustrated on a data set on colorectal cancer. From the practical point of view, besides having a more flexible modelling for fitting survival data in presence of cure fraction, questions of medical interesting can be answered. Particularly, treatment comparison can be made straightforwardly. Moreover, we can estimate the proportion of patients disease-free after a determined treatment.

Keywords: Bayesian procedure, colorectal cancer, cure rate models, frailty model,survival models.