Modelos bayesianos com fração de cura e erro de medida com distribuição na família mistura de escala da normal

Abstract

The medical advances in cancer treatment and the development of efficient diagnosis techniques in the recent years have contributed to the increase in the fraction of cured patients. Because of this, it can be noted an increasing the interest to develop statistical models to appropriately deal with lifetime data in the presence of cure fraction. It is well known that some covariates that may influence the patient lifetime can be mismeasured. In this work, we propose a Bayesian cure rate model that accommodates covariates of this nature. Our proposal extends models that have already been discussed in the literature by: (i) assuming that the measurement error belongs to the scale mixture of normal distributions class; (ii) by estimating the variance of the measurement error and also by (iii) considering Bayesian approaches to the models already proposed. Three different prior specifications are proposed to model this parameter. In all models, the expressions of the posterior distributions does not have a closed form. For this reason we used the Gibbs Sampler with Adaptative Metropolis to obtain samples from the posterior distributions. A Monte Carlo simulation study is presented and also an analysis of a melanoma clinical trial date that has already been explored in the literature.