Modelos de sobrevivência induzidos por fragilidade discreta com fração de cura e riscos proporcionais

Abstract

This work presents two new survival models induced by discrete frailty with unobserved heterogeneity and proportional hazards structure, for lifetime data. The first model consider the discrete frailty variable with Katz distribution and the second with Generalized Poisson distribution, which have overdispersion, equidispersion and underdispersion properties. The new models encompasses as particular case the promotion cure rate model. The proposed model with katz discrete frailty also encompasses the mixture cure rate model and cure rate model with dispersion. Inference aspects for proposed models as discussed, in a classical approach for Katz distribution, for which the maximum likelihood tools were used and regression models were presented to evaluate the effects of covariates in the cured fraction. Furthermore, an expectation maximization algorithm for determining the maximum likelihood estimates of the parameters of the model was presented. For Generalized Poisson model, a baysean aprouch was also used, through Markov chain Monte Carlo simulation method, especifically Metropolis–Hastings algorithm. Finally, the modeling was fully illustrated on cervical cancer data sets.