Modelos de fração de cura com fragilidade inflacionado de zero sob diferentes esquemas de ativação

Abstract

In this doctoral thesis, the proposed methodology is based on zero-inflated survival data to deal with situations where there is a fraction of inflated (or adjusted) zeros and cured cases considering different activation schemes. In this approach, we assume that the occurrence of the event of interest is generated by a latent activation structure: first, last, and random, allowing different competing activation mechanisms to explain the occurrence of the phenomenon of interest. In this context, the new model called the zero-inflated cure rate model under different activation schemes is an extension of the zero-inflated model proposed by \citeonline{de2017zero}; the model proposed by \citeonline{roman2013modelos} the promotion time model proposed by \citeonline{yakovlev1996threshold} e \citeonline{chen1999new}, as we incorporate zero-inflation and activation schemes in the modeling. For the estimation of the parameters of the model with long duration and zero-inflation, we consider classical and Bayesian approaches. The cure rate models or zero cure rate models indirectly assume that all patients exposed to the event of interest have homogeneous risk, but the existence of heterogeneity can be measured through the inclusion of covariates. Thus, it is possible to measure a portion of this heterogeneity by covariates, but there is a degree of heterogeneity induced by unobserved causes. Models that include this unobserved heterogeneity among subjects are known as frailty models. In this context, the frailty term is incorporated into the risk function of the proposed modeling to control the unobserved heterogeneity of patients, and we assume a gamma distribution for the frailty variable. Simulation studies are performed, as well as applications to real data.