Decomposição da variância para o modelo de regressão destrutivo Waring de longa duração

Abstract

The goal of this work is to formulate a two-stage regression long-term model, whose destructive mechanism of the competitive risk factors is flexible for measuring the impact on the survival function or cure rate of three variance components induced by: randomness effects, external effects or external frailties (unknown covariates) and destruction or internal frailty (destructive mechanism). The number of the risk factors which were not eliminated is unobservable random variable, called discrete frailty, and the choice of the frailty distribution must be appropriate to detect the sources of variability responsible for the variation between patients. The discrete frailty random variable of the first-stage of the model is based on the Waring distribution, which splits the variance into these three components, and was applied with success in the accident theory, epidemiology and biology. A simulation study and an application to a HIV and melanoma data, via likelihood approach, illustrate the utility of the Waring distribution to detect internal frailty, external frailty and model's uncertainty (randomness effect), which are not observable and responsible for the heterogeneity across patients. The cure rate is personalized and the patient is a protagonist for the treatment, and that could be useful to decide on preventive immunotherapy treatment for patients to fight cancer.