Estimação paramétrica do modelo de mistura padrão com fragilidade aditiva gama: aplicação a dados de câncer de mama

Abstract

Breast cancer is caused by the uncontrolled growth of abnormal cells in the breast, which multiply rapidly, aggressively and uncontrollably. This disease affects women all over the world, both in developed and underdeveloped countries, and can also affect men, which is an extremely rare situation. There are several treatments for its cure, which may vary according to the stage of the disease, and, when diagnosed early, it has a high cure rate. Cure rate models have been extensively studied to analyze time-to-event data with the presence of a cure fraction of patients. In this context, the objective of this work is to incorporate frailty, the degree of heterogeneity induced by unobservable risk factors, in the cure rate model, to describe this type of data. The proposed model is an extension of Aalen's additive model (Aalen, 1980b) and incorporates two portions of the population, non-susceptible and susceptible individuals to the event of interest. An advantage of the proposed model is the possibility of jointly considering the heterogeneity between patients due to their frailties and the presence of a cured fraction of them. In addition, covariates that influence the survival function and the proportion of cured in the population will be considered. Some properties of these models will be discussed, as well as adequate estimation methods. The proposed methodology will be applied to a set of breast cancer data from studies carried out at Hospital A.C.Camargo Cancer Center - São Paulo, Brazil