Modelos semiparamétricos para dados de sobrevivência com censura intervalar

Abstract

In survival analysis we say that the data is subejct to interval-censored when it is known that the survival time of the individuals is in a interval time. Thus, this thesis aims to propose extensions to the piecewise exponential model with random grid, via the product partition model clustering structure under a dynamic approach, to survival data subject to interval-censored. We propose models for two types of populations: with and without a cured fraction. For population without a cured fraction, we present three modeling proposal. The first one representing the PEM with random time grid, with time-independent coefficients. In addition two dynamic models representing extensions, one with fixed time grid and another with random time grid, both allowing time-dependent coefficients. For this type of population, we illustrate the proposed models, and those available in the literature, using a breast cancer data, analysing the deterioration time of the patients. The main result shows that the proposed dynamic model with fixed time grid and time-independent coefficient has the best results when compared to the others. For situations with cured fraction in the population, we present two proposals of cure rate models. The first one, is dynamic MEP with fixed time grid, and the second being the random time grid version, using the product partition model clustering structure, built based on the promotion time model. In this scenario, we illustrate an proposed models, using the infection time data. The results show that the dynamic cure rate model with a random time grid, showed the best fit to the data, when compared with the dynamic cure rate model with a fixed grid time.