Uma classe mais flexível de modelos semiparamétricos para dados de sobrevivência

Abstract

The piecewise exponential model (PEM) is a quite attractive and popular alternative to parametric models in survival analysis. Although parametric in a strict sense, the PEM can be thought of as a nonparametric model as far as its hazard function does not have a closed shape. For this reason the PEM has been widely used in the literature to model time-to-event data. Despite its popularity, the greatest challenge of workingwith the PEM is the specification of the time grid needed to fit this model. In this thesis we present some extensions of the approach introduced by Demarqui et al. (2008) to fit the PEM with random time grid. The contributions of this work are twofold. First, we provide a more flexible framework for modeling the randomness of the time grid of the PEM. Then, we show how this new framework can be extended to ccommodate accordingly other well-known approaches available in the literature. The new methodology is suitable for time-to-event data arising from any field of knowledge. It can be used in problems involving hazard function estimation, as well as to fit regression and cure rate models. The proposed approach can be further extended to model multivariate and/or spatially correlated survival times. The mechanism used to model the randomness of the time grid of the PEM has some nice features not shared by other approaches that have been proposed in the literature. In particular, the constrained imposed on the set of possible time grids for the PEM turns possible its estimation after directly prior elicitation. It further guarantees the existence of at least one failure time in each random interval induced by the random time grids. In addition, the arrangement of the failure times on the time axes is taking into account in the modeling of the time grid. The resultant models include other models established in the literature as special cases and provides a flexible framework for survival data modeling. Properties of the proposed models are discussed and the use of the new methodology is exemplified through the the analysis of a real data sets. For comparison purposes, the results obtained are compared with those provided by other methods existing in the literature. The new approaches introduced in this work are quite general and can be applied to model time to event data arising from any field of science, provided that survival times are right censored and the censoring mechanism is not nformative.