Modelo exponencial por partes para dados de sobrevivência com longa duração

Abstract

The Piecewise Exponential Model (PEM) is a very utilized model, mainly in survival analysis. When using this model, one considers a partition of the time axis into a finite number of intervals and, after that, a constant failure rate is considered to each interval. Therefore the PEM approximates a continuous function, the failure rate, through line segments. For this reason, the PEM is a very exible model and, although it is a parametric model, it is often considered as non parametric one. The present work proposes a Bayesian dynamic approach that allows one to obtain the exact smoothed distribution for the parameters representing the failure rate. Moreover, the partition of the time grid(and, consequently, the number of intervals), will be considered as an unknown quantity to be estimated. This entire approach will be used to model the cure fraction in a population, which occurs when a part of the individuals in a study is considered cured and, therefore, will never experience the event of interest. For comparison purposes, the fixed time grid will also be considered. Lastly, in order to illustrate this approach, an application will be shown.