Extensions of the Piecewise Exponential Model

In this paper we present full semi-parametric Bayesian approaches for modeling
survival data using the piecewise exponential model (PEM). We assume that the time
grid needed to fit the PEM is a random quantity and propose a flexible class of prior
distributions for modeling jointly the time grid and its corresponding failure rates.
The mechanism used to model the randomness of the time grid of the PEM has several
advantages over other approaches that have been proposed to address the problem. The
resultant model includes other models established in the literature as special cases and
provides a flexible framework for survival data modeling. Properties of the model are
discussed and the use of the proposed methodology is exemplified through the analysis
of the survival times of patients diagnosed with brain cancer in Windhan-CT, USA,
obtained from the SEER (Surveillance, Epidemiology and End Results) database .