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A Dynamic Approach for the Piecewise Exponential Modelwith Random Time GridFábio Nogueira DemarquiUniversidade Federal de Minas GeraisRosangela H. LoschiUniversidade Federal de Minas GeraisDipak K. DeyUniversity of ConnecticutEnrico A. ColosimoUniversidade Federal de Minas GeraisA novel fully Bayesian approach for modeling survival data with explanatory variables using thePiecewise Exponential Model (PEM) with random time grid is proposed. We consider a class of correlatedGamma prior distributions for the failure rates. Such prior specification is obtained via the dynamicgeneralized modeling approach jointly with a random time grid for the PEM. A product distribution isconsidered for modeling the prior uncertainty about the random time grid, turning possible the use ofthe structure of the Product Partition Model (PPM) to handle the problem. A unifying notation forthe construction of the likelihood function of the PEM, suitable for both static and dynamic modelingapproaches, is considered. Procedures to evaluate the performance of the proposed model are presented.The use of the new methodology is exemplified by the analysis of a real data set of survival times ofpatients with brain cancer obtained from SEER (Surveillance Epidemiology and End Results) database.For comparison purposes, the data set is also fitted using the dynamic model with fixed time gridestablished in the literature. The results obtained show the superiority of the proposed model. Finally,the authors would like to thank FAPEMIG for supporting this work.75