Estimating the grid of timepoints for the piecewi

Authors: Fabio N Demarqui Rosangela H Loschi Enrico A Colosimo

Publish Date: 2008/05/09

Volume: 14, Issue: 3, Pages: 333-356

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Abstract

One of the greatest challenges related to the use of piecewise exponential models PEMs is to find an adequate grid of timepoints needed in its construction In general the number of intervals in such a grid and the position of their endpoints are adhoc choices We extend previous works by introducing a full Bayesian approach for the piecewise exponential model in which the grid of timepoints and consequently the endpoints and the number of intervals is random We estimate the failure rates using the proposed procedure and compare the results with the nonparametric piecewise exponential estimates Estimates for the survival function using the most probable partition are compared with the Kaplan–Meier estimators KMEs A sensitivity analysis for the proposed model is provided considering different prior specifications for the failure rates and for the grid We also evaluate the effect of different percentage of censoring observations in the estimates An application to a real data set is also provided We notice that the posteriors are strongly influenced by prior specifications mainly for the failure rates parameters Thus the priors must be fairly built say really disclosing the expert prior opinion

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