ABSTRACT
In this paper, we consider a piecewise exponential model (PEM) with random time grid to develop a full semiparametric Bayesian cure rate model. An elegant mechanism enjoying several attractive features for modeling the randomness of the time grid of the PEM is assumed. To model the prior behavior of the failure rates of the PEM we assume a hierarchical modeling approach that allows us to control the degree of parametricity in the right tail of the survival curve. Properties of the proposed model are discussed in detail. In particular, we investigate the impact of assuming a random time grid for the PEM on the estimation of the cure fraction. We further develop an efficient collapsed Gibbs sampler algorithm for carrying out posterior computation. A Bayesian diagnostic method for assessing goodness of fit and performing model comparisons is briefly discussed. Finally, we illustrate the usefulness of the new methodology with the analysis of a melanoma clinical trial that has been discussed in the literature.
Subject(s)
Biometry/methods , Models, Statistical , Algorithms , Bayes Theorem , Clinical Trials as Topic , Female , Humans , Male , Melanoma/therapy , Survival Analysis , Treatment OutcomeABSTRACT
One of the greatest challenges related to the use of piecewise exponential models (PEMs) is to find an adequate grid of time-points needed in its construction. In general, the number of intervals in such a grid and the position of their endpoints are ad-hoc choices. We extend previous works by introducing a full Bayesian approach for the piecewise exponential model in which the grid of time-points (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 non-parametric 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.
