Statistical Analysis of Medical Lifetime Data in Presence of Censored Data and Covariates Using Semiparametric Transformation Models Under a Bayesian Approach

Abstract

Emerson Barili and Jorge Alberto Achcar

A very promising alternative recently considered in the literature for the analysis of lifetime data in presence of covariates and censored data is given by the class of semiparametric or transformation models. This class of models generalizes the usual proportional hazards models, the proportional odds models, and the accelerated failure time models, extensively used in lifetime data analysis. In the analysis of lifetime data, especially in medicine, the proportional hazards model has been the most used model due to its flexibility without the need to assume a parametric model for the data [1]. Despite this advantage, in some applications the needed assumption (proportional hazards) may not be verified and the class of transformation models can be quite attractive in data analysis. In obtaining inferences of interest, especially obtaining point estimators for the regression parameters assuming transformation models, several proposals have been introduced in the literature, as alternatives to the use of the partial likelihood proposed assuming proportional hazards models [1, 2]. In this work, we introduce a simple method to obtain inferences for the regression parameters of semiparametric models or transformation models under a Bayesian approach considering the unknown hazard rates as latent variables. The posterior summaries of interest are obtained using existing MCMC (Markov Chain Monte Carlo) simulation methods. An application with real-time medical data illustrates the proposed methodology.

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