Survival analysis of critically ill patients with cancer: use of semiparametric (transformation models) under a hierarchical Bayesian approach
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Abstract
Survival medical data in presence of covariates and censored data usually are analyzed assuming non- parametric or parametric regression modeling approaches as the popular proportional hazards models, the proportional odds models and the accelerated failure time models. In medical studies, it is usual the use of the popular proportional hazards models introduced by Cox, 1972 in the data analysis. Maximum likelihood estimation methods assuming the partial likelihood function introduced by Cox, 1975 are used to get the inferences of interest. In many applications, the assumption of proportional hazards could be non-verified which makes the use of the Cox model unfeasible. In this way, the use of semiparametric or transformation models recently introduced in the literature could be a good alternative in the analysis of lifetime data in presence of censoring and covariates. This class of models generalizes the popular class of proportional hazards models proposed by Cox, 1972 without the need to assume a parametric probability distribution for the survival times. In this study, we present a hierarchical Bayesian analysis considering semiparametric models to a data set consisting of the survival times of cancer patients admitted to the intensive treatment unit of the INCA health institute (Instituto Nacional de Câncer - INCA) in Rio de Janeiro, Brazil. The posterior summaries of interest are obtained using existing MCMC (Markov Chain Monte Carlo) simulation methods.
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