Semiparametric transformation model in presence of cure fraction: a hierarchical Bayesian approach assuming the unknown hazards as latent factors

The class of semiparametric or transformation models has been presented in the literature as a promising alternative for the analysis of lifetime data in the presence of covariates and censored data. This class of models generalizes the popular class of proportional hazards models proposed by Cox (J R Stat Soc: Ser B (Methodol) 34(2):187–202, 1972) where it is not needed to assume a parametric probability distribution for the survival times. In addition to our focus on semipametric models, we also explore the situation where the population of interest is a mixture of susceptible individuals, who experience the event of interest and non-susceptible individuals that will never experience the event of interest. These individuals are not at risk with respect to the event of interest and are considered immune, non-susceptible, or cured. In this study, we present a simple method to obtain inferences for the parameters of semiparametric or transformation models in the presence of censoring, covariates and cure fraction under a Bayesian approach assuming the unknown hazard rates as latent variables with a given probability distribution. The posterior summaries of interest are obtained using existing Markov Chain Monte Carlo (MCMC) simulation methods. Some applications with real medical survival data illustrate the proposed methodology.