Bayesian semiparametric analysis of short- and long-term hazard ratios with covariates

A full Bayesian analysis is developed for an extension to the short-term and long-term hazard ratios model that has been previously introduced. This model is specified by two parameters, short- and long-term hazard ratios respectively, and an unspecified baseline function. Furthermore, the model also allows for crossing hazards in two groups and includes the proportional hazards, and the proportional odds models as particular cases. The model is extended to include covariates in both, the short- and long-term parameters, and uses a Bayesian nonparametric prior, based on increasing additive processes mixtures, to model the baseline function. Posterior distributions are characterized via their full conditionals. Latent variables are introduced wherever needed to simplify computations. The algorithm is tested with a simulation study and posterior inference is illustrated with a survival study of ovarian cancer patients who have undergone a treatment with erythropoietin stimulating agents.