This paper introduces a class of survival models for discrete time-to-event data with random right censoring. Flexible distributions for the survival times are constructed by modelling the random survival functions as discrete-time beta-Stacy processes (DBS) and by introducing the regression effects via their prior means. Identifiability is attained by defining the DBS precision parameters as appropriate functions of the regression coefficients. By the conjugacy of the beta-Stacy process with respect to random right censoring, marginal posterior inferences for all model parameters can be efficiently approximated using the standard Gibbs sampler. The latter also yields a Monte Carlo approximation for the predictive distributions of the survival probabilities for future covariate profiles. We provide three clinical applications of the DBS survival regression framework comparing its estimates with those of parametric, semiparametric and non-parametric survival models.
