F Rigat and P Muliere
Beta-Stacy survival regression models
Date: April 2007
Abstract: 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 the discrete-time beta-Stacy process (DBS) and by introducing the regression effects via their prior means. Identifability is attained by defining the DBS precision parameter as an appropriate function 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. We show that the DBS approach is preferable to simpler parametric models for its exibility and that its reliance on specific formulations of the regression component is milder than that of semi-parametric models.
Keywords: survival analysis, random right censoring, beta-Stacy process, Bayesian hierarchical models, Markov chain Monte Carlo, melanoma, cerebral palsy.