A general Bayesian bootstrap for censored data based on the beta-Stacy process

We introduce a novel procedure to perform Bayesian non-parametric inference with right-censored data, the beta-Stacy bootstrap. This approximates the posterior law of summaries of the survival distribution (e.g. the mean survival time). More precisely, our procedure approximates the joint posterior law of functionals of the beta-Stacy process, a non-parametric process prior that generalizes the Dirichlet process and that is widely used in survival analysis. The beta-Stacy bootstrap generalizes and unifies other common Bayesian bootstraps for complete or censored data based on non-parametric priors. It is defined by an exact sampling algorithm that does not require tuning of Markov Chain Monte Carlo steps. We illustrate the beta-Stacy bootstrap by analyzing survival data from a real clinical trial.