Reinforced urns and the subdistribution beta-Stacy process prior for competing risks analysis

In this paper, we introduce the subdistribution beta-Stacy process, a novel Bayesian nonparametric process prior for subdistribution functions useful for the analysis of competing risks data. In particular, we (i) characterize this process from a predictive perspective by means of an urn model with reinforcement, (ii) show that it is conjugate with respect to right-censored data, and (iii) highlight its relations with other prior processes for competing risks data. Additionally, we consider the subdistribution beta-Stacy process prior in a nonparametric regression model for competing risks data, which, contrary to most others available in the literature, is not based on the proportional hazards assumption.