Survival analysis via hierarchically dependent mixture hazards

Hierarchical nonparametric processes are popular tools for defining priors on collections of probability distributions, which induce dependence across multiple samples. In survival analysis problems one is typically interested in modeling the hazard rates, rather than the probability distributions themselves, and the currently available methodologies are not applicable. Here we fill this gap by introducing a novel, and analytically tractable, class of multivariate mixtures whose distribution acts as a prior for the vector of sample–specific baseline hazard rates. The dependence is induced through a hierarchical specification for the mixing random measures that ultimately corresponds to a composition of random discrete combinatorial structures. Our theoretical results allow to develop a full Bayesian analysis for this class of models, which can also account for right–censored survival data and covariates, and we also show posterior consistency. In particular, we emphasize that the posterior characterization we achieve is the key for devising both marginal and conditional algorithms for evaluating Bayesian inferences of interest. The effectiveness of our proposal is illustrated through some synthetic and real data examples.