Agenda

Antonio Lijoi (Bocconi University) - Hierarchical random measures for competing risks: from dependence to prediction

Abstract:

Hierarchical nonparametric priors provide a natural framework for the Bayesian modeling of heterogeneous, yet related, populations. Under partial exchangeability, population-specific random measures are conditionally independent given a common random measure, allowing information to be shared while preserving heterogeneity. The same hierarchical idea can also be useful in a seemingly different setting, in which the observations themselves are exchangeable. In competing-risks problems, each observation consists of a survival time and an event type, and inference requires the joint modeling of cause-specific hazards. We construct a flexible prior for the transition probabilities of the associated multi-state model by transforming a vector of hierarchical completely random measures. The common level of the hierarchy induces dependence and information sharing across causes. The resulting latent partition structure and a representation based on marked random measures lead to tractable marginal, posterior, and predictive distributions. Besides providing estimates of the survival and cause-specific cumulative incidence functions, the framework yields a novel predictive quantity: the prediction curve. This curve gives, conditionally on the observed data, the probability that a future event is of a particular type as a function of its occurrence time. Applications to clinical data illustrate its interpretation and practical relevance.