🤖 AI Summary
This study addresses the challenge of jointly predicting event types and their occurrence times under competing risks by proposing a Bayesian nonparametric approach within a multi-state modeling framework. The method employs a prior defined through a hierarchical completely random measure to model transition probabilities. By deriving the joint marginal and posterior distributions of the observed data and latent random partitions, the work constructs, for the first time in a Bayesian nonparametric setting, theoretically grounded “prediction curves” that enable joint inference on the time-evolving probabilities of competing events and identifies a class of conditionally conjugate priors. Simulation studies and real-world clinical data analyses demonstrate that the proposed approach effectively estimates survival functions, cause-specific hazard rates, and subdistribution functions, confirming its strong predictive performance and practical utility.
📝 Abstract
Competing risks occur in survival analysis when multiple causes of death are present. They play a prominent role in several domains extending beyond biostatistics to encompass epidemiology, actuarial sciences, and reliability theory. This paper adopts a multi-state modeling framework to competing risks. We introduce a class of flexible nonparametric priors, defined through hierarchical completely random measures, to model the transition probabilities, and identify the specific (conditionally) conjugate member of this general class. Furthermore, we determine the joint marginal distribution of the data and of a latent random partition, and characterize the posterior distribution of the model. Leveraging these distributional results, we evaluate the predictive probability that a future event is of a specific type (e.g. death from a particular cause), as a function of the time at which the event occurs. The resulting function, derived on sound principles, is termed the prediction curve, and represents a major innovation in the literature. In addition, we provide posterior estimates for the survival function, and for the cause-specific incidence and subdistribution functions. Suitable simulation algorithms for posterior inference are also devised. The model's performance, as well as the algorithms' effectiveness, is evaluated through simulation studies. Finally, we illustrate our approach on clinical datasets.