Principled Estimation and Prediction with Competing Risks: a Bayesian Nonparametric Approach
本文提出一种贝叶斯非参数方法，通过分层完全随机测度构建灵活的先验，用于竞争风险下的多状态建模，并推导出预测曲线，为流行病学、精算学等领域提供新的估计与预测工具。
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.