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.

翻译：在生存分析中，当存在多种死亡原因时会出现竞争风险。它们在生物统计学之外的多个领域起着重要作用，涵盖流行病学、精算科学和可靠性理论。本文采用多状态建模框架来处理竞争风险。我们引入一类通过层次完全随机测度定义的灵活非参数先验，用于建模转移概率，并识别该一般类中的特定（条件）共轭成员。此外，我们确定数据和潜在随机划分的联合边际分布，并描述模型的后验分布。利用这些分布结果，我们评估未来事件属于特定类型（例如，特定原因导致的死亡）的预测概率，作为事件发生时间的函数。基于可靠原理推导出的这一函数被称为预测曲线，代表了文献中的一项重大创新。此外，我们提供生存函数以及原因特异性发病率和子分布函数的后验估计。我们还设计了适用于后验推断的模拟算法。通过模拟研究评估模型性能以及算法的有效性。最后，我们在临床数据集上说明了我们的方法。