Abstract The Fine–Gray proportional subdistribution hazards model has been puzzling many people since its introduction. The main reason for the uneasy feeling is that the approach considers individuals still at risk for an event of cause 1 after they fell victim to the competing risk of cause 2. The subdistribution hazard and the extended risk sets, where subjects who failed of the competing risk remain in the risk set, are generally perceived as unnatural . One could say it is somewhat of a riddle why the Fine–Gray approach yields valid inference. To take away these uneasy feelings, we explore the link between the Fine–Gray and cause‐specific approaches in more detail. We introduce the reduction factor as representing the proportion of subjects in the Fine–Gray risk set that has not yet experienced a competing event. In the presence of covariates, the dependence of the reduction factor on a covariate gives information on how the effect of the covariate on the cause‐specific hazard and the subdistribution hazard relate. We discuss estimation and modeling of the reduction factor, and show how they can be used in various ways to estimate cumulative incidences, given the covariates. Methods are illustrated on data of the European Society for Blood and Marrow Transplantation.

中文翻译：

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关于特定原因危害与竞争风险数据的子分布率之间的关系：重新审视细灰色模型

摘要 Fine-Gray 比例子分布风险模型自推出以来一直困扰着很多人。感到不安的主要原因是该方法认为个人在成为原因 2 的竞争风险的受害者后仍然处于原因 1 事件的风险中。 子分布风险和扩展风险集，其中竞争失败的受试者风险留在风险集中，通常被认为是不自然的。可以说为什么 Fine-Gray 方法会产生有效的推理有点像一个谜。为了消除这些不安的感觉，我们更详细地探讨了精细灰色和特定原因方法之间的联系。我们引入了减少因子作为表示尚未经历竞争事件的 Fine-Gray 风险集中的受试者比例。在存在协变量的情况下，减少因子对协变量的依赖性提供了关于协变量对特定原因危害和子分布危害的影响如何相关的信息。我们讨论了减少因子的估计和建模，并展示了如何在给定协变量的情况下以各种方式使用它们来估计累积发生率。欧洲血液和骨髓移植学会的数据说明了方法。