ICES, Toronto, Ontario, Canada.
Institute of Health Management, Policy and Evaluation, University of Toronto, Toronto, Ontario, Canada.
Stat Med. 2021 Aug 30;40(19):4200-4212. doi: 10.1002/sim.9023. Epub 2021 May 9.
The Fine-Gray subdistribution hazard model has become the default method to estimate the incidence of outcomes over time in the presence of competing risks. This model is attractive because it directly relates covariates to the cumulative incidence function (CIF) of the event of interest. An alternative is to combine the different cause-specific hazard functions to obtain the different CIFs. A limitation of the subdistribution hazard approach is that the sum of the cause-specific CIFs can exceed 1 (100%) for some covariate patterns. Using data on 9479 patients hospitalized with acute myocardial infarction, we estimated the cumulative incidence of both cardiovascular death and non-cardiovascular death for each patient. We found that when using subdistribution hazard models, approximately 5% of subjects had an estimated risk of 5-year all-cause death (obtained by combining the two cause-specific CIFs obtained from subdistribution hazard models) that exceeded 1. This phenomenon was avoided by using the two cause-specific hazard models. We provide a proof that the sum of predictions exceeds 1 is a fundamental problem with the Fine-Gray subdistribution hazard model. We further explored this issue using simulations based on two different types of data-generating process, one based on subdistribution hazard models and other based on cause-specific hazard models. We conclude that care should be taken when using the Fine-Gray subdistribution hazard model in situations with wide risk distributions or a high cumulative incidence, and if one is interested in the risk of failure from each of the different event types.
在存在竞争风险的情况下，Fine-Gray 亚分布风险模型已成为估计随时间推移发生结果的发生率的默认方法。该模型很有吸引力，因为它直接将协变量与感兴趣事件的累积发生率函数（CIF）相关联。另一种方法是将不同的特定原因风险函数组合起来以获得不同的 CIF。亚分布风险方法的一个限制是，对于某些协变量模式，特定原因的 CIF 之和可能超过 1（100％）。使用 9479 名因急性心肌梗死住院的患者的数据，我们估计了每位患者的心血管死亡和非心血管死亡的累积发生率。我们发现，当使用亚分布风险模型时，大约有 5％的患者的 5 年全因死亡风险（通过将从亚分布风险模型获得的两个特定原因 CIF 组合获得）估计超过 1。通过使用两个特定原因的风险模型，可以避免这种现象。我们提供了一个证明，即预测的总和超过 1 是 Fine-Gray 亚分布风险模型的一个基本问题。我们进一步使用基于两种不同数据生成过程的模拟来探讨这个问题，一种基于亚分布风险模型，另一种基于特定原因的风险模型。我们的结论是，在风险分布广泛或累积发生率较高的情况下，以及如果对每种不同事件类型的失败风险感兴趣时，应谨慎使用 Fine-Gray 亚分布风险模型。
