The semi-competing risks problem arises when one is interested in the effect of an exposure or treatment on both intermediate (e.g., having cancer) and primary events (e.g., death) where the intermediate event may be censored by the primary event, but not vice versa. Here we propose a nonparametric approach casting the semi-competing risks problem in the framework of causal mediation modeling. We set up a mediation model with the intermediate and primary events, respectively as the mediator and the outcome, and define an indirect effect as the effect of the exposure on the primary event mediated by the intermediate event and a direct effect as that not mediated by the intermediate event. A nonparametric estimator with time-varying weights is proposed for direct and indirect effects where the counting process at time t of the primary event $N_{2n_1}(t)$ and its compensator $A_{n_1}(t)$ are both defined conditional on the status of the intermediate event right before t, $N_1(t^{-})=n_1$. We show that $N_{2n_1}(t)-A_{n_1}(t)$ is a zero-mean martingale. Based on this, we further establish theoretical properties for the proposed estimators. Simulation studies are presented to illustrate the finite sample performance of the proposed method. Its advantage in causal interpretation over existing methods is also demonstrated in a hepatitis study.

中文翻译：

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半竞争风险的因果中介

当人们对暴露或治疗对中间事件（例如，患有癌症）和主要事件（例如，死亡）的影响感兴趣时，就会出现半竞争风险问题，其中中间事件可能会被主要事件审查，但不会被审查。反之亦然。在这里，我们提出了一种非参数方法，在因果中介建模的框架内解决半竞争风险问题。我们建立了一个以中间事件和主要事件分别作为中介和结果的中介模型，并将间接影响定义为暴露对主要事件的影响，由中间事件介导，直接影响定义为未由中间事件介导的影响。中间事件。提出了一种具有时变权重的非参数估计器，用于直接和间接影响，其中在时间t的计数过程主要事件的${ñ}_{2n_1}(吨)$及其补偿器${\mathrm{一种}}_{n_1}(吨)$都以t之前的中间事件的状态为条件定义，${ñ}_1({吨}^{-})=n_1$. 我们表明${ñ}_{2n_1}(吨)-{\mathrm{一种}}_{n_1}(吨)$是一个零均值鞅。在此基础上，我们进一步建立了所提出的估计量的理论性质。仿真研究说明了所提出方法的有限样本性能。一项肝炎研究也证明了它在因果解释方面优于现有方法的优势。