Many research questions involve time-to-event outcomes that can be prevented from occurring due to competing events. In these settings, we must be careful about the causal interpretation of classical statistical estimands. In particular, estimands on the hazard scale, such as ratios of cause-specific or subdistribution hazards, are fundamentally hard to interpret causally. Estimands on the risk scale, such as contrasts of cumulative incidence functions, do have a clear causal interpretation, but they only capture the total effect of the treatment on the event of interest; that is, effects both through and outside of the competing event. To disentangle causal treatment effects on the event of interest and competing events, the separable direct and indirect effects were recently introduced. Here we provide new results on the estimation of direct and indirect separable effects in continuous time. In particular, we derive the nonparametric influence function in continuous time and use it to construct an estimator that has certain robustness properties. We also propose a simple estimator based on semiparametric models for the two cause-specific hazard functions. We describe the asymptotic properties of these estimators and present results from simulation studies, suggesting that the estimators behave satisfactorily in finite samples. Finally, we reanalyze the prostate cancer trial from Stensrud et al. (2020).

中文翻译：

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连续时间内可分离的直接和间接影响的估计

许多研究问题涉及事件发生时间的结果，这些结果可以避免因竞争事件而发生。在这些设置中，我们必须小心经典统计估计值的因果解释。特别是，危害规模的估计值，例如特定原因或子分布危害的比率，从根本上很难解释因果关系。风险量表上的估计值，如累积发生率函数的对比，确实有明确的因果解释，但它们只捕捉了治疗对感兴趣事件的总体影响；也就是说，比赛活动内外的影响。为了理清因果治疗对感兴趣事件和竞争事件的影响，最近引入了可分离的直接和间接影响。在这里，我们提供了关于连续时间中直接和间接可分离效应估计的新结果。特别地，我们推导了连续时间的非参数影响函数，并用它来构造一个具有一定稳健性的估计量。我们还针对两个特定原因的危险函数提出了一个基于半参数模型的简单估计器。我们描述了这些估计量的渐近特性，并展示了模拟研究的结果，表明这些估计量在有限样本中的表现令人满意。最后，我们重新分析 Stensrud 的前列腺癌试验 我们还针对两个特定原因的危险函数提出了一个基于半参数模型的简单估计器。我们描述了这些估计量的渐近特性，并展示了模拟研究的结果，表明这些估计量在有限样本中的表现令人满意。最后，我们重新分析 Stensrud 的前列腺癌试验 我们还针对两个特定原因的危险函数提出了一个基于半参数模型的简单估计器。我们描述了这些估计量的渐近特性，并展示了模拟研究的结果，表明这些估计量在有限样本中的表现令人满意。最后，我们重新分析 Stensrud 的前列腺癌试验等。（2020）。