Scientists regularly pose questions about treatment effects on outcomes conditional on a post-treatment event. However, causal inference in such settings requires care, even in perfectly executed randomized experiments. Recently, the conditional separable effect (CSE) was proposed as an interventionist estimand that corresponds to scientifically meaningful questions in these settings. However, existing results for the CSE require no unmeasured confounding between the outcome and post-treatment event, an assumption frequently violated in practice. In this work, we address this concern by developing new identification and estimation results for the CSE that allow for unmeasured confounding. We establish nonparametric identification of the CSE in observational and experimental settings with time-varying confounders, provided that certain proxy variables for hidden common causes of the post-treatment event and outcome are available. For inference, we characterize an influence function for the CSE under a semiparametric model where nuisance functions are a priori unrestricted. Using modern machine learning methods, we construct nonparametric nuisance function estimators and establish convergence rates that improve upon existing results. Moreover, we develop a consistent, asymptotically linear, and locally semiparametric efficient estimator of the CSE. We illustrate our framework with simulation studies and a real-world cancer therapy trial.

翻译：科学家经常提出关于治疗对结果的影响，条件于治疗后事件的问题。然而，在此类设定中进行因果推断需要谨慎，即使在完美执行的随机化实验中也是如此。最近，条件可分离效应被提出作为一种干预主义可估量，对应于这些设定中具有科学意义的问题。然而，现有关于条件可分离效应的结果要求结果与治疗后事件之间不存在未测混杂，这一假设在实践中经常被违背。在本工作中，我们通过为条件可分离效应开发新的识别和估计结果来解决这一问题，这些结果允许未测混杂的存在。我们证明了在具有时变混杂因素的观察性和实验性设定中，只要能够获得治疗后事件与结果的隐藏共同原因的某些代理变量，条件可分离效应的非参数识别是成立的。对于推断，我们在一个半参数模型下刻画了条件可分离效应的影响函数，其中干扰函数是先验无限制的。利用现代机器学习方法，我们构建了非参数干扰函数估计器，并建立了优于现有结果的收敛速率。此外，我们开发了一个一致、渐近线性且局部半参数有效的条件可分离效应估计器。我们通过模拟研究和一项真实世界的癌症治疗试验来说明我们的框架。