Scientists often pose questions about treatment effects on outcomes conditional on a post-treatment event. However, defining, identifying, and estimating causal effects conditional on post-treatment events requires care, even in perfectly executed randomized experiments. Recently, the conditional separable effect (CSE) was proposed as an interventionist estimand, corresponding to scientifically meaningful questions in these settings. However, while being a single-world estimand, which can be queried experimentally, existing identification results for the CSE require no unmeasured confounding between the outcome and post-treatment event. This assumption can be violated in many applications. In this work, we address this concern by developing new identification and estimation results for the CSE in the presence of unmeasured confounding. We establish nonparametric identification of the CSE in both observational and experimental settings when certain proxy variables are available for hidden common causes of the post-treatment event and outcome. We characterize the efficient influence function for the CSE under a semiparametric model of the observed data law in which nuisance functions are a priori unrestricted. Moreover, we develop a consistent, asymptotically linear, and locally semiparametric efficient estimator of the CSE using modern machine learning theory. 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在治疗后的条件事件下处理效应的因果问题。然而，即使在完美执行的随机实验中，定义、识别和估计治疗后条件事件下的因果效应也需要谨慎。近期，条件可分效应（CSE）被提出作为一种干预性估计量，对应于这些场景中具有科学意义的问题。尽管CSE是一种可在实验中查询的单世界估计量，但现有的识别结果要求结果与治疗后事件之间不存在未测量的混淆因素。这一假设在许多应用中可能被违反。本文中，我们通过开发在存在未测量混淆因素时CSE的识别和估计新结果来解决这一问题。我们证明，当存在某些代理变量用于治疗后事件与结果的隐藏共同原因时，CSE在观察性和实验性设置中均可实现非参数识别。我们在观测数据规律半参数模型下刻画了CSE的有效影响函数，其中干扰函数先验无限制。此外，我们利用现代机器学习理论开发了一种一致、渐近线性且局部半参数有效的CSE估计器。我们通过模拟研究和一个真实世界的癌症治疗试验来展示我们的框架。