We propose a set of causal estimands that we call ``the mediated probabilities of causation.'' These estimands quantify the probabilities that an observed negative outcome was induced via a mediating pathway versus a direct pathway in a stylized setting involving a binary exposure or intervention, a single binary mediator, and a binary outcome. We outline a set of conditions sufficient to identify these effects given observed data, and propose a doubly-robust projection based estimation strategy that allows for the use of flexible non-parametric and machine learning methods for estimation. We argue that these effects may be more relevant than the probability of causation, particularly in settings where we observe both some negative outcome and negative mediating event, and we wish to distinguish between settings where the outcome was induced via the exposure inducing the mediator versus the exposure inducing the outcome directly. We motivate our quantities of interest by discussing applications to legal and medical questions of causal attribution.

翻译：我们提出一组称为“中介因果概率”的因果估计量。这些估计量在涉及二元暴露或干预、单一二元中介变量及二元结果的典型设定中，量化了观测到的负面结果经由中介路径与直接路径被诱发的概率。我们概述了在给定观测数据下足以识别这些效应的条件集合，并提出一种基于投影的双稳健估计策略，该策略允许使用灵活的非参数与机器学习方法进行估计。我们认为这些效应可能比因果概率更具相关性，尤其是在我们同时观测到某种负面结果与负面中介事件的情况下，并且我们希望区分结果是由暴露通过中介变量诱发，还是由暴露直接诱发的情形。我们通过讨论在法律与医学因果关系归因问题中的应用，来激发我们对这些感兴趣量的研究动机。