Primary Submission Category: Mediation
A Covariance Perspective on Randomized Interventional Analogues of Mediation Estimands
Authors: Ang Yu, Li Ge,
Presenting Author: Ang Yu*
In causal mediation analysis, the natural indirect effect (NIE) typically requires the cross-world independence assumption for identification, an assumption often unrealistic in many settings. Alternatively, the randomized interventional analogue (RIA) of the NIE circumvents this assumption. However, Miles (2023) demonstrates through specific counterexamples that the RIA of the NIE fails to meet certain null criteria essential for a valid indirect effect measure. This paper elucidates that the discrepancy between the NIE and its RIA is representable as a covariance between the mediator and outcome. Specifically, when both are binary, this difference equates to the covariance between the treatment’s effect on the mediator and the mediator’s effect on the outcome. Thus, we demystify the violation of the null criteria, detail the conditions under which this occurs, and highlight the uniquity of such violation. Similarly, we examine the differences between the natural direct effect, the total effect, and their RIAs. Furthermore, our work also enriches the extensive literature on causal U-statistics, including Wilcoxon-Mann-Whitney parameters, win ratio, and probability of causation. We observe that the estimands commonly used in practice are frequently misinterpreted and mistaken for their more intuitively interpretable counterparts. We establish that the differences between these commonly used estimands and their misinterpretations can also be represented as covariances.