Detecting and Understanding the Difference between Natural Mediation Effects and Their Randomized Interventional Analogues

Abstract

In causal mediation analysis, the natural direct and indirect effects (natural effects) are nonparametrically unidentifiable in the presence of treatment-induced confounding, which motivated the development of randomized interventional analogues (RIAs) of the natural effects. Being easier to identify, the RIAs are becoming widely used in practice. However, applied researchers often interpret RIA estimates as if they were the natural effects, even though the RIAs can be poor proxies for the natural effects. This calls for practical and theoretical guidance on when the RIAs differ from or coincide with the natural effects. We develop the first empirical test to detect the divergence between the natural effects and their RIAs under the weak assumptions sufficient for identifying the RIAs and illustrate the test using the Moving to Opportunity Study. We also provide new theoretical insights on the relationship between the natural effects and the RIAs both using a covariance formulation and from a structural equation perspective. This analysis also reveals previously undocumented connections between the natural effects, the RIAs, and estimands in instrumental variable analysis and Wilcoxon-Mann-Whitney tests.