Natural Effects and Separable Effects: Insights into Mediation Analysis

Abstract

We compare natural effects and separable effects under nonparametric structural equation models with independent errors, highlighting their similarities and differences. By examining their required properties and sufficient conditions for identification, we aim to provide deeper insights into mediation analysis. If certain assumptions about confounding, positivity, and consistency are met, we can identify natural direct and indirect effects under nonparametric structural equation models with independent errors. However, these effects have been criticized because they rely on a specific cross-world quantity, and the so-called cross-world independence assumption cannot be empirically verified. Furthermore, interventions on the mediator may sometimes be challenging to even conceive. As an alternative approach, separable effects have recently been proposed and applied in mediation analysis, often under finest fully randomized causally interpretable structured tree graph models. These effects are defined without relying on any cross-world quantities and are claimed to be identifiable under assumptions that are testable in principle, thereby addressing some of the challenges associated with natural direct and indirect effects. To conduct meaningful mediation analysis, it is crucial to clearly define the research question of interest, and the choice of methods should align with the nature of the question and the assumptions researchers are willing to make. Examining the underlying philosophical perspectives on causation and manipulation can provide valuable insights.