On relation between separable indirect effect, natural indirect effect, and interventional indirect effect

TL;DR

This paper compares the assumptions and interpretability of separable, natural, and interventional indirect effects, highlighting the conditions under which each measure is valid and proposing a unified analysis framework.

Contribution

It provides a systematic comparison of causal assumptions for different indirect effects and introduces a new identification result for the NIE with intermediate confounders.

Findings

Separable indirect effect lacks mediational interpretation without additional assumptions.

NIE remains valid with intermediate confounders, satisfying the mediation null criterion.

New identification result for NIE in the presence of intermediate confounders.

Abstract

Recently, the separable indirect effect (SIE) has gained attention due to its identifiability without requiring the untestable cross-world assumption necessary for the natural indirect effect (NIE). This article systematically compares the causal assumptions underlying the SIE, NIE, and interventional indirect effect (IIE) and evaluates their feasibility for mediational interpretation using the mediation null criterion, with a particular focus on the SIE. We demonstrate that, in the absence of intermediate confounders, the SIE lacks a mediational interpretation unless additional unverifiable assumptions are imposed. When intermediate confounders are present, separable effect methods fail to accurately capture the indirect effect, whereas the NIE still satisfy the mediation null criterion. Additionally, we present a new identification result for the NIE in the presence of intermediate confounders. Finally, we propose an integrated framework for practical analysis. This article emphasizes that the NIE is the most fundamental definition of indirect effect among the three measures and highlights the trade-off between mediational interpretability and assumption falsifiability.