Cumulative Natural Direct and Indirect Effects for Causal Mediation Analysis

2026-06-20

AI Summary

This study addresses the limitations of traditional natural direct and indirect effects (NDE/NIE) in causal mediation analysis, which lack skew-symmetry and additivity, often leading to interpretational paradoxes. To overcome these issues, the authors propose cumulative natural direct and indirect effects (CNDE/CNIE), a novel framework that decomposes local causal effects and, under standard identification assumptions, yields valid measures for both continuous and ordinal treatment variables. The proposed CNDE/CNIE satisfy skew-symmetry and additivity, thereby enabling a coherent decomposition of the total effect. Empirical evaluations in linear mediation models—including those with interaction terms—and real-world data demonstrate that CNDE/CNIE provide more robust and interpretable causal estimates compared to conventional NDE/NIE.

Abstract

Causal mediation analysis provides a fundamental framework for quantifying the contributions of different pathways from a treatment $X$ to an outcome $Y$ through a mediator. The natural direct and indirect effects (NDE and NIE) are widely used to decompose the total effect. In this paper, we observe that NDE and NIE can give rise to paradoxical interpretations due to their failure to satisfy two desirable properties of interpretable causal effects: skew-symmetry and additivity. To address these limitations, we introduce new measures of direct and indirect effects for continuous treatments, termed the cumulative natural direct and indirect effects (CNDE and CNIE), constructed by decomposing local causal effects $\mathbb{E}[\partial_xY_{x}]$ into local direct and indirect effects. CNDE and CNIE yield a decomposition of the total effect that preserves both skew-symmetry and additivity. We further extend this framework to ordinal treatments by defining discrete analogues of the cumulative effects over ordered treatment levels that preserve these structural properties. We establish decomposition and identification results for the proposed measures under standard causal assumptions. We illustrate their behavior, in comparison with NDE and NIE, using canonical linear mediation models with interaction and a real-world dataset.

Problem

• causal mediation analysis
• natural direct effect
• natural indirect effect
• skew-symmetry
• additivity

Innovation

• cumulative natural direct effect
• cumulative natural indirect effect
• causal mediation analysis
• skew-symmetry
• additivity