Regression-based approach for natural direct and indirect relative risk in case of multiple mediators

2026-08-03

AI Summary

This study addresses the challenge of estimating natural direct and indirect relative risk effects of a binary exposure on a binary outcome in settings involving multiple mediators—continuous, binary, or mixed—under the sequential ignorability assumption. The authors develop a unified regression framework that, for the first time, yields closed-form expressions for causal effects on the relative risk scale while accounting for inter-mediator dependence and interactions between exposure–mediator and mediator–mediator pairs. By operating directly on the relative risk scale, the approach circumvents interpretational difficulties arising from non-collapsibility and enables flexible modeling alongside rigorous uncertainty quantification. Leveraging likelihood-based inference and analytical derivations, the proposed method demonstrates strong validity and practical utility in two empirical applications.

Abstract

Mediation analysis investigates whether part of the treatment effect is channelled through one or more mediators along the causal pathway between the treatment and the primary outcome. However, the presence of multiple, potentially dependent mediators raises substantial challenges, particularly when the outcome is binary, the mediators are measured on different scales, and interactions are present. We consider on causal mediation analysis with a binary treatment and a binary outcome, defining natural direct, indirect, and total effects on the relative-risk scale, thereby avoiding the interpretational difficulties associated with non-collapsible effect measures. Under a sequential ignorability assumption, we develop a unified regression-based framework that accommodates multiple continuous, binary, or mixed mediators. The proposed framework accounts for dependence among mediators and allows for both exposure-mediator and mediator-mediator interactions. We derive closed-form expressions for the causal effects across the different mediator settings and develop a likelihood-based inference procedure for estimating the causal effects and quantifying their uncertainty. The methodology is illustrated through two empirical applications.

Problem

• mediation analysis
• multiple mediators
• relative risk
• binary outcome
• causal effects

Innovation

• causal mediation analysis
• relative risk
• multiple mediators
• mediator interactions
• regression-based framework