Decomposition of the total effect for two mediators: A natural mediated interaction effect framework

Mediation analysis has been used in many disciplines to explain the mechanism or process that underlies an observed relationship between an exposure variable and an outcome variable via the inclusion of mediators. Decompositions of the total effect (TE) of an exposure variable into effects characterizing mediation pathways and interactions have gained an increasing amount of interest in the last decade. In this work, we develop decompositions for scenarios where two mediators are causally sequential or non-sequential. Current developments in this area have primarily focused on either decompositions without interaction components or with interactions but assuming no causally sequential order between the mediators. We propose a new concept called natural mediated interaction (MI) effect that captures the two-way and three-way interactions for both scenarios and extends the two-way MIs in the literature. We develop a unified approach for decomposing the TE into the effects that are due to mediation only, interaction only, both mediation and interaction, neither mediation nor interaction within the counterfactual framework. Finally, we compare our proposed decomposition to an existing method in a non-sequential two-mediator scenario using simulated data, and illustrate the proposed decomposition for a sequential two-mediator scenario using a real data analysis.