  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 causal effect 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 the 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 counterfactual interaction effect that captures the two-way and
three-way interactions for both scenarios that extend the two-way mediated
interactions in literature. We develop a unified approach for decomposing the
total effect 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 illustrate the proposed decomposition
method using a real data analysis where the two mediators are causally
sequential.
