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Mediation analysis serves as a crucial tool to obtain causal inference basedon directed acyclic graphs, which has been widely employed in the areas ofbiomedical science, social science, epidemiology and psychology. Decompositionof total effect provides a deep insight to fully understand the casualcontribution from each path and interaction term. Since the four-waydecomposition method was proposed to identify the mediated interaction effectin counterfactual framework, the idea had been extended to a more sophisticatedscenario with non-sequential multiple mediators. However, the method exhibitslimitations as the causal structure contains direct causal edges betweenmediators, such as inappropriate modeling of dependence andnon-identifiability. We develop the notion of natural counterfactualinteraction effect and find that the decomposition of total effect can beconsistently realized with our proposed notion. Furthermore, naturalcounterfactual interaction effect overcomes the drawbacks and possesses a clearand significant interpretation, which may largely improve the capacity ofresearchers to analyze highly complex causal structures.

Decomposition of Total Effect with the Notion of Natural Counterfactual Interaction Effect