Robust inference on effects attributable to mediators: A controlled‐direct‐effect‐based approach for causal effect decomposition with multiple mediators

Abstract Effect decomposition is a critical technique for mechanism investigation in settings with multiple causally ordered mediators. Causal mediation analysis is a standard method for effect decomposition, but the assumptions required for the identification process are extremely strong. Moreover, mediation analysis focuses on addressing mediating mechanisms rather than interacting mechanisms. Mediation and interaction for mediators both contribute to the occurrence of disease, and therefore unifying mediation and interaction in effect decomposition is important to causal mechanism investigation. By extending the framework of controlled direct effects, this study proposes the effect attributable to mediators (EAM) as a novel measure for effect decomposition. For policymaking, EAM represents how much an effect can be eliminated by setting mediators to certain values. From the perspective of mechanism investigation, EAM contains information about how much a particular mediator or set of mediators is involved in the causal mechanism through mediation, interaction, or both. EAM is more appropriate than the conventional path‐specific effect for application in clinical or medical studies. The assumptions of EAM for identification are considerably weaker than those of causal mediation analysis. We develop a semiparametric estimator of EAM with robustness to model misspecification. The asymptotic property is fully realized. We applied EAM to assess the magnitude of the effect of hepatitis C virus infection on mortality, which was eliminated by controlling alanine aminotransferase and treating hepatocellular carcinoma.