Disentangling indirect effects through multiple mediators without assuming any causal structure among the mediators

When multiple mediators exist on the causal pathway from treatment to outcome, path analysis prevails for disentangling indirect effects along paths linking possibly several mediators. However, separately evaluating each indirect effect along different posited paths demands stringent assumptions, such as correctly specifying the mediators' causal structure, and no unobserved confounding among the mediators. These assumptions may be unfalsifiable in practice and, when they fail to hold, can result in misleading conclusions about the mediators. Nevertheless, these assumptions are avoidable when substantive interest is in inference about the indirect effects specific to each distinct mediator. In this article, we introduce a new definition of indirect effects called interventional indirect effects from the causal inference and epidemiology literature. Interventional indirect effects can be unbiasedly estimated without the assumptions above while retaining scientifically meaningful interpretations. We show that under a typical class of linear and additive mean models, estimators of interventional indirect effects adopt the same analytical form as prevalent product-of-coefficient estimators assuming a parallel mediator model. Prevalent estimators are therefore unbiased when estimating interventional indirect effects - even when there are unknown causal effects among the mediators - but require a different causal interpretation. When other mediators moderate the effect of each mediator on the outcome, and the mediators' covariance is affected by treatment, such an indirect effect due to the mediators' mutual dependence (on one another) cannot be attributed to any mediator alone. We exploit the proposed definitions of interventional indirect effects to develop novel estimators under such settings.