Exposure-induced mediator-outcome confounders in causal mediation: implications and visualisation

In their thoughtful review on causal mediation methods, Pearce et al1 highlighted the challenges posed by exposure-induced mediator–outcome confounders for identifying natural direct and indirect effects.2 Here, we briefly provide a broader perspective on this issue using causal directed acyclic graphs (DAGs).

We let A denote an exposure, Y an outcome, M a mediator and L an exposure-induced mediator–outcome confounder (figure 1a). In the counterfactual framework, we let denote the potential outcomes of Y if, possibly contrary to fact, there had been interventions to set A to a and to set M to m. Similarly, we let and denote the potential outcomes of M and L, respectively, had A been set to a. We assume that positivity and consistency hold.

In non-parametric structural equation models with independent errors (NPSEM-IE), the natural direct and indirect effects (ie, and , respectively) can be identified…

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