Non-agency interventions for causal mediation in the presence of intermediate confounding

Abstract: Recent approaches to causal inference have focused on causal effects defined as contrasts between the distribution of counterfactual outcomes under hypothetical interventions on the nodes of a graphical model. In this article we develop theory for causal effects defined with respect to a different type of intervention, one which alters the information propagated through the edges of the graph. These information transfer interventions may be more useful than node interventions in settings in which causes are non-manipulable, for example when considering race or genetics as a causal agent. Furthermore, information transfer interventions allow us to define path-specific decompositions which are identified in the presence of treatment-induced mediator-outcome confounding, a practical problem whose general solution remains elusive. We prove that the proposed effects provide valid statistical tests of mechanisms, unlike popular methods based on randomized interventions on the mediator. We propose efficient non-parametric estimators for a covariance version of the proposed effects, using data-adaptive regression coupled with semi-parametric efficiency theory to address model misspecification bias while retaining $\sqrt{n}$-consistency and asymptotic normality. We illustrate the use of our methods in two examples using publicly available data.