Causal organic direct and indirect effects: closer to Baron and Kenny
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Baron and Kenny (1986, 80,433 Google Scholar citations) proposed estimators of direct and indirect effects: the part of a treatment effect that is mediated by a covariate and the part that is not. Subsequent work on natural direct and indirect effects provides a formal causal interpretation. Natural direct and indirect effects use cross-worlds counterfactuals: outcomes under treatment with the mediator `set' to its value without treatment. Organic direct and indirect effects (Lok 2016) avoid cross-worlds counterfactuals, using `organic' interventions on the mediator while keeping the initial treatment fixed at `treatment'. Organic direct and indirect effects apply also to settings where the mediator cannot be `set'. In linear models where there is no treatment-mediator interaction, both organic and natural indirect effects lead to the same estimators as in Baron and Kenny (1986). In this article, I propose organic interventions on the mediator that keep the initial treatment fixed at `no treatment', leading to an alternative version of organic direct and indirect effects. I show that the product method, proposed in Baron and Kenny (1986), holds for these new direct and indirect effects even if there is treatment-mediator interaction. Furthermore, I argue that this alternative organic indirect effect is more relevant for drug development than the traditional natural or organic indirect effect.
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