Causal organic indirect and direct effects: closer to Baron and Kenny, with a product method for binary mediators

Mediation analysis, which started with Baron and Kenny (1986), is used extensively by applied researchers. Indirect and direct effects are the part of a treatment effect that is mediated by a covariate and the part that is not. Subsequent work on natural indirect and direct effects provides a formal causal interpretation, based on cross-worlds counterfactuals: outcomes under treatment with the mediator set to its value without treatment. Organic indirect and direct effects (Lok 2016) avoid cross-worlds counterfactuals, using so-called organic interventions on the mediator while keeping the initial treatment fixed at treatment. Organic indirect and direct effects apply also to settings where the mediator cannot be set. In linear models where the outcome model does not have treatment-mediator interaction, both organic and natural indirect and direct effects lead to the same estimators as in Baron and Kenny (1986). Here, we generalize organic interventions on the mediator to include interventions combined with the initial treatment fixed at no treatment. We show that the product method holds in linear models for organic indirect and direct effects relative to no treatment even if there is treatment-mediator interaction. Moreover, we find a product method for binary mediators. Furthermore, we argue that the organic indirect effect relative to no treatment is very relevant for drug development. We illustrate the benefits of our approach by estimating the organic indirect effect of curative HIV-treatments mediated by two HIV-persistence measures, using ART-interruption data without curative HIV-treatments combined with an estimated/hypothesized effect of the curative HIV-treatments on these mediators.