Causal Organic Indirect and Direct Effects: Closer to the Original Approach to Mediation Analysis, with a Product Method for Binary Mediators.

Abstract

Mediation analysis, which started in the mid-1980s, 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 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 the original formulation of mediation analysis. 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 data on interruption of antiretroviral therapy without curative HIV treatments combined with an estimated or hypothesized effect of the curative HIV treatments on these mediators.