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Most of the literature on direct and indirect effects assumes that there areno post-treatment common causes of the mediator and the outcome. In contrast tonatural direct and indirect effects, organic direct and indirect effects, whichwere introduced in Lok (2016, 2020), can be extended to provide anidentification result for settings with post-treatment common causes of themediator and the outcome. This article provides a definition and anidentification result for organic direct and indirect effects in the presenceof post-treatment common causes of mediator and outcome. These new organicindirect and direct effects have interpretations in terms of interventioneffects. Organic indirect effects in the presence of post-treatment commoncauses are an addition to indirect effects through multivariate mediators.Organic indirect effects in the presence of post-treatment common causes can beused e.g. 1. to predict the effect of the initial treatment if its side affectsare suppressed through additional interventions or 2. to predict the effect ofa treatment that does not affect the post-treatment common cause and affectsthe mediator the same way as the initial treatment.

Organic direct and indirect effects with post-treatment common causes of mediator and outcome