  Most of the literature on direct and indirect effects assumes that there are
no post-treatment common causes of the mediator and the outcome. In contrast to
natural direct and indirect effects, organic direct and indirect effects, which
were introduced in Lok (2016, 2020), can be extended to provide an
identification result for settings with post-treatment common causes of the
mediator and the outcome. This article provides a definition and an
identification result for organic direct and indirect effects in the presence
of post-treatment common causes of mediator and outcome. These new organic
indirect and direct effects have interpretations in terms of intervention
effects. Organic indirect effects in the presence of post-treatment common
causes are an addition to indirect effects through multivariate mediators.
Organic indirect effects in the presence of post-treatment common causes can be
used e.g. 1. to predict the effect of the initial treatment if its side affects
are suppressed through additional interventions or 2. to predict the effect of
a treatment that does not affect the post-treatment common cause and affects
the mediator the same way as the initial treatment.
