  Causal mediation analysis has historically been limited in two important
ways: (i) a focus has traditionally been placed on binary treatments and static
interventions, and (ii) direct and indirect effect decompositions have been
pursued that are only identifiable in the absence of intermediate confounders
affected by treatment. We present a theoretical study of an (in)direct effect
decomposition of the population intervention effect, defined by stochastic
interventions jointly applied to the treatment and mediators. In contrast to
existing proposals, our causal effects can be evaluated regardless of whether a
treatment is categorical or continuous and remain well-defined even in the
presence of intermediate confounders affected by treatment. Our (in)direct
effects are identifiable without a restrictive assumption on cross-world
counterfactual independencies, allowing for substantive conclusions drawn from
them to be validated in randomized controlled trials. Beyond the novel effects
introduced, we provide a careful study of nonparametric efficiency theory
relevant for the construction of flexible, multiply robust estimators of our
(in)direct effects, while avoiding undue restrictions induced by assuming
parametric models of nuisance parameter functionals. To complement our
nonparametric estimation strategy, we introduce inferential techniques for
constructing confidence intervals and hypothesis tests, and discuss open source
software implementing the proposed methodology.
