  Decomposing an exposure effect on an outcome into separate natural indirect
effects through multiple mediators requires strict assumptions, such as
correctly postulating the causal structure of the mediators, and no unmeasured
confounding among the mediators. In contrast, interventional indirect effects
for multiple mediators can be identified even when - as often - the mediators
either have an unknown causal structure, or share unmeasured common causes, or
both. Existing estimation methods for interventional indirect effects require
calculating each distinct indirect effect in turn. This can quickly become
unwieldy or unfeasible, especially when investigating indirect effect measures
that may be modified by observed baseline characteristics. In this article, we
introduce simplified estimation procedures for such heterogeneous
interventional indirect effects using interventional effect models.
Interventional effect models are a class of marginal structural models that
encode the interventional indirect effects as causal model parameters, thus
readily permitting effect modification by baseline covariates using
(statistical) interaction terms. The mediators and outcome can be continuous or
noncontinuous. We propose two estimation procedures: one using inverse
weighting by the counterfactual mediator density or mass functions, and another
using Monte Carlo integration. The former has the advantage of not requiring an
outcome model, but is susceptible to finite sample biases due to highly
variable weights. The latter has the advantage of consistent estimation under a
correctly specified (parametric) outcome model, but is susceptible to biases
due to extrapolation.
