  Interventional effects have been proposed as a solution to the
unidentifiability of natural (in)direct effects under mediator-outcome
confounders affected by the exposure. Such confounders are an intrinsic
characteristic of studies with time-varying exposures and mediators, yet the
generalization of the interventional effect framework to the time-varying case
has received little attention in the literature. We present an identification
result for interventional effects in a general longitudinal data structure that
allows flexibility in the specification of treatment-outcome,
treatment-mediator, and mediator-outcome relationships. Identification is
achieved under the standard no-unmeasured-confounders and positivity
assumptions. We also present a theoretical and computational study of the
properties of the identifying functional based on the efficient influence
function (EIF). We use the EIF to propose a sequential regression estimation
algorithm that yields doubly robust, $\sqrt{n}$-consistent, asymptotically
Gaussian, and efficient estimators under slow convergence rates for the
regression algorithms used. This allows the use of flexible machine learning
for regression while permitting uncertainty quantification through confidence
intervals and p-values. A free and open source \texttt{R} package implementing
our proposed estimators is made available on GitHub. We apply the proposed
estimator to an application from a comparative effectiveness trial of two
medications for opioid use disorder. In the application, we estimate the extent
to which differences between the two treatments' on subsequent risk of opioid
use is mediated by craving symptoms.
