  Causal mediation analysis can improve understanding of the mechanisms
underlying epidemiologic associations. However, the utility of natural direct
and indirect effect estimation has been limited by the assumption of no
confounder of the mediator-outcome relationship that is affected by prior
exposure---an assumption frequently violated in practice. We build on recent
work that identified alternative estimands that do not require this assumption
and propose a flexible and double robust semiparametric targeted minimum
loss-based estimator for data-dependent stochastic direct and indirect effects.
The proposed method treats the intermediate confounder affected by prior
exposure as a time-varying confounder and intervenes stochastically on the
mediator using a distribution which conditions on baseline covariates and
marginalizes over the intermediate confounder. In addition, we assume the
stochastic intervention is given, conditional on observed data, which results
in a simpler estimator and weaker identification assumptions. We demonstrate
the estimator's finite sample and robustness properties in a simple simulation
study. We apply the method to an example from the Moving to Opportunity
experiment. In this application, randomization to receive a housing voucher is
the treatment/instrument that influenced moving to a low-poverty neighborhood,
which is the intermediate confounder. We estimate the data-dependent stochastic
direct effect of randomization to the voucher group on adolescent marijuana use
not mediated by change in school district and the stochastic indirect effect
mediated by change in school district. We find no evidence of mediation. Our
estimator is easy to implement in standard statistical software, and we provide
annotated R code to further lower implementation barriers.
