Robust and Flexible Estimation of Stochastic Mediation Effects: A Proposed Method and Example in a Randomized Trial Setting

Abstract Background 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 (which we call an intermediate confounder)–-an assumption frequently violated in practice. Methods We build on recent work that identified alternative estimands that do not require this assumption and propose a flexible and double robust targeted minimum loss-based estimator for stochastic direct and indirect effects. The proposed method intervenes stochastically on the mediator using a distribution which conditions on baseline covariates and marginalizes over the intermediate confounder. Results 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 with the voucher out of public housing, which is the intermediate confounder. We estimate the 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. Conclusions Our estimator is easy to implement in standard statistical software, and we provide annotated R code to further lower implementation barriers.