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-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 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.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 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.Conclusions: Our estimator is easy to implement in standard statistical software, and we provide annotated R code to further lower implementation barriers.

Unconventional natural gas development and adverse birth outcomes in Pennsylvania: The potential mediating role of antenatal anxiety and depression

“…We z-transformed the activity metrics for each phase of development and summed them to create a composite UNGD activity metric. The programming for the stochastic mediation method we used currently requires a binary exposure variable (Rudolph et al, 2017). Therefore, for analysis, we defined exposure to UNGD as living in the highest quartile of UNGD activity during pregnancy.…”

“…We estimated stochastic direct and indirect effects (Rudolph et al, 2017), which rely on contrasts of potential outcomes or counterfactual scenarios (Rubin, 2005). Since each study participant received just one level of a binary exposure, we only observed one potential outcome in the data.…”

“…Since each study participant received just one level of a binary exposure, we only observed one potential outcome in the data. To calculate stochastic direct and indirect effects, we estimated alternative potential outcomes by assigning mothers counterfactual values of the mediator that we drew from a distribution that corresponded to the exposure scenario of interest and the strata of covariates (Rudolph et al, 2017;VanderWeele and Tchetgen Tchetgen, 2017). The stochastic direct effect provided an estimate of the population average of the difference in individual-level adverse birth outcomes contrasting if the mother was exposed to UNGD or not and in each case allowing her antenatal anxiety/depression status to be drawn from a distribution of antenatal anxiety/depression status among nonexposed mothers, conditional on baseline covariates.…”

“…Mediation analyses can help uncover mechanisms of action that may explain the association between environmental exposures and perinatal health outcomes (Anthopolos et al, 2014;Ferguson et al, 2016;Rahman et al, 2017). In the present retrospective cohort study, we used stochastic direct and indirect effects (also called randomized interventional effects) (Rudolph et al, 2017;VanderWeele and Tchetgen Tchetgen, 2017) to evaluate maternal mental health during pregnancy as a potential mediator of a previously observed relationship between UNGD and adverse birth outcomes in Pennsylvania (Casey et al, 2016). We hypothesized that UNGD could lead to worse maternal mental health and subsequently more adverse birth outcomes.…”

Causal Mediation Analysis for Stochastic Interventions

“…Our methods also share similarities with a family of new direct and indirect effects (Didelez et al ., ; VanderWeele et al ., ; Lok, ; Vansteelandt and Daniel, ; Zheng and van der Laan, ; Rudolph et al ., ; Lok, ), which have been collectively termed interventional effects (Nguyen et al ., ). This family of effects deals with binary exposures and deterministic interventions on the exposure and is thus not entirely related to our approach, which deals with both continuous and categorical exposures and stochastic interventions on the exposure.…”