Efficient and flexible mediation analysis with time-varying mediators, treatments, and confounders

Understanding the mechanisms of action of interventions is a major general goal of scientific inquiry. The collection of statistical methods that use data to achieve this goal is referred to as mediation analysis. Natural direct and indirect effects provide a definition of mediation that matches scientific intuition, but they are not identified in the presence of time-varying confounding. Interventional effects have been proposed as a solution to this problem, but existing estimation methods are limited to assuming simple (e.g., linear) and unrealistic relations between the mediators, treatments, and confounders. 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. In this article, we study semi-parametric efficiency theory for the functional identifying the mediation parameter, including the non-parametric efficiency bound, and was used to propose non-parametrically efficient estimators. Implementation of our estimators only relies on the availability of regression algorithms, and the estimators in a general framework that allows the analyst to use arbitrary regression machinery were developed. The estimators are doubly robust, n\sqrt{n}-consistent, asymptotically Gaussian, 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 pp-values. A free and open-source R package implementing the methods is available on GitHub. The proposed estimator to a motivating example from a trial of two medications for opioid-use disorder was applied, where we estimate the extent to which differences between the two treatments on risk of opioid use are mediated by craving symptoms.