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

TL;DR

This paper develops a flexible framework for causal mediation analysis with time-varying treatments, mediators, and confounders, providing efficient estimators that incorporate machine learning and are applicable to longitudinal data.

Contribution

It introduces a novel identification result and an efficient estimation method for interventional effects in longitudinal settings with time-varying confounders affected by treatment.

Findings

Proposed a doubly robust, efficient estimator using the EIF.

Developed an R package for practical implementation.

Demonstrated the method on opioid use disorder treatment data.

Abstract

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.