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

Iván Díaz; Nicholas Williams; Kara E. Rudolph

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arXiv · 2203.15085

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

Iván Díaz·Nicholas Williams·Kara E. Rudolph

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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.

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Iván Díaz, Nicholas Williams, Kara E. Rudolph. 2022-03-28. Efficient and flexible causal mediation with time-varying mediators, treatments, and confounders. https://arxiv.org/abs/2203.15085

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