Non-parametric efficient causal mediation with intermediate confounders

TL;DR

This paper develops and evaluates non-parametric estimators for causal mediation effects involving intermediate confounders, providing theoretical guarantees and practical tools for complex causal analysis.

Contribution

It introduces two asymptotically optimal estimators based on the efficient influence function for interventional effects in mediation analysis with intermediate confounders.

Findings

Estimators are consistent, multiply robust, and efficient under certain conditions.

Simulation studies confirm the theoretical properties and finite-sample performance.

Application to housing intervention data reveals causal mechanisms affecting adolescent girls' risk behavior.

Abstract

Interventional effects for mediation analysis were proposed as a solution to the lack of identifiability of natural (in)direct effects in the presence of a mediator-outcome confounder affected by exposure. We present a theoretical and computational study of the properties of the interventional (in)direct effect estimands based on the efficient influence fucntion (EIF) in the non-parametric statistical model. We use the EIF to develop two asymptotically optimal, non-parametric estimators that leverage data-adaptive regression for estimation of the nuisance parameters: a one-step estimator and a targeted minimum loss estimator. A free and open source \texttt{R} package implementing our proposed estimators is made available on GitHub. We further present results establishing the conditions under which these estimators are consistent, multiply robust, $n^{1/2}$-consistent and efficient. We illustrate the finite-sample performance of the estimators and corroborate our theoretical results in a simulation study. We also demonstrate the use of the estimators in our motivating application to elucidate the mechanisms behind the unintended harmful effects that a housing intervention had on adolescent girls' risk behavior.