# Non-parametric efficient causal mediation with intermediate confounders

arXiv: https://arxiv.org/abs/1912.09936 · HTML: https://mlsanity.com/paper/1912.09936/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2019.

## Built on by (most cited first, 8 of 8)

- [A Reinforcement Learning Framework for Dynamic Mediation Analysis](https://mlsanity.com/paper/2301.13348/) (2023)
- [General targeted machine learning for modern causal mediation analysis](https://mlsanity.com/paper/2408.14620/) (2024)
- [Causal Mediation Analysis with Multiple Mediators: A Simulation Approach](https://mlsanity.com/paper/2506.14019/) (2025)
- [Proximal Path-Specific Inference](https://mlsanity.com/paper/2605.09462/) (2026)
- [Assessing Racial Disparities in Healthcare Expenditures via Mediator Distribution Shifts](https://mlsanity.com/paper/2504.21688/) (2025)
- [M-learner:A Flexible And Powerful Framework To Study Heterogeneous Treatment Effect In Mediation Model](https://mlsanity.com/paper/2505.17917/) (2025)
- [Identifying and Estimating Causal Direct Effects Under Unmeasured Confounding](https://mlsanity.com/paper/2604.01501/) (2026)
- [Bayesian Mediation Analysis for Individualized Treatment Rules](https://mlsanity.com/paper/2607.28804/) (2026)

## Abstract (arXiv)

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 textttR 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, n1/2-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.