# Proximal Path-Specific Inference

arXiv: https://arxiv.org/abs/2605.09462 · HTML: https://mlsanity.com/paper/2605.09462/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 55 references that are in the map.
- First posted on arXiv 10 May 2026.

## Builds on (most cited first, 25 of 25)

- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Minimax Estimation of Conditional Moment Models](https://mlsanity.com/paper/2006.07201/) (2020)
- [Semiparametric proximal causal inference](https://mlsanity.com/paper/2011.08411/) (2020)
- [Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach](https://mlsanity.com/paper/2103.14029/) (2021)
- [Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confounding](https://mlsanity.com/paper/2105.01187/) (2021)
- [Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference](https://mlsanity.com/paper/2104.02929/) (2021)
- [Proximal Causal Inference for Complex Longitudinal Studies](https://mlsanity.com/paper/2109.07030/) (2021)
- [Proximal mediation analysis](https://mlsanity.com/paper/2109.11904/) (2021)
- [Theory for identification and Inference with Synthetic Controls: A Proximal Causal Inference Framework](https://mlsanity.com/paper/2108.13935/) (2021)
- [Non-parametric efficient causal mediation with intermediate confounders](https://mlsanity.com/paper/1912.09936/) (2019)
- [On semiparametric estimation of a path-specific effect in the presence of mediator-outcome confounding](https://mlsanity.com/paper/1710.02011/) (2017)
- [Causal Inference with Hidden Mediators](https://mlsanity.com/paper/2111.02927/) (2021)
- [Proximal Causal Inference for Marginal Counterfactual Survival Curves](https://mlsanity.com/paper/2204.13144/) (2022)
- [Proximal Survival Analysis to Handle Dependent Right Censoring](https://mlsanity.com/paper/2208.07014/) (2022)
- [Optimal Treatment Regimes for Proximal Causal Learning](https://mlsanity.com/paper/2212.09494/) (2022)
- [Proximal Causal Inference for Synthetic Control with Surrogates](https://mlsanity.com/paper/2308.09527/) (2023)
- [Doubly Robust Proximal Causal Learning for Continuous Treatments](https://mlsanity.com/paper/2309.12819/) (2023)
- [On Identification of Optimal Dynamic Treatment Regimes with Proxies of Hidden Confounders](https://mlsanity.com/paper/2402.14942/) (2024)
- [Identification and multiply robust estimation of causal effects via instrumental variables from an auxiliary population](https://mlsanity.com/paper/2407.18166/) (2024)
- [On Multiple Robustness of Proximal Dynamic Treatment Regimes](https://mlsanity.com/paper/2510.20451/) (2025)
- [General targeted machine learning for modern causal mediation analysis](https://mlsanity.com/paper/2408.14620/) (2024)
- [Nonparametric Estimation of Path-specific Effects in Presence of Nonignorable Missing Covariates](https://mlsanity.com/paper/2409.01248/) (2024)

## Built on by (most cited first, 1 of 1)

- [Proximal Mediation Analysis with Hidden Recanting Witnesses](https://mlsanity.com/paper/2606.17600/) (2026)

## Abstract (arXiv)

Causal mediation analysis has been extended to estimate path-specific effects with multiple intermediate variables, isolating treatment effects through a mediator of interest while excluding pathways through its ancestors. Such analyses address bias from recanting witnesses, i.e., treatment-induced mediator-outcome confounders. However, existing methods typically rely on stringent assumptions precluding general unmeasured confounding, which are often violated in practice. In this paper, we relax these restrictions by leveraging observed covariates as proxy variables to accommodate unmeasured confounding among the treatment, recanting witness, mediator, and outcome. Using proximal confounding bridge functions, we develop four nonparametric identification strategies for the path-specific effect. We further derive the efficient influence function and propose a quadruply robust, locally efficient estimator. To handle high-dimensional nuisance parameters, we propose a proximal debiased machine learning approach. We theoretically guarantee that our estimator achieves √n-consistency and asymptotic normality even when machine learning estimators for nuisance functions converge at slower rates. Our approaches are validated via semiparametric and nonparametric simulations and an application to the CDC WONDER Natality study, estimating the path-specific effect of prenatal care on preterm birth through preeclampsia, independent of maternal smoking during pregnancy.