Proximal Identification and Estimation in Front-Door Causal Structures with Unobserved Confounding of the Mediator

2026-07-11

AI Summary

This study addresses the challenge of identifying causal effects in front-door mediation settings when the mediator is subject to unobserved confounding. By introducing proxy variables for the unmeasured confounders, the authors extend the classical front-door criterion and achieve, for the first time, nonparametric identification of causal effects in scenarios involving both treatment-outcome and mediator-outcome unobserved confounding. The work proposes three novel identification strategies that preserve identifiability of the front-door path even when the mediator is influenced by latent confounders. Integrating proxy variable modeling, nonparametric identification theory, and influence function–based estimation techniques, the method is supported by rigorous theoretical analysis establishing its feasibility, while simulation studies demonstrate the validity and robustness of the proposed estimators.

Abstract

Unobserved confounding is a fundamental obstacle in causal inference problems. In the graphical modeling literature, a general theory has been developed that allows identification in the presence of hidden variables, with some limitations. In particular, Pearl's celebrated front-door criterion allows nonparametric identification in the presence of unobserved common causes of the treatment and the outcome, however it requires the presence of an unconfounded variable that mediates all causal influence from the treatment to the outcome. This stringent requirement limits the applicability of the front-door criterion. We propose proximal generalizations of the front-door criterion, allowing both arbitrary treatment/outcome confounding, and unobserved confounders of the mediator, provided informative proxies for the latter type of confounders are observed. In addition to deriving three new identification strategies in this setting, we provide plug-in and influence function-based estimation strategies for the resulting functionals, and evaluate their performance through simulations.

Problem

• front-door criterion
• unobserved confounding
• causal identification
• mediator
• proximal inference

Innovation

• proximal causal inference
• front-door criterion
• unobserved confounding
• mediator proxies
• nonparametric identification