proximal mediation analysis

This study addresses the non-identifiability of natural indirect effects in mediation analysis due to unobserved treatment-induced confounding. To overcome this challenge, the authors introduce an observable proxy variable for the unmeasured confounder and establish sufficient conditions for identifying causal mediation effects. Four proxy-based identification strategies are proposed, accompanied by a multiply robust and semiparametric locally efficient estimator that incorporates flexible machine learning techniques to model nuisance parameters. The validity and practical utility of the proposed approach are demonstrated through comprehensive simulation studies and an empirical application examining the mediating mechanisms through which racial discrimination affects life satisfaction.

This study addresses the challenge in mediation analysis posed by treatment-induced mediator–outcome confounding—often termed “defiers”—which is typically unobserved and violates standard identification assumptions, thereby complicating estimation of path-specific effects. The paper introduces proximal causal inference into this setting for the first time, proposing three novel identification strategies and developing a semiparametric inference framework based on product-of-robust estimators and minimax debiased learning. The resulting estimator is consistent if at least one of the auxiliary models is correctly specified and achieves the semiparametric efficiency bound when all models are correctly specified and satisfy appropriate convergence rate conditions. Both simulation studies and empirical applications demonstrate the method’s validity and robustness.

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.

This study addresses the challenge of reliably estimating path-specific effects in causal mediation analysis when unmeasured confounding is present, particularly treatment-induced mediator–outcome confounding. The authors propose a novel approach that integrates proxy variables with proximal causal inference, constructing proximal confounding bridge functions based on observed covariates. They develop four nonparametric identification strategies and introduce a quadruply robust, locally efficient debiased machine learning estimator. Under relatively weak assumptions, the proposed method achieves √n-consistency and asymptotic normality, maintaining robustness even when nuisance functions converge at slow rates. Simulations and an application to CDC birth data demonstrate its empirical validity, successfully identifying the independent pathway through which prenatal care affects preterm birth via preeclampsia.

This study addresses the challenge of identifying and estimating long-term causal effects when observational data suffer from unmeasured confounding and experimental data provide only short-term outcomes—neither source alone supports valid long-term causal inference. To bridge this gap, we propose three novel data fusion frameworks: (i) the equal-confounding-bias assumption, (ii) the partially observable equal-association assumption, and (iii) a proximal causal inference framework leveraging proxy variables—thereby relaxing restrictive external validity assumptions. Integrating proximal causal reasoning, influence function estimation, and potential outcomes modeling, our methods deliver unbiased, efficient, and doubly robust estimators for both the average treatment effect (ATE) and average treatment effect on the treated (ATT). For each framework, we establish rigorous identifiability conditions, construct explicit estimators, and prove their consistency and asymptotic normality. Moreover, the estimators exhibit robustness to certain forms of model misspecification.

This study addresses the challenging problem of identifying and estimating long-term treatment effects in the presence of unobserved confounding. By integrating experimental data with only short-term outcomes and observational data containing long-term outcomes but unknown treatment assignment, the authors leverage proxy variables to account for unmeasured confounders and construct a proximal proxy index that enables nonparametric identification of long-term causal effects. The proposed approach synthesizes proximal causal inference, multiply robust estimation, and semiparametric inference techniques, establishing—for the first time—the nonparametric identifiability of long-term treatment effects under unobserved confounding. In an empirical application to the Job Corps data, the method successfully replicates benchmark experimental findings and substantially outperforms conventional proxy index approaches that are susceptible to confounding bias.

This work addresses the challenge of identifying causal effects in the presence of categorical unobserved confounders by proposing a novel mixture-learning approach. The method models the unobserved confounding structure as a discrete mixture distribution and, leveraging proxy variables or multiple treatment settings, establishes the first rigorous identifiability result for causal effects under such conditions. By employing tensor decomposition techniques, the approach consistently recovers the latent confounding structure from observational data and yields an estimator with non-asymptotic error guarantees. Both theoretical analysis and empirical evaluations demonstrate that the proposed method accurately estimates causal effects even with finite samples, achieving superior performance on synthetic and real-world datasets.

This study addresses the problem of testing whether a treatment effect operates entirely through observed mediators and identifying causal mechanisms under control for covariates. The authors propose a statistical test based on double machine learning, extending— for the first time—the joint evaluation of full mediation and causal mechanism identification to non-randomized treatment settings. By integrating conditional independence testing, the method achieves root-n consistent and asymptotically normal inference even in the presence of high-dimensional covariates. Simulation studies demonstrate favorable finite-sample performance, and the approach is successfully applied to two randomized experiments examining maternal mental health and social norms.

Identifying causal effects in the presence of unobserved confounders remains fundamentally challenging. This paper systematically compares two dominant proxy-variable approaches: bridge function methods—based on solving integral equations—and tensor decomposition methods—relying on uniqueness in feature space. We rigorously characterize their essential differences in identifiability conditions, assumption strength (e.g., proxy relevance, nonlinearity requirements, higher-order moment restrictions), and practical applicability boundaries. For the first time, we unify the identification mechanisms and failure modes of both paradigms, precisely delineating their respective minimal sufficient conditions. Through latent factor modeling and feature-space analysis, we quantify how violations of these conditions propagate into estimation bias. Our results establish a rigorous, theoretically grounded framework for selecting and applying proxy methods under complex causal structures, thereby enhancing both the reliability and interpretability of causal inference in settings with unmeasured confounding.

This study addresses the challenge of estimating long-term causal effects in digital platform experiments, where such effects are often indirectly inferred through numerous noisy short-term proxy variables that reflect a low-dimensional latent mediator. The authors formulate this as a latent variable estimation problem and propose using regularized regression methods—such as ridge regression—to effectively distill information from high-dimensional proxies. Theoretical analysis reveals that ridge regression exhibits diminishing bias as the number of proxies increases and yields a closed-form solution for the bias–variance trade-off, thereby overcoming limitations of conventional proxy selection approaches. Empirical evaluations on both simulated data and the California GAIN experiment demonstrate that the proposed method substantially outperforms naive proxy selection strategies in accurately estimating long-term treatment effects.