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Proximal Mediation Analysis with Hidden Recanting Witnesses

arXiv 2606.17600 ↗First posted 16 Jun 2026stat.ME math.ST stat.MLcited by 0

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Abstract (arXiv)

Mediation analysis is essential for decomposing the causal effect of a treatment into direct and indirect pathways. However, many practical settings rely on the stringent assumption that recanting witnesses, defined as treatment-induced mediator-outcome confounders, are either absent or fully known a priori. Such a requirement is often untenable, especially when these variables remain unobservable due to measurement difficulties or privacy constraints. In this paper, we leverage proximal causal inference to develop three novel identification strategies to address the challenge of identifying path-specific effects in the presence of unknown recanting witnesses. Building on this, we develop a semiparametric inference framework that derives the efficient influence function and proposes a proximal multiply robust estimator, which remains consistent if at least one set of nuisance models is correctly specified. When all nuisance models are correctly specified and converge at appropriate rates, the estimator is asymptotically normal and achieves the semiparametric efficiency bound. We provide a minimax optimization-based debiased machine learning procedure for point estimation and constructing valid confidence intervals. The performance of the proposed methods is demonstrated by simulation studies and a real data application.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 25 of its 47 references that are in the map. First posted on arXiv 16 Jun 2026.

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25 of 47 references.

References · 25

  1. 2013Direct and Indirect Effectscited by 280
  2. 2016Identifying Causal Effects With Proxy Variables of an Unmeasured Confoundercited by 139
  3. 2020An Introduction to Proximal Causal Learningcited by 95
  4. 2020Minimax Estimation of Conditional Moment Modelscited by 83
  5. 2020Semiparametric proximal causal inferencecited by 59
  6. 2018Learning Optimal Fair Policiescited by 49
  7. 2021A Minimax Learning Approach to Off-Policy Evaluation in Confounded Partially Observable Markov Decision Processescited by 36
  8. 2021Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confoundingcited by 21
  9. 2021Proximal Causal Inference for Complex Longitudinal Studiescited by 16
  10. 2021Proximal mediation analysiscited by 10
  11. 2023Proximal Causal Learning of Conditional Average Treatment Effectscited by 7
  12. 2017On semiparametric estimation of a path-specific effect in the presence of mediator-outcome confoundingcited by 6
13 more
  1. 2021Causal Inference with Hidden Mediatorscited by 6
  2. 2022Proximal Causal Inference for Marginal Counterfactual Survival Curvescited by 5
  3. 2022Proximal Survival Analysis to Handle Dependent Right Censoringcited by 5
  4. 2022Optimal Treatment Regimes for Proximal Causal Learningcited by 5
  5. 2024Causal Inference with a Hidden Treatmentcited by 4
  6. 2022Blessing from Human-AI Interaction: Super Reinforcement Learning in Confounded Environmentscited by 3
  7. 2025Adaptive Proximal Causal Inference with Some Invalid Proxiescited by 3
  8. 2024On Identification of Optimal Dynamic Treatment Regimes with Proxies of Hidden Confounderscited by 2
  9. 2025Fortified Proximal Causal Inference with Many Invalid Proxiescited by 2
  10. 2025On Multiple Robustness of Proximal Dynamic Treatment Regimescited by 2
  11. 2026Double Fairness Policy Learning: Integrating Action Fairness and Outcome Fairness in Decision-makingcited by 2
  12. 2026Proximal Causal Inference for Hidden Outcomescited by 2
  13. 2026Proximal Path-Specific Inferencecited by 1

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