mlsanityData to 7 Oct 2026

Long-term Causal Inference Under Persistent Confounding via Data Combination

arXiv 2202.07234 ↗First posted 15 Feb 2022stat.ME econ.EM stat.MLcited by 27

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Abstract (arXiv)

We study the identification and estimation of long-term treatment effects when both experimental and observational data are available. Since the long-term outcome is observed only after a long delay, it is not measured in the experimental data, but only recorded in the observational data. However, both types of data include observations of some short-term outcomes. In this paper, we uniquely tackle the challenge of persistent unmeasured confounders, i.e., some unmeasured confounders that can simultaneously affect the treatment, short-term outcomes and the long-term outcome, noting that they invalidate identification strategies in previous literature. To address this challenge, we exploit the sequential structure of multiple short-term outcomes, and develop three novel identification strategies for the average long-term treatment effect. We further propose three corresponding estimators and prove their asymptotic consistency and asymptotic normality. We finally apply our methods to estimate the effect of a job training program on long-term employment using semi-synthetic data. We numerically show that our proposals outperform existing methods that fail to handle persistent confounders.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). Builds on 40 of its 95 references that are in the map. First posted on arXiv 15 Feb 2022.

Builds on

40 of 95 references.

References · 40

  1. 2016Identifying Causal Effects With Proxy Variables of an Unmeasured Confoundercited by 138
  2. 2019Kernel Instrumental Variable Regressioncited by 118
  3. 2020An Introduction to Proximal Causal Learningcited by 91
  4. 2019Deep Generalized Method of Moments for Instrumental Variable Analysiscited by 88
  5. 2020Minimax Estimation of Conditional Moment Modelscited by 83
  6. 2019Off-Policy Evaluation in Partially Observable Environmentscited by 65
  7. 2018Removing Hidden Confounding by Experimental Groundingcited by 64
  8. 2020Semiparametric proximal causal inferencecited by 58
  9. 2021Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restrictioncited by 54
  10. 2020Causal inference methods for combining randomized trials and observational studies: a reviewcited by 50
  11. 2021Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approachcited by 43
  12. 2021Proximal Reinforcement Learning: Efficient Off-Policy Evaluation in Partially Observed Markov Decision Processescited by 40
28 more
  1. 2021Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluationcited by 39
  2. 2018A confounding bridge approach for double negative control inference on causal effectscited by 36
  3. 2020On the role of surrogates in the efficient estimation of treatment effects with limited outcome datacited by 36
  4. 2018De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representerscited by 34
  5. 2018Combining multiple observational data sources to estimate causal effectscited by 29
  6. 2020Combining Observational and Experimental Datasets Using Shrinkage Estimatorscited by 28
  7. 2020Using Experiments to Correct for Selection in Observational Studiescited by 28
  8. 2020Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instrumentscited by 27
  9. 2020Targeting for long-term outcomescited by 23
  10. 2020The Variational Method of Momentscited by 23
  11. 2021Adaptive Combination of Randomized and Observational Datacited by 22
  12. 2021Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confoundingcited by 21
  13. 2021Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inferencecited by 20
  14. 2020Elastic Integrative Analysis of Randomized Trial and Real-World Data for Treatment Heterogeneity Estimationcited by 17
  15. 2021Proximal Causal Inference for Complex Longitudinal Studiescited by 16
  16. 2021Proximal mediation analysiscited by 10
  17. 2018Propensity Score Methods for Merging Observational and Experimental Datasetscited by 9
  18. 2020Data fusion methods for the heterogeneity of treatment effect and confounding functioncited by 9
  19. 2021Theory for identification and Inference with Synthetic Controls: A Proximal Causal Inference Frameworkcited by 9
  20. 2021Minimax Rates and Adaptivity in Combining Experimental and Observational Datacited by 8
  21. 2021Estimating the Long-Term Effects of Novel Treatmentscited by 7
  22. 2021Controlling for Unmeasured Confounding in Panel Data Using Minimal Bridge Functions: From Two-Way Fixed Effects to Factor Modelscited by 4
  23. 2021Nested Nonparametric Instrumental Variable Regressioncited by 4
  24. 2022Kernel methods for long term dose response curvescited by 4
  25. 2017Semiparametric Estimation of Structural Functions in Nonseparable Triangular Modelscited by 1
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 3; 2024: 10; 2025: 8; 2026: 3.

27 papers.

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  1. 2022Combining Observational and Randomized Data for Estimating Heterogeneous Treatment Effectscited by 32
  2. 2022Detecting hidden confounding in observational data using multiple environmentscited by 13
  3. 2022Long-term Causal Effects Estimation via Latent Surrogates Representation Learningcited by 11
  4. 2023Estimating long-term causal effects from short-term experiments and long-term observational data with unobserved confoundingcited by 11
  5. 2024Meta-Learners for Partially-Identified Treatment Effects Across Multiple Environmentscited by 11
  6. 2024Policy Learning for Balancing Short-Term and Long-Term Rewardscited by 7
  7. 2024Constructing Confidence Intervals for Average Treatment Effects from Multiple Datasetscited by 6
  8. 2023Non-parametric identifiability and sensitivity analysis of synthetic control modelscited by 5
  9. 2024The Odyssey of Commonsense Causality: From Foundational Benchmarks to Cutting-Edge Reasoningcited by 5
  10. 2024Spillover Detection for Donor Selection in Synthetic Control Modelscited by 4
  11. 2024Estimating Long-term Heterogeneous Dose-response Curve: Generalization Bound Leveraging Optimal Transport Weightscited by 4
  12. 2025Long-Term Individual Causal Effect Estimation via Identifiable Latent Representation Learningcited by 3
15 more
  1. 2024Estimating Heterogeneous Treatment Effects by Combining Weak Instruments and Observational Datacited by 2
  2. 2024On the Role of Surrogates in Conformal Inference of Individual Causal Effectscited by 2
  3. 2025Nonparametric Heterogeneous Long-term Causal Effect Estimation via Data Combinationcited by 2
  4. 2025Long-term Causal Inference via Modeling Sequential Latent Confoundingcited by 2
  5. 2023Identification and Estimation for Nonignorable Missing Data: A Data Fusion Approachcited by 1
  6. 2025A General Framework for Off-Policy Learning with Partially-Observed Rewardcited by 1
  7. 2024Pareto-Optimal Estimation and Policy Learning on Short-term and Long-term Treatment Effectscited by 0
  8. 2024Online Data Collection for Efficient Semiparametric Inferencecited by 0
  9. 2025Optimal Policy Adaptation under Covariate Shiftcited by 0
  10. 2025Identification and Estimation of Long-Term Treatment Effects with Monotone Missingcited by 0
  11. 2025Transferring Causal Effects using Proxiescited by 0
  12. 2025Integrating RCTs, RWD, AI/ML and Statistics: Next-Generation Evidence Synthesiscited by 0
  13. 2026Testing Effect Homogeneity and Confounding in High-Dimensional Experimental and Observational Studiescited by 0
  14. 2026Orthogonal Learner for Estimating Heterogeneous Long-Term Treatment Effectscited by 0
  15. 2026Representation Learning for Sample-Efficient CATE Estimation by Leveraging Multiple Outcomescited by 0