mlsanityData to 7 Oct 2026

Bounds on the conditional and average treatment effect with unobserved confounding factors

arXiv 1808.09521 ↗First posted 28 Aug 2018stat.MEcited by 39

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Abstract (arXiv)

For observational studies, we study the sensitivity of causal inference when treatment assignments may depend on unobserved confounders. We develop a loss minimization approach for estimating bounds on the conditional average treatment effect (CATE) when unobserved confounders have a bounded effect on the odds ratio of treatment selection. Our approach is scalable and allows flexible use of model classes in estimation, including nonparametric and black-box machine learning methods. Based on these bounds for the CATE, we propose a sensitivity analysis for the average treatment effect (ATE). Our semi-parametric estimator extends/bounds the augmented inverse propensity weighted (AIPW) estimator for the ATE under bounded unobserved confounding. By constructing a Neyman orthogonal score, our estimator of the bound for the ATE is a regular root-n estimator so long as the nuisance parameters are estimated at the op(n-1/4) rate. We complement our methodology with optimality results showing that our proposed bounds are tight in certain cases. We demonstrate our method on simulated and real data examples, and show accurate coverage of our confidence intervals in practical finite sample regimes with rich covariate information.

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Aug 2018.

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Citing papers per year: 2021: 5; 2022: 10; 2023: 7; 2024: 6; 2025: 6; 2026: 5.

39 papers.

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  1. 2021Quantifying Ignorance in Individual-Level Causal-Effect Estimates under Hidden Confoundingcited by 50
  2. 2023Diagnosing Model Performance Under Distribution Shiftcited by 37
  3. 2021Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confoundingcited by 28
  4. 2023B-Learner: Quasi-Oracle Bounds on Heterogeneous Causal Effects Under Hidden Confoundingcited by 28
  5. 2021Causal-BALD: Deep Bayesian Active Learning of Outcomes to Infer Treatment-Effects from Observational Datacited by 27
  6. 2021Long Story Short: Omitted Variable Bias in Causal Machine Learningcited by 23
  7. 2022What's the Harm? Sharp Bounds on the Fraction Negatively Affected by Treatmentcited by 14
  8. 2022Model-Free and Model-Based Policy Evaluation when Causality is Uncertaincited by 12
  9. 2022Inference on Strongly Identified Functionals of Weakly Identified Functionscited by 12
  10. 2022Learning from a Biased Samplecited by 12
  11. 2022Partial Identification with Noisy Covariates: A Robust Optimization Approachcited by 10
  12. 2022Falsification before Extrapolation in Causal Effect Estimationcited by 10
27 more
  1. 2021Individualized Decision-Making Under Partial Identification: Three Perspectives, Two Optimality Results, and One Paradoxcited by 8
  2. 2023Hidden yet quantifiable: A lower bound for confounding strength using randomized trialscited by 8
  3. 2022Partial Identification of Dose Responses with Hidden Confounderscited by 7
  4. 2022Robust Design and Evaluation of Predictive Algorithms under Unobserved Confoundingcited by 7
  5. 2024Auditing Fairness under Unobserved Confoundingcited by 6
  6. 2024Anytime-Valid Inference for Double/Debiased Machine Learning of Causal Parameterscited by 5
  7. 2024Minimax Regret Estimation for Generalizing Heterogeneous Treatment Effects with Multisite Datacited by 5
  8. 2024Distributionally Robust Policy Learning under Concept Driftscited by 5
  9. 2025Efficient and Sharp Off-Policy Learning under Unobserved Confoundingcited by 5
  10. 2022Minimax Optimal Estimation of Stability Under Distribution Shiftcited by 4
  11. 2023Confounding-Robust Policy Improvement with Human-AI Teamscited by 4
  12. 2025StatEval: A Comprehensive Benchmark for Large Language Models in Statisticscited by 4
  13. 2024Distributionally robust risk evaluation with an isotonic constraintcited by 3
  14. 2025The Limits of Predicting Agents from Behaviourcited by 3
  15. 2022Distributionally Robust Causal Inference with Observational Datacited by 2
  16. 2023Causal Falsification of Digital Twinscited by 2
  17. 2023Operationalizing Counterfactual Metrics: Incentives, Ranking, and Information Asymmetrycited by 2
  18. 2026Information-Theoretic Causal Bounds under Unmeasured Confoundingcited by 2
  19. 2026Multi-Distribution Robust Conformal Predictioncited by 1
  20. 2023AI for Anticipatory Action: Moving Beyond Climate Forecastingcited by 0
  21. 2024A/B testing under Interference with Partial Network Informationcited by 0
  22. 2025Estimating Misreporting in the Presence of Genuine Modification: A Causal Perspectivecited by 0
  23. 2025Data Fusion for High-Resolution Estimationcited by 0
  24. 2025Assessment of the conditional exchangeability assumption in causal machine learning models: a simulation studycited by 0
  25. 2026Bayesian X-Learner: Calibrated Posterior Inference for Heterogeneous Treatment Effects under Heavy-Tailed Outcomescited by 0
  26. 2026Data-Poisoning Audits for Causal Effect Estimationcited by 0
  27. 2026Learning Risk Scores Robust to Unobserved Confounderscited by 0