mlsanityData to 14 Oct 2026

Orthogonal Learner for Estimating Heterogeneous Long-Term Treatment Effects

arXiv 2604.00915 ↗First posted 1 Apr 2026cs.LG stat.MLcited by 0

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Abstract (arXiv)

Estimation of heterogeneous long-term treatment effects (HLTEs) is relevant for personalized decision-making in marketing, economics, and medicine, where short-term observational datasets are often combined with long-term observational datasets. However, HLTE estimation is challenging due to limited overlap in treatment assignments or in long-term outcomes for certain subpopulations, which can lead to unstable HLTE estimates with large finite-sample variance. To address this challenge, we introduce the LT-O-learners (Long-Term Orthogonal Learners), a set of novel orthogonal learners for HLTE estimation in the canonical HLTE setting with surrogacy. The key idea of our LT-O-learners is to retarget the loss via custom overlap weights that downweight low-overlap samples. We show that the retargeted loss recovers the true HLTE pointwise and satisfies Neyman-orthogonality. We further prove two key theoretical results: (i) The nuisance error enters the error bound only through higher-order terms, which means our learners are robust to nuisance estimation error. (ii) Under a linear function class, the retargeting effectively controls the asymptotic variance of the HLTE estimator via the overlap weights in low-overlap regimes. We conduct experiments on synthetic and real-world datasets to confirm the theoretical properties of our LT-O-learners, particularly robustness in low-overlap regimes. To our knowledge, ours are the first orthogonal learners for HLTE estimation robust to low overlap in long-term settings.

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References · 35

  1. 2017Quasi-Oracle Estimation of Heterogeneous Treatment Effectscited by 332
  2. 2019Orthogonal Statistical Learningcited by 151
  3. 2021Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithmscited by 144
  4. 2022Semiparametric doubly robust targeted double machine learning: a reviewcited by 133
  5. 2024Causal machine learning for predicting treatment outcomescited by 74
  6. 2020Identifying Causal-Effect Inference Failure with Uncertainty-Aware Modelscited by 57
  7. 2020Causal inference methods for combining randomized trials and observational studies: a reviewcited by 51
  8. 2020On the role of surrogates in the efficient estimation of treatment effects with limited outcome datacited by 38
  9. 2022Combining Observational and Randomized Data for Estimating Heterogeneous Treatment Effectscited by 32
  10. 2018Combining multiple observational data sources to estimate causal effectscited by 29
  11. 2022Long-term Causal Inference Under Persistent Confounding via Data Combinationcited by 27
  12. 2020Targeting for long-term outcomescited by 23
23 more
  1. 2024Model-agnostic meta-learners for estimating heterogeneous treatment effects over timecited by 19
  2. 2023Impatient Bandits: Optimizing Recommendations for the Long-Term Without Delaycited by 17
  3. 2021A Tree-based Model Averaging Approach for Personalized Treatment Effect Estimation from Heterogeneous Data Sourcescited by 14
  4. 2016Estimating Treatment Effects using Multiple Surrogates: The Role of the Surrogate Score and the Surrogate Indexcited by 12
  5. 2022Long-term Causal Effects Estimation via Latent Surrogates Representation Learningcited by 12
  6. 2023Estimating long-term causal effects from short-term experiments and long-term observational data with unobserved confoundingcited by 12
  7. 2023Methods for Integrating Trials and Non-Experimental Data to Examine Treatment Effect Heterogeneitycited by 10
  8. 2025Orthogonal Survival Learners for Estimating Heterogeneous Treatment Effects from Time-to-Event Datacited by 10
  9. 2024Long-term Off-Policy Evaluation and Learningcited by 9
  10. 2022Combining Experimental and Observational Data for Identification and Estimation of Long-Term Causal Effectscited by 7
  11. 2024Constructing Confidence Intervals for Average Treatment Effects from Multiple Datasetscited by 6
  12. 2023A Double Machine Learning Approach to Combining Experimental and Observational Datacited by 5
  13. 2022Kernel methods for long term dose response curvescited by 4
  14. 2023Comparison of Methods that Combine Multiple Randomized Trials to Estimate Heterogeneous Treatment Effectscited by 4
  15. 2024Estimating Long-term Heterogeneous Dose-response Curve: Generalization Bound Leveraging Optimal Transport Weightscited by 4
  16. 2023The Connection Between R-Learning and Inverse-Variance Weighting for Estimation of Heterogeneous Treatment Effectscited by 3
  17. 2023Estimating Effects of Long-Term Treatmentscited by 3
  18. 2025Long-Term Individual Causal Effect Estimation via Identifiable Latent Representation Learningcited by 3
  19. 2025Overlap-weighted orthogonal meta-learner for treatment effect estimation over timecited by 3
  20. 2025Nonparametric Heterogeneous Long-term Causal Effect Estimation via Data Combinationcited by 2
  21. 2025Long-term Causal Inference via Modeling Sequential Latent Confoundingcited by 2
  22. 2024Combining Incomplete Observational and Randomized Data for Heterogeneous Treatment Effectscited by 1
  23. 2024Identification of Long-Term Treatment Effects via Temporal Links, Observational, and Experimental Datacited by 1

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