# Orthogonal Learner for Estimating Heterogeneous Long-Term Treatment Effects

arXiv: https://arxiv.org/abs/2604.00915 · HTML: https://mlsanity.com/paper/2604.00915/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 65 references that are in the map.
- First posted on arXiv 1 Apr 2026.

## Builds on (most cited first, 30 of 35)

- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Causal machine learning for predicting treatment outcomes](https://mlsanity.com/paper/2410.08770/) (2024)
- [Identifying Causal-Effect Inference Failure with Uncertainty-Aware Models](https://mlsanity.com/paper/2007.00163/) (2020)
- [Causal inference methods for combining randomized trials and observational studies: a review](https://mlsanity.com/paper/2011.08047/) (2020)
- [On the role of surrogates in the efficient estimation of treatment effects with limited outcome data](https://mlsanity.com/paper/2003.12408/) (2020)
- [Combining Observational and Randomized Data for Estimating Heterogeneous Treatment Effects](https://mlsanity.com/paper/2202.12891/) (2022)
- [Combining multiple observational data sources to estimate causal effects](https://mlsanity.com/paper/1801.00802/) (2018)
- [Long-term Causal Inference Under Persistent Confounding via Data Combination](https://mlsanity.com/paper/2202.07234/) (2022)
- [Targeting for long-term outcomes](https://mlsanity.com/paper/2010.15835/) (2020)
- [Model-agnostic meta-learners for estimating heterogeneous treatment effects over time](https://mlsanity.com/paper/2407.05287/) (2024)
- [Impatient Bandits: Optimizing Recommendations for the Long-Term Without Delay](https://mlsanity.com/paper/2307.09943/) (2023)
- [A Tree-based Model Averaging Approach for Personalized Treatment Effect Estimation from Heterogeneous Data Sources](https://mlsanity.com/paper/2103.06261/) (2021)
- [Estimating Treatment Effects using Multiple Surrogates: The Role of the Surrogate Score and the Surrogate Index](https://mlsanity.com/paper/1603.09326/) (2016)
- [Long-term Causal Effects Estimation via Latent Surrogates Representation Learning](https://mlsanity.com/paper/2208.04589/) (2022)
- [Estimating long-term causal effects from short-term experiments and long-term observational data with unobserved confounding](https://mlsanity.com/paper/2302.10625/) (2023)
- [Methods for Integrating Trials and Non-Experimental Data to Examine Treatment Effect Heterogeneity](https://mlsanity.com/paper/2302.13428/) (2023)
- [Orthogonal Survival Learners for Estimating Heterogeneous Treatment Effects from Time-to-Event Data](https://mlsanity.com/paper/2505.13072/) (2025)
- [Long-term Off-Policy Evaluation and Learning](https://mlsanity.com/paper/2404.15691/) (2024)
- [Combining Experimental and Observational Data for Identification and Estimation of Long-Term Causal Effects](https://mlsanity.com/paper/2201.10743/) (2022)
- [Constructing Confidence Intervals for Average Treatment Effects from Multiple Datasets](https://mlsanity.com/paper/2412.11511/) (2024)
- [A Double Machine Learning Approach to Combining Experimental and Observational Data](https://mlsanity.com/paper/2307.01449/) (2023)
- [Kernel methods for long term dose response curves](https://mlsanity.com/paper/2201.05139/) (2022)
- [Comparison of Methods that Combine Multiple Randomized Trials to Estimate Heterogeneous Treatment Effects](https://mlsanity.com/paper/2303.16299/) (2023)
- [Estimating Long-term Heterogeneous Dose-response Curve: Generalization Bound Leveraging Optimal Transport Weights](https://mlsanity.com/paper/2406.19195/) (2024)
- [The Connection Between R-Learning and Inverse-Variance Weighting for Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/2307.09700/) (2023)
- [Estimating Effects of Long-Term Treatments](https://mlsanity.com/paper/2308.08152/) (2023)
- [Long-Term Individual Causal Effect Estimation via Identifiable Latent Representation Learning](https://mlsanity.com/paper/2505.05192/) (2025)

## 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.