Orthogonal Learner for Estimating Heterogeneous Long-Term Treatment Effects

• URL: http://arxiv.org/abs/2604.00915v1
• Date: Wed, 01 Apr 2026 13:56:19 GMT
• Title: Orthogonal Learner for Estimating Heterogeneous Long-Term Treatment Effects
• Abstract summary: We introduce the LT-O-learners (Long-Term Orthogonal learners) for HLTE estimation.<n>The learners are designed for the canonical HLTE setting that combines a short-term randomized dataset with a long-term historical dataset.<n>We show that the learners are robust to errors in the nuisance estimation.
• Score: 56.15663253912398
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Estimation of heterogeneous long-term treatment effects (HLTEs) is widely used for personalized decision-making in marketing, economics, and medicine, where short-term randomized experiments are often combined with long-term observational data. However, HLTE estimation is challenging due to limited overlap in treatment or in observing 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. The learners are designed for the canonical HLTE setting that combines a short-term randomized dataset $\mathcal{D}_1$ with a long-term historical dataset $\mathcal{D}_2$. The key idea of our LT-O-Learners is to retarget the learning objective by introducing custom overlap weights that downweight samples with low overlap in treatment or in long-term observation. We show that the retargeted loss is equivalent to the weighted oracle loss and satisfies Neyman-orthogonality, which means our learners are robust to errors in the nuisance estimation. We further provide a general error bound for the LT-O-Learners and give the conditions under which quasi-oracle rate can be achieved. Finally, our LT-O-learners are model-agnostic and can thus be instantiated with arbitrary machine learning models. We conduct empirical evaluations on synthetic and semi-synthetic benchmarks to confirm the theoretical properties of our LT-O-Learners, especially the robustness in low-overlap settings. To the best of our knowledge, ours are the first orthogonal learners for HLTE estimation that are robust to low overlap that is common in long-term outcomes.

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