Orthogonal Learner for Estimating Heterogeneous Long-Term Treatment Effects

TL;DR

This paper introduces LT-O-learners, a novel set of orthogonal learners designed for estimating heterogeneous long-term treatment effects, robust to low overlap in observational data.

Contribution

The paper proposes the first orthogonal learners for HLTE estimation that are specifically robust to low overlap scenarios, combining theoretical guarantees with empirical validation.

Findings

LT-O-learners are robust to low overlap in treatment and outcomes.

Theoretical error bounds and quasi-oracle rates are established.

Empirical results confirm robustness and effectiveness in synthetic benchmarks.

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.