Title: Orthogonal Learner for Estimating Heterogeneous Long-Term Treatment Effects

Abstract:

Accurately estimating heterogeneous long-term treatment effects (HLTEs) is crucial for personalized decision-making across fields such as medicine, economics, and marketing. These estimates often rely on combining short-term observational data with long-term datasets. However, this process is frequently complicated by insufficient overlap in either treatment assignments or long-term outcomes for specific subgroups, resulting in unstable estimates with high finite-sample variance.

To mitigate these issues, we propose the LT-O-learners (Long-Term Orthogonal Learners), a new class of orthogonal estimators designed for HLTE estimation within the standard setting involving surrogacy. The core mechanism of the LT-O-learners involves adjusting the loss function through custom overlap weights, which reduce the influence of samples with low overlap. We demonstrate that this adjusted loss function successfully recovers the true HLTE at each point and adheres to Neyman-orthogonality.

Our analysis yields two significant theoretical findings: first, the error bound for our estimators includes nuisance errors only in higher-order terms, ensuring robustness against inaccuracies in nuisance parameter estimation. Second, when assuming a linear function class, we prove that the retargeting mechanism effectively manages the asymptotic variance of the HLTE estimator, particularly in scenarios characterized by low overlap.

We validate the theoretical advantages of the LT-O-learners through experiments on both synthetic and real-world datasets, highlighting their stability in low-overlap environments. To the best of our knowledge, these represent the first orthogonal learners for HLTE estimation that maintain robustness despite low overlap in long-term settings.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC