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.

翻译：异质长期治疗效应（HLTE）的估计对于市场营销、经济学和医学中的个性化决策具有重要意义，在这些领域中，短期观测数据集常与长期观测数据集相结合。然而，由于治疗分配或某些亚群长期结局的重叠有限，HLTE估计面临挑战，这可能导致估计不稳定并出现大样本有限方差。为解决这一问题，我们提出了LT-O学习器（长期正交学习器），这是一组用于典型代理HLTE设定下的新型正交学习器。LT-O学习器的核心思想是通过自定义重叠权重重新定位损失函数，以降低低重叠样本的权重。我们证明，重新定位后的损失函数能够逐点恢复真实HLTE，并满足奈曼正交性。我们还证明了两个关键理论结果：（i）干扰误差仅通过高阶项进入误差界，这意味着我们的学习器对干扰估计误差具有鲁棒性；（ii）在线性函数类下，通过低重叠区域中的重叠权重，重新定位有效控制了HLTE估计量的渐近方差。我们在合成数据集和真实世界数据集上开展实验，验证了LT-O学习器的理论性质，特别是在低重叠区域中的鲁棒性。据我们所知，这是首个在长期设定中对低重叠问题具有鲁棒性的HLTE估计正交学习器。