Positivity violations, which occur when some subgroups either always or never receive a treatment of interest, pose significant challenges for causal effect estimation with observational data. Recent balancing weight methods have proved to be highly effective in confounding control, however their utility is diminished in the presence of positivity violations, resulting in bias and excess variance. Approaches that deal with positivity violations, on the other hand, work by targeting a modified estimand that may be misaligned with the original research question. To address these challenges, we propose a novel balancing weights approach, which mitigates positivity violations while attempting to retain the original estimand by a targeted relaxation of the balancing constraints. Our proposed weighted estimator is consistent for the original estimand when either 1) the implied propensity score model is correct; or 2) all treatment effect modifiers are balanced to the target population. When these conditions do not hold, our estimator is consistent for a slightly modified treatment effect estimand. Furthermore, our proposed weighted estimator has reduced asymptotic variance when positivity does not hold. We evaluate our approach through applications to synthetic data, an observational study, and when transporting a treatment effect from a randomized trial.

翻译：正性假设违反（即某些亚组始终接受或从未接受目标治疗）对基于观测数据的因果效应估计构成了重大挑战。近年来，平衡权重方法在混杂控制方面已证明极为有效，但在正性假设违反的情况下其效用会降低，导致估计偏差和方差增大。另一方面，处理正性假设违反的方法通常通过调整估计目标来实现，这可能与原始研究问题不一致。为解决这些挑战，我们提出了一种新颖的平衡权重方法，该方法通过对平衡约束进行定向松弛，在缓解正性假设违反的同时尽可能保留原始估计目标。我们提出的加权估计量在以下任一条件下对原始估计目标具有一致性：1）隐含的倾向得分模型正确；或2）所有治疗效应修饰因子在目标群体中达到平衡。当这些条件不满足时，我们的估计量对轻微调整后的治疗效应估计目标保持一致性。此外，当正性假设不成立时，所提出的加权估计量具有更小的渐近方差。我们通过合成数据、一项观察性研究以及从随机试验中迁移治疗效应的应用场景对该方法进行了评估。