In causal inference, treatment effects are typically estimated under the ignorability, or unconfoundedness, assumption, which is often unrealistic in observational data. By relaxing this assumption and conducting a sensitivity analysis, we introduce novel bounds and derive confidence intervals for the Average Potential Outcome (APO) - a standard metric for evaluating continuous-valued treatment or exposure effects. We demonstrate that these bounds are sharp under a continuous sensitivity model, in the sense that they give the smallest possible interval under this model, and propose a doubly robust version of our estimators. In a comparative analysis with the method of Jesson et al. (2022) (arXiv:2204.10022), using both simulated and real datasets, we show that our approach not only yields sharper bounds but also achieves good coverage of the true APO, with significantly reduced computation times.

翻译：在因果推断中，处理效应的估计通常基于可忽略性或无混杂性假设，这一假设在观测数据中往往不成立。通过放宽该假设并进行敏感性分析，我们针对平均潜在结果（APO）——一种评估连续值处理或暴露效应的标准度量——提出了新颖的界并推导了置信区间。我们证明这些界在连续敏感性模型下是尖锐的，即在该模型下能给出可能的最小区间，并提出了我们估计量的双重稳健版本。通过与Jesson等人（2022）（arXiv:2204.10022）的方法进行对比分析，在模拟和真实数据集上均表明，我们的方法不仅能产生更尖锐的界，还能实现对真实APO的良好覆盖，同时显著减少了计算时间。