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，我们针对评估连续值处理或暴露效应的标准指标——平均潜在结果（APO），提出了新颖的界并推导了置信区间。我们证明，在连续敏感性模型下，这些界是锐利的，即在该模型下给出了可能的最小区间，并提出了我们估计量的双重稳健版本。在与Jesson等人（2022）（arXiv:2204.10022）方法的对比分析中，通过使用模拟和真实数据集，我们表明，我们的方法不仅产生了更锐利的界，而且能良好覆盖真实APO，同时显著减少了计算时间。