In observational studies, exposures are often continuous rather than binary or discrete. At the same time, sensitivity analysis is an important tool that can help determine the robustness of a causal conclusion to a certain level of unmeasured confounding, which can never be ruled out in an observational study. Sensitivity analysis approaches for continuous exposures have now been proposed for several causal estimands. In this article, we focus on the average derivative effect (ADE). We obtain closed-form bounds for the ADE under a sensitivity model that constrains the odds ratio (at any two dose levels) between the latent and observed generalized propensity score. We propose flexible, efficient estimators for the bounds, as well as point-wise and simultaneous (over the sensitivity parameter) confidence intervals. We examine the finite sample performance of the methods through simulations and illustrate the methods on a study assessing the effect of parental income on educational attainment and a study assessing the price elasticity of petrol.

翻译：在观察性研究中，暴露变量通常是连续的而非二元或离散的。与此同时，敏感性分析作为一种重要工具，有助于评估因果结论对特定水平未测量混杂因素的稳健性——这在观察性研究中永远无法完全排除。针对连续暴露变量的敏感性分析方法目前已针对多种因果估计量提出。本文聚焦于平均导数效应（ADE）。我们在一个敏感性模型下推导了ADE的闭式边界，该模型约束了潜在广义倾向得分与观测广义倾向得分之间的比值比（任意两个剂量水平）。我们提出了边界估计的灵活高效估计器，以及点态和同步（针对敏感性参数）置信区间。通过模拟实验评估了方法的有限样本性能，并在两项研究中展示了方法应用：一项评估父母收入对教育成就的影响，另一项评估汽油价格弹性。