In causal inference, sensitivity models assess how unmeasured confounders could alter causal analyses. However, the sensitivity parameter in these models -- which quantifies the degree of unmeasured confounding -- is often difficult to interpret. For this reason, researchers will sometimes compare the magnitude of the sensitivity parameter to an estimate for measured confounding. This is known as calibration. We propose novel calibrated sensitivity models, which directly incorporate measured confounding, and bound the degree of unmeasured confounding by a multiple of measured confounding. We illustrate how to construct calibrated sensitivity models via several examples. We also demonstrate their advantages over standard sensitivity analyses and calibration; in particular, the calibrated sensitivity parameter is an intuitive unit-less ratio of unmeasured divided by measured confounding, unlike standard sensitivity parameters, and one can correctly incorporate uncertainty due to estimating measured confounding, which standard calibration methods fail to do. By incorporating uncertainty due to measured confounding, we observe that causal analyses can be less robust or more robust to unmeasured confounding than would have been shown with standard approaches. We develop efficient estimators and methods for inference for bounds on the average treatment effect with three calibrated sensitivity models, and establish that our estimators are doubly robust and attain parametric efficiency and asymptotic normality under nonparametric conditions on their nuisance function estimators. We illustrate our methods with data analyses on the effect of exposure to violence on attitudes towards peace in Darfur and the effect of mothers' smoking on infant birthweight.

翻译：在因果推断中，敏感性模型用于评估未测量混杂因素如何改变因果分析结果。然而，这些模型中的敏感性参数——用于量化未测量混杂程度——往往难以解释。为此，研究者有时会将敏感性参数的幅度与测量混杂的估计值进行比较，这被称为校准。我们提出了新型校准敏感性模型，该模型直接纳入测量混杂因素，并将未测量混杂程度限定为测量混杂程度的倍数。通过多个实例，我们阐述了如何构建校准敏感性模型，并展示了其相较于标准敏感性分析与校准的优势：特别是，校准敏感性参数是一个直观的无量纲比值（未测量混杂与测量混杂之比），而标准敏感性参数并不具备这一特性；同时，该模型能正确纳入因估计测量混杂而产生的不确定性，而标准校准方法无法做到这一点。通过纳入测量混杂的不确定性，我们观察到因果分析对未测量混杂的稳健性可能比标准方法所显示的结果更强或更弱。针对三种校准敏感性模型，我们开发了平均处理效应界限的高效估计量与推断方法，并证明在非参数条件下，我们的估计量具有双重稳健性，且能通过其干扰函数估计量达到参数效率与渐近正态性。通过分析达尔富尔地区暴力暴露对和平态度的影响以及母亲吸烟对婴儿出生体重的影响数据，我们展示了这些方法的实际应用。