In causal inference, sensitivity models assess how unmeasured confounders could alter causal analyses, but the sensitivity parameter -- which quantifies the degree of unmeasured confounding -- is often difficult to interpret. For this reason, researchers sometimes compare the sensitivity parameter to an estimate for measured confounding. This is known as calibration. Although calibration can aid interpretation, it is typically conducted post hoc, and uncertainty in the point estimate for measured confounding is rarely accounted for. To address these limitations, we propose novel calibrated sensitivity models, which directly bound the degree of unmeasured confounding by a multiple of measured confounding. The calibrated sensitivity parameter is interpretable as an intuitive unit-less ratio of unmeasured to measured confounding, and uncertainty due to estimating measured confounding can be incorporated. Incorporating this uncertainty shows causal analyses can be less or more robust to unmeasured confounding than would have been suggested by standard approaches. We develop efficient estimators and inferential methods for bounds on the average treatment effect with three calibrated sensitivity models, establishing parametric efficiency and asymptotic normality under doubly robust style nonparametric conditions. We illustrate our methods with a data analysis of 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，但敏感性参数——用于量化未测量混杂程度——通常难以解释。因此，研究人员有时会将敏感性参数与已测量混杂的估计值进行比较，这种方法被称为校准。尽管校准有助于解释，但它通常是事后进行的，并且很少考虑已测量混杂点估计中的不确定性。为解决这些局限性，我们提出了新颖的校准敏感性模型，该模型直接以已测量混杂的倍数来约束未测量混杂的程度。校准敏感性参数可解释为未测量混杂与已测量混杂之间直观的无量纲比率，并且可以纳入估计已测量混杂所产生的不确定性。纳入这种不确定性表明，因果分析对未测量混杂的稳健性可能比标准方法所暗示的更强或更弱。我们针对三种校准敏感性模型，开发了平均处理效应界限的高效估计器和推断方法，并在双重稳健风格的非参数条件下建立了参数效率和渐近正态性。我们通过对母亲吸烟对婴儿出生体重影响的数据分析来阐述我们的方法。