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 of measured confounding. This is known as calibration, or benchmarking. Although it can aid interpretation, calibration is typically conducted post hoc, and uncertainty in the estimate for unmeasured confounding is rarely accounted for. To address these limitations, we propose calibrated sensitivity models, which directly bound the degree of unmeasured confounding by a multiple of measured confounding. The calibrated sensitivity parameter is interpretable as a 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 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 an 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或基准测试。尽管校准有助于解释，但它通常是在事后进行的，且很少考虑未测量混杂估计中的不确定性。为解决这些局限性，我们提出了校准敏感性模型，该模型直接以已测量混杂的倍数来界定未测量混杂的程度。校准敏感性参数可解释为未测量混杂与已测量混杂的比率，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有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有效性和渐近正态性。我们通过分析母亲吸烟对婴儿出生体重的影响来阐释我们的方法。