Weighting methods are popular tools for estimating causal effects; assessing their robustness under unobserved confounding is important in practice. In the following paper, we introduce a new set of sensitivity models called "variance-based sensitivity models". Variance-based sensitivity models characterize the bias from omitting a confounder by bounding the distributional differences that arise in the weights from omitting a confounder, with several notable innovations over existing approaches. First, the variance-based sensitivity models can be parameterized with respect to a simple $R^2$ parameter that is both standardized and bounded. We introduce a formal benchmarking procedure that allows researchers to use observed covariates to reason about plausible parameter values in an interpretable and transparent way. Second, we show that researchers can estimate valid confidence intervals under a set of variance-based sensitivity models, and provide extensions for researchers to incorporate their substantive knowledge about the confounder to help tighten the intervals. Last, we highlight the connection between our proposed approach and existing sensitivity analyses, and demonstrate both, empirically and theoretically, that variance-based sensitivity models can provide improvements on both the stability and tightness of the estimated confidence intervals over existing methods. We illustrate our proposed approach on a study examining blood mercury levels using the National Health and Nutrition Examination Survey (NHANES).

翻译：加权方法是估计因果效应的常用工具；在实践中评估其在未观测混杂下的稳健性至关重要。本文提出了一类新的敏感性模型，称为“基于方差的敏感性模型”。通过约束因遗漏混杂变量而引起的权重分布差异，这类模型刻画了遗漏混杂变量导致的偏倚，并在现有方法基础上实现了多项显著创新。首先，基于方差的敏感性模型可通过一个既标准化又有界的简洁$R^2$参数进行参数化。我们引入了一套正式的基准化流程，使研究者能够利用已观测协变量以可解释且透明的方式推断合理的参数值。其次，研究表明研究者可在基于方差的敏感性模型集合下估计有效的置信区间，并提供了扩展方法，使研究者能纳入关于混杂变量的实质性知识以缩小区间。最后，我们强调了所提方法与现有敏感性分析之间的联系，并从实证和理论两方面证明，相较于现有方法，基于方差的敏感性模型能够提升估计置信区间的稳定性和紧致性。我们将所提方法应用于一项利用美国国家健康与营养调查数据（NHANES）分析血汞水平的研究。