Sensitivity analysis for the unconfoundedness assumption is crucial in observational studies. For this purpose, the marginal sensitivity model gained popularity recently due to good interpretability and mathematical properties. However, most existing models only consider a worst-case parameter that bounds the logit difference between the observed and full data propensity scores, which may not fully capture the extent of unmeasured confounding. We propose a new sensitivity model that is parameterized by the second moment of the propensity score ratio, requiring only the average strength of unmeasured confounding to be bounded. By characterizing the associated sensitivity analysis as an optimization problem, we derive sharp closed-form bounds of the average potential outcomes under our model. We propose efficient one-step estimators for these bounds based on the corresponding efficient influence functions. Additionally, we apply multiplier bootstrap to construct simultaneous confidence bands to cover the sensitivity curve that consists of bounds at different values of the sensitivity parameters. Through a real-data study, we illustrate how this average-case sensitivity analysis can provide tighter bounds and facilitate calibration of the results using observed covariates.

翻译：观测研究中，对无混淆假设进行敏感性分析至关重要。近年来，边际敏感性模型因其良好的可解释性和数学性质而广受欢迎。然而，现有模型大多仅考虑一个最坏情况参数来约束观测数据与完整数据倾向性得分之间的对数差值，这可能无法完全反映未测混杂的程度。我们提出一种新的敏感性模型，该模型以倾向性得分比率的二阶矩为参数，仅要求未测混杂的平均强度有界。通过将相应的敏感性分析表述为优化问题，我们推导出该模型下平均潜在结果的精确闭式界。我们基于相应的有效影响函数，提出这些界的高效一步估计量。此外，我们应用乘子自助法构建同步置信带，以覆盖由不同敏感性参数值下的边界构成的敏感性曲线。通过一项真实数据研究，我们展示了这种平均情况敏感性分析如何提供更紧的界限，并利用观测协变量促进结果的校准。