Sensitivity analysis for the unconfoundedness assumption is a crucial component of observational studies. The marginal sensitivity model has become increasingly popular for this purpose due to its interpretability and mathematical properties. After reviewing the original marginal sensitivity model that imposes a $L^\infty$-constraint on the maximum logit difference between the observed and full data propensity scores, we introduce a more flexible $L^2$-analysis framework; sensitivity value is interpreted as the "average" amount of unmeasured confounding in the analysis. We derive analytic solutions to the stochastic optimization problems under the $L^2$-model, which can be used to bound the average treatment effect (ATE). We obtain the efficient influence functions for the optimal values and use them to develop efficient one-step estimators. We show that multiplier bootstrap can be applied to construct a simultaneous confidence band of the ATE. Our proposed methods are illustrated by simulation and real-data studies.

翻译：对无根据假设的敏感性分析是观测研究的一个关键组成部分。边际敏感模型由于可解释性和数学特性,为此越来越受欢迎。在审查了最初的边际敏感模型,该模型对观察到的和完整的数据偏度分数之间的最大日志差异施加了美元辛菲提-约束,我们引入了一个更灵活的2美元分析框架;敏感值被解释为分析中未计量混杂的“平均”数量。我们从该模型中得出了可用于约束平均治疗效果(ATE)的随机优化问题的分析性解决方案。我们获得了关于最佳值的有效影响功能,并利用这些功能开发高效的一步测算器。我们表明,可运用倍增球杆来同时构建一个ATE的信任带。我们提出的方法通过模拟和真实数据研究加以说明。