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. As the basis of $L^\infty$-sensitivity analysis, it assumes the logit difference between the observed and full data propensity scores is uniformly bounded. In this article, we introduce a new $L^2$-sensitivity analysis framework which is flexible, sharp and efficient. We allow the strength of unmeasured confounding to vary across units and only require it to be bounded marginally for partial identification. We derive analytical solutions to the optimization problems under our $L^2$-models, which can be used to obtain sharp bounds for the average treatment effect (ATE). We derive efficient influence functions and use them to develop efficient one-step estimators in both analyses. We show that multiplier bootstrap can be applied to construct simultaneous confidence bands for our ATE bounds. In a real-data study, we demonstrate that $L^2$-analysis relaxes the interpretation of $L^\infty$-analysis and provides a much more reliable calibration process using observed covariates. Finally, we provide an extension of our theoretical results to the conditional average treatment effect (CATE).

翻译：针对无混杂性假设的敏感性分析是观察性研究的关键组成部分。边际敏感性模型因其可解释性和数学特性在此类分析中日益普及。作为L^∞-敏感性分析的基础，该模型假设观测数据与完整数据倾向得分的对数几率差具有一致有界性。本文提出一种兼具灵活性、尖锐性和高效性的新型L^2-敏感性分析框架。我们允许未测量混杂强度在不同单元间变化，仅要求其在部分识别中具有边际有界性。通过推导L^2-模型下优化问题的解析解，可获得平均处理效应(ATE)的尖锐界。我们推导出有效影响函数，并据此在两种分析框架中开发高效一步估计量。研究表明，乘子自助法可用于构建ATE界的同步置信带。在真实数据研究中，我们发现L^2-分析放宽了L^∞-分析的解释条件，并利用观测协变量提供更可靠的校准流程。最后，我们将理论结果推广至条件平均处理效应(CATE)。