An average-case sensitivity analysis for unmeasured confounding
提出一种基于倾向性评分比二阶矩的敏感性模型，仅要求平均混杂强度有界，推导出平均潜在结果的紧界，并给出高效一步估计量和同时置信带，用于观察性研究中无混杂假设的敏感性分析。
Summary Sensitivity analysis for the unconfoundedness assumption is crucial in observational studies. For this purpose, the marginal sensitivity model has gained popularity in recent years owing to its good interpretability and mathematical properties. However, most existing models only consider a worst-case parameter that bounds the logit difference between the observed-data 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 on 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 use the multiplier bootstrap to construct simultaneous confidence bands to cover the sensitivity curve, consisting 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.