论文标题
$ l^{\ infty} $ - 和$ l^2 $ - 敏感性分析因果推断与未衡量的混杂
$L^{\infty}$- and $L^2$-sensitivity analysis for causal inference with unmeasured confounding
论文作者
论文摘要
在观察性研究中，对不致性假设的敏感性分析至关重要。为此，由于其良好的解释性和数学特性，边际灵敏度模型（MSM）最近获得了受欢迎程度。但是，作为对混杂强度的量化，$ l^{\ infty} $ - 在观察到的数据倾向分数和完整的数据倾向分数之间所限制的结合可能会使分析保守。在本文中，我们提出了一个新的灵敏度模型，该模型限制了倾向得分比的$ l^2 $ norm，只需要未能遇到的混杂的平均强度才能受到界限。通过将灵敏度分析表征为优化问题，我们得出了模型下平均潜在结果的封闭形式锐利边界。我们根据相应的有效影响函数提出了这些边界的有效的一步估计器。此外，我们将乘数引导程序应用于同时置信带，以覆盖由不同灵敏度参数组成的灵敏度曲线。通过一项真实数据研究，我们说明了新的$ l^2 $ - 敏感性分析如何使用观察到的混杂因子来改进校准，并在另外假定未衡量的混杂因素独立于测量的混杂因素而仅具有对潜在胜利的添加作用时，提供了更严格的界限。
Sensitivity analysis for the unconfoundedness assumption is crucial in observational studies. For this purpose, the marginal sensitivity model (MSM) gained popularity recently due to its good interpretability and mathematical properties. However, as a quantification of confounding strength, the $L^{\infty}$-bound it puts on the logit difference between the observed and full data propensity scores may render the analysis conservative. In this article, we propose a new sensitivity model that restricts the $L^2$-norm of the propensity score ratio, requiring only the average strength of unmeasured confounding to be bounded. By characterizing sensitivity analysis as an optimization problem, we derive closed-form sharp 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 sensitivity parameters. Through a real-data study, we illustrate how the new $L^2$-sensitivity analysis can improve calibration using observed confounders and provide tighter bounds when the unmeasured confounder is additionally assumed to be independent of the measured confounders and only have an additive effect on the potential outcomes.
