Tang Chengyao, Zhou Yi, Huang Ao, Hattori Satoshi
Department of Biomedical Statistics, Graduate School of Medicine, Osaka University, Osaka, Japan.
Beijing International Center for Mathematical Research, Peking University, Beijing, China.
Stat Med. 2025 Feb 10;44(3-4):e10288. doi: 10.1002/sim.10288.
In estimating the average treatment effect in observational studies, the influence of confounders should be appropriately addressed. To this end, the propensity score is widely used. If the propensity scores are known for all the subjects, bias due to confounders can be adjusted by using the inverse probability weighting (IPW) by the propensity score. Since the propensity score is unknown in general, it is usually estimated by the parametric logistic regression model with unknown parameters estimated by solving the score equation under the strongly ignorable treatment assignment (SITA) assumption. Violation of the SITA assumption and/or misspecification of the propensity score model can cause serious bias in estimating the average treatment effect (ATE). To relax the SITA assumption, the IPW estimator based on the outcome-dependent propensity score has been successfully introduced. However, it still depends on the correctly specified parametric model and its identification. In this paper, we propose a simple sensitivity analysis method for unmeasured confounders. In the standard practice, the estimating equation is used to estimate the unknown parameters in the parametric propensity score model. Our idea is to make inferences on the (ATE) by removing restrictive parametric model assumptions while still utilizing the estimating equation. Using estimating equations as constraints, which the true propensity scores asymptotically satisfy, we construct the worst-case bounds for the ATE with linear programming. Differently from the existing sensitivity analysis methods, we construct the worst-case bounds with minimal assumptions. We illustrate our proposal by simulation studies and a real-world example.
在估计观察性研究中的平均治疗效果时，应适当考虑混杂因素的影响。为此，倾向得分被广泛使用。如果所有受试者的倾向得分已知，则可以通过使用倾向得分的逆概率加权（IPW）来调整混杂因素导致的偏差。由于倾向得分通常是未知的，所以通常通过参数逻辑回归模型进行估计，其中未知参数通过在强可忽略治疗分配（SITA）假设下求解得分方程来估计。违反SITA假设和/或倾向得分模型的错误设定可能会在估计平均治疗效果（ATE）时导致严重偏差。为了放宽SITA假设，基于结果依赖倾向得分的IPW估计器已被成功引入。然而，它仍然依赖于正确设定的参数模型及其识别。在本文中，我们提出了一种针对未测量混杂因素的简单敏感性分析方法。在标准实践中，估计方程用于估计参数倾向得分模型中的未知参数。我们的想法是在仍然利用估计方程的同时，通过去除限制性参数模型假设来对（ATE）进行推断。利用估计方程作为真实倾向得分渐近满足的约束条件，我们通过线性规划构建ATE的最坏情况界限。与现有的敏感性分析方法不同，我们在最小假设下构建最坏情况界限。我们通过模拟研究和一个实际例子来说明我们的建议。
