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. 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 inference on the average causal effect 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 average treatment effect with linear programming. Different 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.

翻译：在观察性研究中估计平均处理效应时，需恰当处理混杂因素的影响。为此，倾向得分被广泛使用。若所有受试者的倾向得分已知，可通过倾向得分的逆概率加权（IPW）调整混杂偏倚。由于倾向得分通常未知，常通过参数逻辑回归模型在强可忽略处理分配（SITA）假设下求解得分方程估计未知参数。SITA假设违背和/或倾向得分模型误设可能导致平均处理效应估计产生严重偏倚。为放宽SITA假设，基于结果依赖倾向得分的IPW估计量已被成功引入，但仍依赖于正确设定的参数模型及其识别。本文提出一种针对未测量混杂因素的简单敏感性分析方法。标准实践中，使用估计方程估计参数倾向得分模型中的未知参数。我们的思路是通过移除限制性参数模型假设，同时仍利用估计方程，对平均因果效应进行推断。以真实倾向得分渐近满足的估计方程为约束条件，通过线性规划构建平均处理效应的最坏情况边界。与现有敏感性分析方法不同，我们在最小假设下构建最坏情况边界。通过模拟研究和实际案例验证本文方法的有效性。