Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, China.
Beijing Airdoc Technology Co., Ltd., Beijing, 100089, China.
Biometrics. 2024 Jul 1;80(3). doi: 10.1093/biomtc/ujae063.
This article addresses the challenge of estimating receiver operating characteristic (ROC) curves and the areas under these curves (AUC) in the context of an imperfect gold standard, a common issue in diagnostic accuracy studies. We delve into the nonparametric identification and estimation of ROC curves and AUCs when the reference standard for disease status is prone to error. Our approach hinges on the known or estimable accuracy of this imperfect reference standard and the conditional independent assumption, under which we demonstrate the identifiability of ROC curves and propose a nonparametric estimation method. In cases where the accuracy of the imperfect reference standard remains unknown, we establish that while ROC curves are unidentifiable, the sign of the difference between two AUCs is identifiable. This insight leads us to develop a hypothesis-testing method for assessing the relative superiority of AUCs. Compared to the existing methods, the proposed methods are nonparametric so that they do not rely on the parametric model assumptions. In addition, they are applicable to both the ROC/AUC analysis of continuous biomarkers and the AUC analysis of ordinal biomarkers. Our theoretical results and simulation studies validate the proposed methods, which we further illustrate through application in two real-world diagnostic studies.
本文针对在不完美金标准背景下估计受试者工作特征 (ROC) 曲线和这些曲线下面积 (AUC) 的挑战，这在诊断准确性研究中是一个常见问题。我们深入研究了在疾病状态的参考标准容易出错的情况下，ROC 曲线和 AUC 的非参数识别和估计。我们的方法取决于这种不完美参考标准的已知或可估计的准确性以及条件独立性假设，根据该假设，我们证明了 ROC 曲线的可识别性，并提出了一种非参数估计方法。在不完美参考标准的准确性未知的情况下，我们确定虽然 ROC 曲线不可识别，但两个 AUC 之间差异的符号是可识别的。这一见解促使我们开发了一种用于评估 AUC 相对优势的假设检验方法。与现有方法相比，所提出的方法是非参数的，因此它们不依赖于参数模型假设。此外，它们适用于连续生物标志物的 ROC/AUC 分析和有序生物标志物的 AUC 分析。我们的理论结果和模拟研究验证了所提出的方法，我们通过在两个实际诊断研究中的应用进一步说明了这些方法。
