The Area Under the Receiving Operating Characteristic Curve (AUC) is frequently used for assessing the overall accuracy of a diagnostic marker. However, estimation of AUC relies on knowledge of the true outcomes of subjects: diseased or non-diseased. Because disease verification based on a gold standard is often expensive and/or invasive, only a limited number of patients are sent to verification at doctors' discretion. Estimation of AUC is generally biased if only small verified samples are used and it is thus necessary to make corrections for such lack of information. However, correction based on the ignorable missingness assumption (or missing at random) is also biased if the missing mechanism indeed depends on the unknown disease outcome, which is called nonignorable missing. In this paper, we propose a propensity-score-adjustment method for estimating AUC based on the instrumental variable assumption when the missingness of disease status is nonignorable. The new method makes parametric assumptions on the verification probability, and the probability of being diseased for verified samples rather than for the whole sample. The proposed parametric assumption on the observed sample is easier to be verified than the parametric assumption on the full sample. We establish the asymptotic properties of the proposed estimators. A simulation study is performed to compare the proposed method with existing methods. The proposed method is also applied to an Alzheimer's disease data collected by National Alzheimer's Coordinating Center.

中文翻译：

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不可忽略验证偏差下 ROC 曲线下面积的估计


接收操作特征曲线下面积 (AUC) 经常用于评估诊断标记物的整体准确性。然而，AUC 的估计依赖于对受试者真实结果的了解：患病或未患病。由于基于金标准的疾病验证通常费用昂贵且/或具有侵入性，因此医生可酌情仅将有限数量的患者送去验证。如果仅使用经过验证的小样本，AUC 的估计通常会存在偏差，因此有必要对信息的缺乏进行修正。然而，如果缺失机制确实取决于未知的疾病结果，则基于可忽略缺失假设（或随机缺失）的校正也会有偏差，这称为不可忽略缺失。在本文中，我们提出了一种当疾病状态缺失不可忽略时基于工具变量假设估计 AUC 的倾向评分调整方法。新方法对验证概率以及验证样本而不是整个样本的患病概率进行参数假设。对观察样本提出的参数假设比对完整样本的参数假设更容易验证。我们建立了所提出的估计量的渐近性质。进行模拟研究以将所提出的方法与现有方法进行比较。所提出的方法也适用于国家阿尔茨海默病协调中心收集的阿尔茨海默病数据。