Yu Wenbao, Park Eunsik, Chang Yuan-Chin Ivan
a Department of Statistics , Chonnam National University , Gwangju , South Korea.
J Biopharm Stat. 2015;25(5):881-902. doi: 10.1080/10543406.2014.920874. Epub 2014 Jun 6.
The area under the receiver operating characteristic (ROC) curve (AUC) is a popularly used index when comparing two ROC curves. Statistical tests based on it for analyzing the difference have been well developed. However, this index is less informative when two ROC curves cross and have similar AUCs. In order to detect differences between ROC curves in such situations, a two-stage nonparametric test that uses a shifted area under the ROC curve (sAUC), along with AUCs, is proposed for paired designs. The new procedure is shown, numerically, to be effective in terms of power under a wide range of scenarios; additionally, it outperforms two conventional ROC-type tests, especially when two ROC curves cross each other and have similar AUCs. Larger sAUC implies larger partial AUC at the range of low false-positive rates in this case. Because high specificity is important in many classification tasks, such as medical diagnosis, this is an appealing characteristic. The test also implicitly analyzes the equality of two commonly used binormal ROC curves at every operating point. We also apply the proposed method to synthesized data and two real examples to illustrate its usefulness in practice.
在比较两条受试者工作特征（ROC）曲线时，ROC曲线下面积（AUC）是一个常用指标。基于它来分析差异的统计检验已得到充分发展。然而，当两条ROC曲线相交且AUC相似时，该指标提供的信息较少。为了在这种情况下检测ROC曲线之间的差异，针对配对设计提出了一种两阶段非参数检验，该检验使用ROC曲线下的移位面积（sAUC）以及AUC。数值结果表明，新方法在广泛的场景下具有较高的检验效能；此外，它优于两种传统的ROC类检验，尤其是当两条ROC曲线相交且AUC相似时。在这种情况下，较大的sAUC意味着在低假阳性率范围内有较大的部分AUC。由于高特异性在许多分类任务（如医学诊断）中很重要，所以这是一个吸引人的特性。该检验还隐式地分析了两个常用双正态ROC曲线在每个操作点的相等性。我们还将所提出的方法应用于合成数据和两个实际例子，以说明其在实际中的有用性。
