Hanley J A, McNeil B J
Radiology. 1982 Apr;143(1):29-36. doi: 10.1148/radiology.143.1.7063747.
A representation and interpretation of the area under a receiver operating characteristic (ROC) curve obtained by the "rating" method, or by mathematical predictions based on patient characteristics, is presented. It is shown that in such a setting the area represents the probability that a randomly chosen diseased subject is (correctly) rated or ranked with greater suspicion than a randomly chosen non-diseased subject. Moreover, this probability of a correct ranking is the same quantity that is estimated by the already well-studied nonparametric Wilcoxon statistic. These two relationships are exploited to (a) provide rapid closed-form expressions for the approximate magnitude of the sampling variability, i.e., standard error that one uses to accompany the area under a smoothed ROC curve, (b) guide in determining the size of the sample required to provide a sufficiently reliable estimate of this area, and (c) determine how large sample sizes should be to ensure that one can statistically detect differences in the accuracy of diagnostic techniques.
本文介绍了通过“评分”方法或基于患者特征的数学预测所获得的受试者工作特征（ROC）曲线下面积的一种表示和解释。结果表明，在这种情况下，该面积表示随机选择的患病受试者比随机选择的非患病受试者被（正确地）评为或排序为更可疑的概率。此外，这种正确排序的概率与已经得到充分研究的非参数威尔科克森统计量所估计的量相同。利用这两种关系来（a）为抽样变异性的近似大小，即用于伴随平滑ROC曲线下面积的标准误差，提供快速的闭式表达式；（b）指导确定为该面积提供足够可靠估计所需的样本大小；以及（c）确定样本大小应多大，以确保能够从统计学上检测诊断技术准确性的差异。
