Gail M H, Green S B
Biometrics. 1976 Sep;32(3):561-70.
Suppose a continuous diagnostic measurement is used to classify patients, and suppose E1 false negative errors and E2 false positive errors result. The quantities E1 and E2, and the total number of misclassifications, L = E1 + E2, depend on the choice of cut-off value. We have determined the null distribution of min L, where minimization is over all possible cut-off values. The statistic, min L, can be used as a quick one-sided two-sample test, and min L is also useful for evaluating publications which present only a 2 X 2 table of false positives, false negatives, true positives and true negatives. In such cases, one can use min L to assess the usefulness of the diagnostic measurement, even if one suspects that the authors chose that particular cut-off value which minimized L after looking at the data. We extend these results to a more general weighted loss L = vE1 + MUE2 where v and mu are positive integers, and we show that min L is a generalization of the one-sided two-sample Kolmogorov-Smirnov statistic, and, indeed, exactly equivalent to that statistic for appropriate choices of v and mu.
假设有一种连续的诊断测量方法用于对患者进行分类，并且假设有(E1)个假阴性错误和(E2)个假阳性错误产生。(E1)和(E2)的值以及错误分类的总数(L = E1 + E2)，取决于截断值的选择。我们已经确定了(min L)的零分布，其中最小化是对所有可能的截断值进行的。统计量(min L)可以用作快速单侧双样本检验，并且(min L)对于评估仅呈现假阳性、假阴性、真阳性和真阴性的(2×2)表格的出版物也很有用。在这种情况下，即使有人怀疑作者在查看数据后选择了使(L)最小的特定截断值，也可以使用(min L)来评估诊断测量的有用性。我们将这些结果扩展到更一般的加权损失(L = vE1 + MUE2)，其中(v)和(\mu)是正整数，并且我们表明(min L)是单侧双样本柯尔莫哥洛夫 - 斯米尔诺夫统计量的推广，并且实际上，对于(v)和(\mu)的适当选择，它与该统计量完全等效。
