A Generalization of the One-Sided Two-Sample Kolmogorov-Smirnov Statistic for Evaluating Diagnostic Tests

Publisher Website
Google Scholar
Abstract
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 misclassification, L = E1 + E2, depend on the choice of cut-off value. The null distribution of min L was determined, where minimization is over all possible cut-off values. The statistic, min [minimum] L, can be used as a quick 1-sided 2-sample test, and min L is useful for evaluating publications which present only a 2 .times. 2 table of false positives, false negatives, true positives and true negatives. In such cases, min L can be used to assess the usefulness of the diagnostic measurement, even if it is suspected that particular cut-off value which minimized L after the data were seen. These results are extended to a more general weighted loss L = .nu.E1 + .mu.E2 where .nu. and .mu. are positive integers, and it is shown that min L is a generalization of the 1-sided 2-sample Kolmogorov-Smirnov statistic, and exactly equivalent to that statistic for appropriate choices of .nu. and .mu.

This publication has 4 references indexed in Scilit: