Eccentric diagnostic tests: redefining sensitivity and specificity.

Abstract

Diagnostic tests exist for which the current definitions of sensitivity and specificity are inadequate. Such tests are called eccentric to distinguish them from normal diagnostic tests, for which the standard definitions are satisfactory. It is shown that when the standard definitions are used with eccentric tests there will be an appreciable range of cutoff values over which the test has no discriminating power. This is demonstrated with ROC analysis and information theory. New definitions of sensitivity and specificity that are valid for both normal and eccentric tests are proposed. These definitions require the use of two cutoffs to distinguish test-positive from test-negative individuals. When the new definitions are used with eccentric tests, performance improves significantly and the anomalous regions of zero discriminating power disappear. In the limit of zero eccentricity the new definitions become identical to the old.