A family of nonparametric statistics for comparing diagnostic markers with paired or unpaired data

In this paper we study a broad class of nonparametric statistics for comparing two diagnostic markers. One can compare the sensitivities of these diagnostic markers over restricted ranges of specificity by selecting an appropriate statistic from this class. As special cases, one can compare the entire area under the receiver-operator curve (Hanley & McNeil, 1982), or one can compare the sensitivities at a fixed common specificity. Usually we would recommend a comparison based on an average of sensitivities over a restricted high level of specificities. Test procedures and confidence intervals are based on asymptotic normality. These procedures are applicable for paired data, in which both diagnostic markers are performed on each subject, and for unpaired data. The procedures may be used to compare two real functions of multiple diagnostic markers as well as to compare individual markers.