Nonparametric Estimation and Hypothesis Testing on the Partial Area Under Receiver Operating Characteristic Curves

ABSTRACT

The area under a receiver operating characteristic curve is a useful index of the accuracy of a diagnostic test. When the diagnostic ability of a new biomarker is of interest only in a certain range of specificity, the partial area under the curve becomes desirable. In this article, we extend Bamber's (1975 Bamber , D. ( 1975 ). The area above the ordinal dominance graph and the area below the receiver operating characteristics graph. J. Math. Psychol. 12 : 387 – 415 . [CSA] [Crossref], [Web of Science ®] , [Google Scholar]) results and show that the partial area under a receiver operating characteristic curve is the probability of a constrained stochastic ordering. We then construct a ‘weighted’ Mann-Whitney statistic as an estimator of the partial area and investigate its statistical properties. A testing procedure is also developed to compare partial area under two receiver operating characteristic curves. The methods are exemplified with data from biomarkers associated with coronary heart disease.