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A solution for the most basic optimization problem associated with an ROC curve
1School of Public Health, Division of Biostatistics and Cancer Center, University of Minnesota, MMC 303, Minneapolis 55455, USA. chap@biostat.umn.edu
Abstract:
In a few cases, such as early pregnancy tests, the test results are dichotomous; many diagnostic tests, however, give results which are not binary. In the diagnosis of prostate cancer, prostate-specific antigen test result is on a continuous scale; or, in radiology, assessment of mammograms is on an ordinal scale. In such cases, the accuracy of the marker or test is often first summarized in a receiver operating characteristic (ROC) curve and then as the area under that curve. The area under the ROC curve, however, only shows the 'potential' of a marker; sooner or later, for practical uses, we still need to dichotomize the test result so that we can classify subjects as 'diseased' or 'healthy'. Finding an 'optimal' cutpoint to dichotomize a continuous marker is desirable and is a very basic problem but, in all or most cases, cutpoints used in practice are arbitrary. The difficulty lies in our failure to define and justify a criterion for optimality. In this paper, we will propose a solution by maximizing a well-known parameter--the Youden's Index--within the framework of the ROC curve.
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