The Inconsistency of “Optimal” Cutpoints Obtained using Two Criteria based on the Receiver Operating Characteristic Curve

The use of biomarkers is of ever-increasing importance in clinical diagnosis of disease. In practice, a cutpoint is required for dichotomizing naturally continuous biomarker levels to distinguish persons at risk of disease from those who are not. Two methods commonly used for establishing the "optimal" cutpoint are the point on the receiver operating characteristic curve closest to (0,1) and the Youden index, J. Both have sound intuitive interpretations--the point closest to perfect differentiation and the point farthest from none, respectively--and are generalizable to weighted sensitivity and specificity. Under the same weighting of sensitivity and specificity, these two methods identify the same cutpoint as "optimal" in certain situations but different cutpoints in others. In this paper, the authors examine situations in which the two criteria agree or disagree and show that J is the only "optimal" cutpoint for given weighting with respect to overall misclassification rates. A data-driven example is used to clarify and demonstrate the magnitude of the differences. The authors also demonstrate a slight alteration in the (0,1) criterion that retains its intuitive meaning while resulting in consistent agreement with J. In conclusion, the authors urge that great care be taken when establishing a biomarker cutpoint for clinical use.