Finding the Optimal Threshold of a Parametric ROC Curve Under a Continuous Diagnostic Measurement

Abstract

The accuracy of a binary diagnostic test can easily be assessed by comparing the sensitivity and specificity with the status of respondents. When the result of a diagnostic test is continuous, the assessment of accuracy depends on a specified threshold. The receiver operating characteristic (ROC) curve, which includes all possible combinations of sensitivity and specificity, provides an appropriate measure for evaluating the overall accuracy of the diagnostic test. Nevertheless, in practice, a cutoff value is still required to make easier its clinical usage easier. The determination of a proper cutoff value depends on how important the practitioner views the specificity and sensitivity. Given particular values of specificity and sensitivity, this paper derives the optimal cutoff value under two parametric assumptions on the outcomes of the diagnostic test. Because the optimal cutoff value does not have a closed form, the numerical results are tabulated for some parameter settings to find the optimal cutoff value. Finally, real data are employed to illustrate the use of the proposed method.