A simplified method to approximate a ROC curve with a Bézier curve to calculate likelihood ratios of quantitative test results

Abstract

In order to calculate likeli hood ratios (LR) values for quantitative test results, a distribution-independent algorithm based on Bézier curves is proposed. Receiver operating characteristic (ROC) analysis provides the LR as the slope of the tangent to the ROC curve at the point corresponding to the test result.• Here, we make use of cubic Bézier curves defined by Bernstein polynomials of degree 3.• A simplified method to adjust a Bézier curve to a ROC curve is presented• The crucial advantage of this procedure is that Bézier curves are constructed by tangents to the ROC curve, whose slopes immediately provide the LR of a specific point on the curve.

Keywords

• Receiver operating characteristics
• Likelihood ratios
• Bézier curves