Considerations on the region of interest in the ROC space

Receiver Operating Characteristic curves have been widely used to represent the performance of diagnostic tests. The corresponding area under the curve, widely used to evaluate their performance quantitatively, has been criticized in several respects. Several proposals have been introduced to improve area under the curve by taking into account only specific regions of the Receiver Operating Characteristic space, that is, the plane to which Receiver Operating Characteristic curves belong. For instance, a region of interest can be delimited by setting specific thresholds for the true positive rate or the false positive rate. Different ways of setting the borders of the region of interest may result in completely different, even opposing, evaluations. In this paper, we present a method to define a region of interest in a rigorous and objective way, and compute a partial area under the curve that can be used to evaluate the performance of diagnostic tests. The method was originally conceived in the Software Engineering domain to evaluate the performance of methods that estimate the defectiveness of software modules. We compare this method with previous proposals. Our method allows the definition of regions of interest by setting acceptability thresholds on any kind of performance metric, and not just false positive rate and true positive rate: for instance, the region of interest can be determined by imposing that $$ (also known as the Matthews Correlation Coefficient) is above a given threshold. We also show how to delimit the region of interest corresponding to acceptable costs, whenever the individual cost of false positives and false negatives is known. Finally, we demonstrate the effectiveness of the method by applying it to the Wisconsin Breast Cancer Data. We provide Python and R packages supporting the presented method.