An alternative parameterization for the binormal ROC curve, with applications to sizing and simulation studies

Because the conventional binormal ROC curve parameters are in terms of the underlying normal diseased and nondiseased rating distributions, transformations of these values are required for the user to understand what the corresponding ROC curve looks like in terms of its shape and size. In this paper I propose an alternative parameterization in terms of parameters that explicitly describe the shape and size of the ROC curve. The proposed two parameters are the mean-to-sigma ratio and the familiar area under the ROC curve (AUC), which are easily interpreted in terms of the shape and size of the ROC curve, respectively. In addition, the mean-to-sigma ratio describes the degree of improperness of the ROC curve and the AUC describes the ability of the corresponding diagnostic test to discriminate between diseased and nondiseased cases. The proposed parameterization simplifies the sizing of diagnostic studies when conjectured variance components are used and simplifies choosing the binormal a and b parameter values needed for simulation studies.