Soft Roc Curves

Receiver operating characteristic (ROC) curves are a popular tool for evaluating continuous diagnostic tests. However, the traditional definition of ROC curves incorporates implicitly the idea of "hard" thresholding, which cannot encompass the situation when some intermediate classes are introduced between test result positive and negative, and also results in the empirical curves being step functions. For this reason, we introduce here the definition of soft ROC curves, which incorporates the idea of "soft" thresholding. The softness of a soft ROC curve is controlled by a regularization parameter that can be selected suitably by a cross-validation procedure. A byproduct of the soft ROC curves is that the corresponding empirical curves are smooth. The methods developed here are then examined through some simulation studies as well as a real illustrative example.