Estimation of a convex ROC curve

Abstract

The receiver operating characteristic curve summarises the accuracy of a binary classifier. Provided that the group probabilities are monotonically related to the diagnostic, it is well known that the receiver operating characteristic (ROC) curve is convex. This article presents a method of computing the maximum likelihood estimator of the ROC curve assuming convexity. Firstly, the estimator is of interest in its own right, when it is believed that the decision variable is monotonically related to the likelihood of disease. Bias and standard error may be estimated using a simply implemented bootstrap technique. Secondly, the new estimator also leads naturally and directly to a new family of ..