In this paper, we propose a semi-parametric maximum likelihood estimate of an ROC curve that satisfies the property of invariance of the ROC curve. In our simulation studies, we demonstrate that the proposed estimator has the best performance among all the existing semi-parametric estimators considered here. Finally, we illustrate the application of the proposed estimator using a real data set.
Zhou, Xiao-Hua and Lin, Hua Zhen, "Semi-Parametric Maximum Likelihood Estimates for ROC Curves of Continuous-Scale Tests" (March 2005). UW Biostatistics Working Paper Series. Working Paper 249.