Transformed ROC Curve for Biomarker Evaluation

To complement the conventional area under the ROC curve (AUC) which cannot fully describe the diagnostic accuracy of some non-standard biomarkers, we introduce a transformed ROC curve and its associated transformed AUC (TAUC) in this article, and show that TAUC can relate the original improper biomarker to a proper biomarker after a non-monotone transformation. We then provide nonparametric estimation of the non-monotone transformation and TAUC, and establish their consistency and asymptotic normality. We conduct extensive simulation studies to assess the performance of the proposed TAUC method and compare with the traditional methods. Case studies on real biomedical data are provided to illustrate the proposed TAUC method. We are able to identify more important biomarkers that tend to escape the traditional screening method.