Restricted ROC curves are useful tools to evaluate the performance of tumour markers

In Clinical Epidemiology, receiver operating characteristic (ROC) analysis is a standard approach for the evaluation of the performance of diagnostic tests for binary classification based on a tumour marker distribution. The area under a ROC curve is a popular indicator of test accuracy, but its use has been questioned when the curve is asymmetric. This situation often happens when the marker concentrations overlap in the two groups under study in the range of low specificity, corresponding to a subset of values useless for classification purposes (non-informative values). The partial area under the curve at a high specificity threshold has been proposed as an alternative, but a method to identify an optimal cut-off that separates informative from non-informative values is not yet available. In this study, a new statistical approach is proposed to perform this task. Furthermore, a statistical test associated with the area under a ROC curve corresponding to informative values only (restricted ROC curve) is provided and its properties are explored by extensive simulations. Finally, the proposed method is applied to a real data set containing peripheral blood levels of six tumour markers proposed for the diagnosis of neuroblastoma. A new approach to combine couples of markers for classification purposes is also illustrated.