The clinical meaning of the area under a receiver operating characteristic curve for the evaluation of the performance of disease markers.

Abstract

The area under a receiver operating characteristic (ROC) curve (AUC) is a popular measure of pure diagnostic accuracy that is independent from the proportion of diseased subjects in the analysed sample. However, its actual usefulness in the clinical context has been questioned, because it does not seem to be directly related to the actual performance of a diagnostic marker in identifying diseased and non-diseased subjects in real clinical settings. This study evaluates the relationship between the AUC and the proportion of correct classifications (global diagnostic accuracy, GDA) in relation to the shape of the corresponding ROC curves. We demonstrate that AUC represents an upward-biased measure of GDA at an optimal accuracy cut-off for balanced groups. The magnitude of bias depends on the shape of the ROC plot and on the proportion of diseased and non-diseased subjects. In proper curves, the bias is independent from the diseased/non-diseased ratio and can be easily estimated and removed. Moreover, a comparison between 2 partial AUCs can be replaced by a more powerful test for the corresponding whole AUCs. Applications to 3 real datasets are provided: a marker for a hormone deficit in children, 2 tumour markers for malignant mesothelioma, and 2 gene expression profiles in ovarian cancer patients. The AUC is a measure of accuracy with potential clinical relevance for the evaluation of disease markers. The clinical meaning of ROC parameters should always be evaluated with an analysis of the shape of the corresponding ROC curve.