On use of partial area under the ROC curve for evaluation of diagnostic performance

Evaluation of diagnostic performance is a necessary component of new developments in many fields including medical diagnostics and decision making. The methodology for statistical analysis of diagnostic performance continues to develop, offering new analytical tools for conventional inferences and solutions for novel and increasingly more practically relevant questions. In this paper, we focus on the partial area under the Receiver Operating Characteristic (ROC) curve or pAUC. This summary index is considered to be more practically relevant than the area under the entire ROC curve (AUC), but because of several perceived limitations, it is not used as often. To improve interpretation, results for pAUC analysis are frequently reported using a rescaled index such as the standardized partial AUC proposed by McClish (1989). We derive two important properties of the relationship between the 'standardized' pAUC and the defined range of interest, which could facilitate a wider and more appropriate use of this important summary index. First, we mathematically prove that the 'standardized' pAUC increases with increasing range of interest for practically common ROC curves. Second, using comprehensive numerical investigations, we demonstrate that, contrary to common belief, the uncertainty about the estimated standardized pAUC can either decrease or increase with an increasing range of interest. Our results indicate that the partial AUC could frequently offer advantages in terms of statistical uncertainty of the estimation. In addition, selection of a wider range of interest will likely lead to an increased estimate even for standardized pAUC.