The partial area under the summary ROC curve

Abstract

The area under the curve (AUC) is commonly used as a summary measure of the receiver operating characteristic (ROC) curve. It indicates the overall performance of a diagnostic test in terms of its accuracy at various diagnostic thresholds used to discriminate cases and non-cases of disease. The AUC measure is also used in meta-analyses, where each component study provides an estimate of the test sensitivity and specificity. These estimates are then combined to calculate a summary ROC (SROC) curve which describes the relationship between-test sensitivity and specificity across studies. The partial AUC has been proposed as an alternative measure to the full AUC. When using the partial AUC, one considers only those regions of the ROC space where data have been observed, or which correspond to clinically relevant values of test sensitivity or specificity. In this paper, we extend the idea of using the partial AUC to SROC curves in meta-analysis. Theoretical and numerical results describe the variation in the partial AUC and its standard error as a function of the degree of inter-study heterogeneity and of the extent of truncation applied to the ROC space. A scaled partial area measure is also proposed to restore the property that the summary measure should range from 0 to 1. The results suggest several disadvantages of the partial AUC measures. In contrast to earlier findings with the full AUC, the partial AUC is rather sensitive to heterogeneity. Comparisons between tests are more difficult, especially if an empirical truncation process is used. Finally, the partial area lacks a useful symmetry property enjoyed by the full AUC. Although the partial AUC may sometimes have clinical appeal, on balance the use of the full AUC is preferred.