Abstract
Wald and Bestwick highlight an interesting point about the area under the ROC curve (AUC), showing that the same AUC values can give rise to different levels of sensitivity at a fixed specificity, depending on the ratio of standard deviations of the marker in cases versus controls. 1 However, it is not clear in practice how important an issue this usually will be. We examined 29 ovarian cancer markers in 68 cases and 475 controls from the Prostate, Lung, Colorectal and Ovarian (PLCO) trial. 2 The ratio of standard deviations (cases to controls) for the log-transformed markers ranged from 0.28 to 3.2, with a mean (SD) of 1.06 (0.73). The AUCs (estimated non-parametrically) of these markers ranged from 0.501 to 0.896, with a median of 0.57. The correlation of AUC with sensitivity at 90% (SE90) and 95% (SE95) specificity was 0.964 and 0.959, respectively, whereas the correlation between SE90 and SE95 was 0.975. Similar correlations were observed when AUC was computed parametrically assuming markers were log-normally distributed. Therefore, in practice, AUC may tend to be highly correlated with sensitivity at fixed specificity, even over a wide range of case-to-control SD ratios. Use of AUC avoids the somewhat arbitrary nature of determining a level at which to fix specificity, though like any metric, it is not perfect. Our analysis of the ovarian markers utilized both metrics, which were complementary in describing predictive ability. 2