ROC curves and the areas under them for dichotomized tests: empirical findings for logistically and normally distributed diagnostic test results.

Many measures, including sensitivity and specificity, predictive values, and likelihood ratios, are available for the assessment of diagnostic tests. A drawback of the use of these measures is that continuous test results are often dichotomized, with consequent loss of information. Receiver operating characteristic (ROC) curves do not depend on discrimination thresholds, and therefore the area under the ROC curve (AUC) is one of the preferred measures. Although quantitative test results are often presented dichotomized, it would be convenient still to be able to estimate the ROC curve and the AUC. The authors present equations for such estimates when only one pair of a true- and a false-positive rate is given, for inherently logistically and normally distributed data. Illustrative empirical data are provided for both distributions. In contradiction to earlier reports, the authors also show that differential disease verification may skew the ROC curve. The ROC curve is thus not invariant to selection bias.