A Comparison of Parametric and Nonparametric Approaches to ROC Analysis of Quantitative Diagnostic Tests

A representation and interpretation of the area under a receiver operating characteristic (ROC) curve obtained by the "rating" method, or by mathematical predictions based on patient characteristics, is presented. It is shown that in such a setting the area represents the probability that a randomly chosen diseased subject is (correctly) rated or ranked with greater suspicion than a randomly chosen non-diseased subject. Moreover, this probability of a correct ranking is the same quantity that is estimated by the already well-studied nonparametric Wilcoxon statistic. These two relationships are exploited to (a) provide rapid closed-form expressions for the approximate magnitude of the sampling variability, i.e., standard error that one uses to accompany the area under a smoothed ROC curve, (b) guide in determining the size of the sample required to provide a sufficiently reliable estimate of this area, and (c) determine how large sample sizes should be to ensure that one can statistically detect differences in the accuracy of diagnostic techniques.

If the performance of a diagnostic imaging system is to be evaluated objectively and meaningfully, one must compare radiologists' image-based diagnoses with actual states of disease and health in a way that distinguishes between the inherent diagnostic capacity of the radiologists' interpretations of the images, and any tendencies to "under-read" or "over-read". ROC methodology provides the only known basis for distinguishing between these two aspects of diagnostic performance. After identifying the fundamental issues that motivate ROC analysis, this article develops ROC concepts in an intuitive way. The requirements of a valid ROC study and practical techniques for ROC data collection and data analysis are sketched briefly. A survey of the radiologic literature indicates the broad variety of evaluation studies in which ROC analysis has been employed.