Receiver operating characteristic (ROC) graph of a varying decision threshold compared with a “useless test.” The three decision thresholds discussed in the previous section are represented on this graph. The best-fit curve drawn through these points is the ROC curve, which represents the overall performance of the diagnostic test across all possible interpretations (decision thresholds). The overall accuracy of this test under varying conditions is determined by the area under the complete curve, 0.85.

The leftmost point shows low sensitivity and high specificity. The middle point shows moderate sensitivity and specificity. The rightmost point shows high sensitivity and low specificity. Yet because they all lie on the same curve they have the same overall statistical accuracy, which is quantified by A_Z.

The 45-degree-angle line represents a series of guesses between two choices, as in a coin toss. This would be considered a “useless test” if the outcome of the test was dichotomous (for example cancer vs. no cancer) for diagnostic purposes. For instance, radiologists reading mammograms with their eyes closed would tend to fall on this line. The number of true positives would approach the number of false negatives.

The area under such a curve, 0.5, represents 50 percent accuracy of the test. In contrast, the ROC curve for a test with 100 percent accuracy will trace the Y-axis up at a false-positive fraction of zero and follow along the top of the graph at a true-positive fraction of one. The area under such a curve would be 1.0 and represent a perfect test.