ROC-ing along: Evaluation and interpretation of receiver operating characteristic curves

It is vital for clinicians to understand and interpret correctly medical statistics as used in clinical studies. In this review, we address current issues and focus on delivering a simple, yet comprehensive, explanation of common research methodology involving receiver operating characteristic (ROC) curves. ROC curves are used most commonly in medicine as a means of evaluating diagnostic tests.

Sample data from a plasma test for the diagnosis of colorectal cancer were used to generate a prediction model. These are actual, unpublished data that have been used to describe the calculation of sensitivity, specificity, positive predictive and negative predictive values, and accuracy. The ROC curves were generated to determine the accuracy of this plasma test. These curves are generated by plotting the sensitivity (true-positive rate) on the y axis and 1 - specificity (false-positive rate) on the x axis.

Curves that approach closest to the coordinate (x = 0, y = 1) are more highly predictive, whereas ROC curves that lie close to the line of equality indicate that the result is no better than that obtained by chance. The optimum sensitivity and specificity can be determined from the graph as the point where the minimum distance line crosses the ROC curve. This point corresponds to the Youden index (J), a function of sensitivity and specificity used commonly to rate diagnostic tests. The area under the curve is used to quantify the overall ability of a test to discriminate between 2 outcomes.

By following these simple guidelines, interpretation of ROC curves will be less difficult and they can then be interpreted more reliably when writing, reviewing, or analyzing scientific papers.