The AUC can be defined as “The probability that a randomly selected case will have a higher test result than a randomly selected control”. Let’s use this definition to calculate and visualize the estimated AUC.
In the figure below, the cases are presented on the left and the controls on the right.
Since we have only 12 patients, we can easily visualize all 32 possible combinations of one case and one control. (Rcode below)
Expanding from this easy-to-follow example, Colman walks us through some of the statistical tests involved. Check it out.