Visualizing PerformanceCode with Python
scikit-learn draws ROC curves for you. roc_curve takes the true labels and the scores, and returns the FPR and TPR at every corner of the staircase (and the thresholds that give them); roc_auc_score returns the area. Here are the eight people of the pair grid. Run it, then change the third patient's score.
AUC by Counting Pairs
The same AUC from scratch: compare every patient with every healthy person and count the wins. Run it with each score and compare with the output above.