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This question already has an answer here:

Calculating AUC for one threshold in the continuous output is simple:

AUC = (TPR - FPR + 1) / 2;

What if I want to calculate AUC for multiple thresholds in continuous output of the classifier?

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marked as duplicate by Sycorax, Michael Chernick, Peter Flom Jul 30 '18 at 11:20

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    $\begingroup$ That is not AUROC. AUROC uses all possible thresholds, or more intuitively, can be defined by a rank correlation between predicted and observed without any notion of thresholds, using a concordance probability ($c$-index). $\endgroup$ – Frank Harrell Nov 29 '16 at 16:59

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