When browsing through literature about ROC - AUC, there seems to be a disparity.

While some plot TPR and FPR, e.g. from Wikipedia: "The ROC curve is created by plotting the true positive rate (TPR) against the false positive rate (FPR)"

Others do it with sensitivity and specificity, e.g. in this paper https://jamanetwork.com/journals/jamacardiology/fullarticle/2789370

What is the difference? and why? Why would you take one over the other?


1 Answer 1


The two ROC curves are equivalent, they just use different names for the same thing. True positive rate equals sensitivity:

$$ \text{TPR} = \text{sensitivity} = \frac{\text{true positives}}{\text{true positives}+\text{false negatives}} $$

False positive rate equals $1 - \text{specificity}$:

$$ \text{FPR}=\frac{\text{false positives}}{\text{false positives}+\text{true negatives}} =1 - \frac{\text{true negatives}}{\text{false positives}+\text{true negatives}} $$

  • $\begingroup$ Correcto. (+1) In general TPR = 1 - FNR and TNR = 1 - FPR; probably some of the most used metrics in "Ethical AI" literature. $\endgroup$
    – usεr11852
    Feb 16, 2023 at 4:22

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