# How to draw an ROC curve?

If I have values for sensitivity and specificity for a group of studies, for example like this:

sensitivity     specificity
-----------     -----------

66.3             74.7
87.2             65.9
56.4             76.4
79.5             94.3


How can I make an ROC curve for such values? Do I divide them by 100 for example and just put the values in the curve straightforward? Or, how exactly does the process work out?

## 1 Answer

You seem to have several readings of $\text{sensitivity}$ and $\text{specificity}$ for some classifier; yet ROC curve does not work that way. It is a way of plotting the performance of a learner giving some numerical confidence that some object is of a class A and not B instead of certain prediction (i.e. this object is A, that is B).
Obviously such confidence-score-giving learner can be converted into a plain two class classifier by defining some threshold $t$ and saying that it votes for class A if the $\text{score}>t$ and for B otherwise. And, for this classifier, one can get $\text{sensitivity}$ and $\text{specificity}$.
Thus, for such learner, you can get two functions: $\text{sensitivity}(t)$ and $\text{specificity}(t)$; ROC is a visualization of those two functions as a parametric curve $(1-\text{specificity}(t),\text{sensitivity}(t))$. In practice $t$ has finite number of unique values (at most equal to number of objects), so the curve is constructed from points for all of them.