Building AUC/ROC curve without probabilities, only with actual/predicted labels

If we dont have access to model and have just actual and predicted labels without probabilities, is it still be possible to plot AUC/ROC curve.

For example can we have the curve from the following information (>1000 values in array in actual)

actual = ["C1","C1","C2","C1","C2"]
predicted = ["C2","C1","C2","C1","C1"]


• Your example gives one point on the ROC curve. You can invent two other points, one with all the predictions C1 and another with all the predictions C2. Whether you think three points leading to two line-segments is really an ROC curve is up to you; I would say probably not, as I think you should be adjusting discrimination thresholds with a little more sophistication than this Commented Aug 5, 2020 at 14:39
• If you assign C1 and C2 distinct numerical values, then you can follow the instructions here stats.stackexchange.com/questions/145566/… to draw a three-point ROC curve with AUC $\approx 0.583$.
– Sycorax
Commented Aug 5, 2020 at 16:32
• @Sycorax, thankyou for the comment, but where will I bring the probability(0-1) that author has as "predicted retention status" in this question, I don't have access to such number
– A.B
Commented Aug 6, 2020 at 3:02
• You don't need it, because ROC curves and AUC are statistics of ranks. Replace all instances of C1 with $0$ and all instances of C2 with $1$. That's what I mean by "assign C1 and C2 distinct numerical values."
– Sycorax
Commented Aug 6, 2020 at 3:10
• Okay thanks, I need to replace in both actual and predicted?
– A.B
Commented Aug 6, 2020 at 3:30