I use R software programme to find optimal cutoff point for a continuous variable.

Firstly, I generate a random continuous variable for a diseased and non-diseased subjects from normal distribution with different parameters, which provides an AUC of 0.80.

Then, I find the optimal cutoff point using "pROC" package and "roc()" function.

Then, I reclassify the original continuous variable according to the cutoff point that I found from "roc()" function.

And, finally I calculate the area under the ROC curve according to this new classification.

But, at every turn, I obtain the same AUC that is 1.00.

Why I obtain the value of 1.00 at every turn.

Thank you very much.