Trying to understand cost matrix in ROC / AUC


I’m totally new to the datascience field and watched a couple of videos to get an understanding about it.

I’ve learned so far, that I can compare different models by using the ROC. Also i can use it to get the best threshold.
If I got it right, the ROC is based on the TPR (Sensitivity) and the FPR (1-Specificity). But what should I do, when there is a cost matrix for my dataset?

The TPR and the FPR are unweighted, so that the cost matrix has no influence to them. But shouldn’t it?

What can i do, to get a weighted ROC or is this just a silly question and i missed something?

Thanks for your help.

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