ROC curve usually looks like the following figure:
If we have enough data, could we safely assume that ROC curve for a model will always be symmetric around the line y = 100 - x? If not, is there any way to make the ROC curve shift up (the red line)?
I am asking this question because my final goal is to optimize sensitivity at a minimum specificity. However, using sensitivity as my evaluation metric seems to be very similar to using AUC. So, I am wondering whether using AUC is highly correlated with using sensitivity as an evaluation metric because you can not intentionally tweak the shape of ROC curve.
I also tried using sample weight, but it seems to only impact the cutoff of the classification model. Please check my attempts with SVM by changing the weight of the positive class.