What is the best classification performance metric for risky medical treatments like surgery? for example a patient should NOT suggest a surgery (negative) if he/she can be treated by medicine (positive). Does Negative predictive value (TN/TN+FN) works for this situation?
This could be the concept you are looking for:
The concept is ROC curve but with cost associated for every type of cost.
For example: False negatives have a cost of 100. False positives have a cost of 5. Using cost-associated ROC curves will help you punishing much more FN than FP or viceversa.