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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?

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  1. Minimizing false negatives is definitely a good strategy.
  2. You can also generalize to using weighted f-measure. It allows you to give tunable weightage.
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Check ROC curve, increase the threshold and measure PPV. Also you can not use only one in isolation, you have to check sensitivity, specificity and PPV in order to understand the complete scenario.

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This could be the concept you are looking for:

Cost curves.

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.

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