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This is a semantic question: When analyzing Receiver Operating Characteric (ROC) curves, we talk about the "usefulness" of a parameter based on its Area Under the Curve (AUC). "Useful" here refers to the discriminative utility of the entire parameter and not just any threshold selected on the spectrum. Let's say I proceeded to select a threshold (cut-point, cut-off) with sensitivity and specificity both >80%. I expect this to be a "useful" threshold in its own sense. Should I be using a different term to describe its utility for me in order to avoid confusion?

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"Usefulness" is not a scientific word

The "usefulness" of a parameter is a pretty subjective quality and not very useful (sic) on its own. Just as words like "best" or "bad", in scientific writing it should never be employed without stating the reason that makes you think it is useful (such as the AUC, etc.) In any case, "useful" doesn't have a reserved meaning, and should always be optional.

You can apply "useful" to anything you want

Similarly you should never associate "useful" to a threshold without stating why you think the threshold is useful (sensitivity, specificity, accuracy etc). However, if it suits you and helps you convey a message, you should feel free to qualify a threshold of useful, keeping in mind that it doesn't provide any additional information to the reader.

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