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What does the area under the ROC curve (AUC) represent?

An ROC curve plots true positive rate (sensitivity) vs false positive rate (1-specificity) across thresholds; AUC represents overall test discrimination ability, with 1.0 perfect and 0.5 no better than chance.

The correlation between true positives and false positives.

Discrimination across thresholds is what the area under the ROC curve measures. It reflects how well a model can separate positive from negative cases by ranking predictions, regardless of the specific threshold you choose. A common interpretation is that the AUC is the probability that a randomly chosen positive instance will receive a higher predicted score than a randomly chosen negative one. Values go from 0.5 (no better than chance) to 1.0 (perfect discrimination). This is different from correlating true positives with false positives, which isn’t what AUC captures, and from calibration, which deals with how close predicted probabilities are to observed outcomes. It’s also not the same as the average sensitivity across thresholds, which is a different way of summarizing performance.

The calibration of predicted probabilities to observed outcomes.

The average sensitivity across all thresholds.

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