Summary
The coordinates and AUC of ROC curves are invariant to class prevalence when the class-conditional score distributions are unchanged (1). However, with rare positives, even a small false-positive rate can yield many false positives; precision-recall curves expose this prevalence-dependent positive predictive value more directly and can make operational differences between classifiers easier to see (2). Robustness to class imbalance therefore does not mean that ROC-AUC captures deployment-specific precision or error costs.
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See also
1.
Richardson E, Trevizani R, Greenbaum JA, Carter H, Nielsen M, Peters B. The receiver operating characteristic curve accurately assesses imbalanced datasets. Patterns. 2024;5(6):100994. Available from: https://doi.org/10.1016/j.patter.2024.100994
2.
Davis J, Goadrich M. The Relationship between Precision-Recall and ROC Curves. In: Proceedings of the 23rd International Conference on Machine Learning. ACM Press; 2006. p. 233–40. Available from: https://doi.org/10.1145/1143844.1143874