Collapsibility of Performance Metrics in Clinical Predictive AI
2026-08-31 • Machine Learning
Machine LearningArtificial Intelligence
AI summaryⓘ
The authors studied how AI performance metrics behave when looking at different groups in a population. They found that some metrics, like AUC, don’t simply average out from subgroups and can give misleading results when comparing groups to the whole population. This means using these metrics without caution could wrongly suggest unfairness or hide problems. The authors suggest being clear about which metrics can be safely broken down by subgroup to make fairness checks more reliable.
Artificial IntelligencePerformance MetricsAUC (Area Under Curve)Fairness EvaluationCollapsibilitySimpson's ParadoxCalibrationPredictive ModelsSubgroup Analysis
Authors
João Matos, Ben Van Calster, Richard D. Riley, Paula Dhiman, Gary S. Collins
Abstract
Background: Population level assessments of predictive artificial intelligence (AI) can conceal performance disparities across subgroups. Fairness evaluations commonly rely on performance analyses across subgroups. However, some performance metrics are non-collapsible, meaning that the overall population performance value does not equal the weighted average of subgroup specific values. Objective: To examine the collapsibility properties of commonly reported performance metrics in predictive AI, with a focus on the area under the receiver operating characteristic curve (AUC, also known as c-statistic). Methods: We investigate the collapsibility of 15 performance metrics, either by expressing each metric as a linear combination of its stratum specific values or, where non-collapsible, by providing a counterexample inspired by Simpson's paradox as a formal disproof. Results: Five performance metrics (AUC, calibration intercept, calibration slope, expected calibration error, and Nagelkerke R^2) are shown to be non-collapsible, and ten (O:E ratio, logloss, Brier score, accuracy, F1-score, true positive rate, true negative rate, positive predictive value, negative predictive value, and net benefit) are shown to be collapsible. The AUC is shown to be non-collapsible because it decomposes into within- and cross-group AUC terms when subpopulations coexist, such that its overall value may fall outside the range of subgroup specific AUCs. Conclusions: Non-collapsibility of performance metrics has important consequences for reporting, model appraisal, and fairness evaluation. It can generate spurious differences between subgroup and overall performance, which may mislead fairness evaluations. Explicitly acknowledging and reporting the collapsibility properties of performance metrics improves both the interpretability and transparency of fairness assessments.