Collapsibility of Performance Metrics in Clinical Predictive AI

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.

Which Metric Reflects the Spelling Rate Accuracy in Event-Related Potential-Based Brain-Computer Interfaces?

For predictive models, the often-reported performance metrics are the loss and accuracy. In synchronous Brain- Computer Interface (BCI) systems, these metrics are informative for most BCI paradigms; however, for Event-Related Potential (ERP) applications the spelling rate, which measures the number of characters correctly selected is more important as it influences the estimation of information transfer rate (ITR) and any related metric measuring spelling performance. Moreover, ERP-based BCIs hold imbalanced data class distributions, which require reporting metrics that can handle the imbalance, such as the area under the receiver operating characteristic curve (ROC AUC). In this work, we study the correlation of the spelling rate with 13 metrics to identify which among them best reflect user spelling performance and how they are affected by trial repetition. The Results of two datasets (a private LARESI ERP dataset and the public OpenBMI ERP dataset) favor the Brier score, Matthews Correlation Coefficient (MCC), and the metrics that account for class imbalance in binary classification: ROC AUC, area under the Precision-Recall curve (PR AUC), Average Precision (AP), and partial AUC (pAUC). These findings encourage researchers and practitioners to report those metrics in ERP-based BCI experiments.