Simulation-Calibrated Estimation of AUC and Brier Score Evaluation Error in Small Tabular Binary Classification

Small tabular datasets can produce uncertain performance estimates because limited sample information affects both model fitting and evaluation. This study developed a procedure calibrated through simulation to estimate the mean absolute discrepancy between performance on out-of-bag observations and performance on an independent reference sample across models fitted to bootstrap samples. The procedure uses quantities that can be observed during bootstrap evaluation. The primary experiment included 60 simulation scenarios, 3000 independent small datasets, four classification algorithms, and 100 bootstrap repetitions per dataset. Large independent reference samples were used during simulation to define the calibration targets. Gradient Boosting calibrators were developed using 40 scenarios and evaluated on 20 reserved scenarios. In reserved evaluation, AUC error estimation achieved an MAE of 0.0164, an R2 of 0.7217, and a Spearman correlation of 0.8855. For Brier Score error, the corresponding values were 0.0090, 0.7848, and 0.9143. The complete calibration model also showed better error estimation than reduced configurations based on bootstrap variability alone. Under the three alternative data-generating mechanisms examined, the calibration models maintained similar performance, while Monte Carlo assessment showed small uncertainty in the main stress-test estimates. A methodological case study with 50 participants illustrated application of the procedure when independent reference performance was unavailable. The procedure complements conventional AUC and Brier Score reporting by estimating the mean absolute discrepancy between out-of-bag and independent reference performance from information available in a small observed dataset.