Per-Class Conformal Risk Control for Multi-Label ECG Classification: Achieving Clinically-Justified False Negative Rate Guarantees

OBJECTIVE: Automated electrocardiogram (ECG) classifiers require uncertainty procedures that address class-specific clinical risk in intrinsically multi-label data. Approach: We propose per-class risk-controlling prediction sets for multi-label ECG classification. For each diagnostic class, binary false-negative-rate (FNR) loss is calibrated with a one-sided exact-binomial upper confidence bound. The nine disease-specific targets are controlled simultaneously at 95% family-wise confidence using Bonferroni allocation. The final operating threshold is the more inclusive of the exact-binomial threshold and a conservative reference threshold derived from a concentration bound; this safeguard uses calibration data only and cannot weaken the exact guarantee. Main results: We evaluated the method on PTB-XL (21,388 retained recordings) and Chapman-Shaoxing (10,199 retained recordings), using a patient-disjoint PTB-XL split and fitting-partition-only normalisation. The proposed method met all 9/9 prespecified disease-specific FNR targets on held-out test sets and produced non-vacuous simultaneous exact-binomial guarantees for all nine targets; uniform standard conformal prediction met 5/9. Test FNR was 0.0% for myocardial infarction (exact 95% upper bound 0.35%, at 80.3% FPR), 1.0% for ST/T changes, and 0.3% for atrial fibrillation; the high-sensitivity operating point is purchased with substantially reduced specificity. Under PTB-XL-to-Chapman shift, macro class coverage fell from 94.3% to 45.5%, demonstrating that the guarantees do not transport without local recalibration. Significance: Exact-binomial per-class risk control provides a transparent high-sensitivity operating point for ECG triage while making its specificity, prediction-set-size, calibration-support, and exchangeability limitations explicit. .