Anomaly-Selective Conformal Calibration for ECG Monitoring: Threshold Divergence and the Limits of Finite-Sample False Alarm Control

Excessive false alarms in ECG monitoring are a recognised patient-safety concern, and the decision threshold, not the model, fixes the false alarm rate (FAR). Split conformal prediction offers a finite-sample FAR bound, not a heuristic. The bound is conditional, and we identify three ways its conditions are not met in deployment. First, adaptive calibration assumes an uncontaminated error signal: genuine arrhythmias are read as evidence that the threshold should rise, and it diverges until recall collapses to 64.48% while FAR appears to improve. An anomaly-selective update corrects this on ECG5000 in all ten partitions but holds in only four of ten under an LSTM autoencoder on PTB-DB, where the exclusion band rises with the threshold it protects. Second, the bound counts exchangeable units, not samples, and beats from one subject are not independent: 7 and 10 calibration subjects fall below the minimum the target requires, and thresholds applied across those boundaries gave mean FARs of 5.90% and 9.28% against a nominal 5%, with run-to-run variation fifteen times what finite sampling predicts; at 1,695 subjects both return to 4.92% and 1.21 times. Third, the unit carrying the guarantee must be the unit raising alarms: infarction is a patient-level event, and a beat-calibrated threshold applied to patients yields 10.70% FAR, which patient-level calibration restores to 4.76%. Percentile, extreme-value and conformal thresholds are separated not by realised FAR but by whether a guarantee accompanies the value. That is what calibration decides: where the operating point sits and whether it is guaranteed.