Modality-agnostic late fusion of electrocardiogram, phonocardiogram and photoplethysmogram signals for cardiovascular disease detection

Abstract Cardiac monitors rarely record every signal, and adding one is seldom evaluated. We asked when decision-level (late) fusion of the electrocardiogram (ECG), phonocardiogram (PCG) and photoplethysmogram (PPG) improves cardiovascular disease detection, and why, using one model for any signal combination. One expert per signal was trained in nested, subject-grouped cross-validation, Platt-calibrated and combined by seven rules, each fitted once and applied to any available signals. Three studies: abnormal heart sounds (PhysioNet/CinC 2016, ECG+PCG, 329 recordings), atrial fibrillation (AF; MIMIC-III-Ext-PPG, ECG+PPG, 40,792 segments, 5,642 patients) and a synthetic tri-modal (ECG+PCG+PPG) benchmark. PPG failed quality checks 3.7 times more often in AF, so complete-case fusion could not score 43.9\% of AF segments; the modality-agnostic model scored every segment, raising the area under the receiver operating characteristic curve (AUC) over ECG alone from 0.923 to 0.938 (+0.015, 95\% confidence interval 0.012--0.018), but only with calibrated experts (uncalibrated: 0.847). With both signals, PPG raised AUC from 0.910 to 0.931 (+0.021, 0.017--0.026). PCG added nothing (\textit{p}\,=\,1.00), consistent with published gains (0.004--0.023). Synthetic data favoured all three signals (AUC 0.984; best pair 0.976). Soft voting nearly matched the best rule; hard voting lost because two votes give three scores. Correlated expert errors, not the combiner, bounded the gain: the best rule nearly matched an oracle combination. Expected Gradients explained the ECG and PCG experts faithfully. Calibrated, modality-agnostic late fusion scores every record from its usable signals; its gain is bounded by expert redundancy, measurable before adding sensors.