Interpretability Guarantees for Federated Clinical Prediction Models Under Heterogeneous Label Noise: A Computer Privacy-Robustness Trade-off Estimation

Federated learning allows clinical prediction models to be trained across institutions without centralising patient records, but the interpretability guarantees that such models can offer are poorly characterised when label noise varies across sites and when privacy protections constrain what can be shared. the present analysis formalises the problem as a constrained estimation of the privacy-robustness-interpretability frontier and characterises the operating characteristics of a before-after-control-impact design for evaluating it. No observational data are used or claimed: the analysis is a replication-based evaluation of the estimator under a declared variance structure with between-cluster SD = 6.0, residual SD = 4.5 and intraclass correlation = 0.640. Power was estimated across 2000 design cells for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The design requires 54 clusters to detect a 5 percentage point effect at 80% power. The results establish that interpretability guarantees degrade predictably as label-noise heterogeneity increases, and that the privacy budget required to preserve a fixed guarantee grows superlinearly with the heterogeneity parameter.