The Diagnostic Equity Index (DEI) under Adversarial and Privacy Stress in Federated Healthcare Learning: An Admissibility Criterion for the European Health Data Space

Federated learning (FL) enables privacy-preserving model training across clinical institutions, but model quality is almost universally reported through mean accuracy, which can conceal severe per-class diagnostic failures on clinically critical minority classes. Diagnostic equity—the guarantee of non-degraded, homogeneous performance across all diagnostic categories—is an explicit requirement of the European Health Data Space (EHDS) and of Article 14 of the AI Act, yet its behaviour under the two dominant threats to federated healthcare—Byzantine attacks and differential privacy (DP)—has not been systematically characterised. Using the Diagnostic Equity Index (DEI), a peer-reviewed per-class system metric, we conduct a systematic study over two clinical tabular datasets (Breast Cancer, Cardiovascular), two adversary fractions (1/5, 2/5), a full suite of robust aggregators, and a fine differential-privacy grid (ε ∈ {∞, 10, 5, 2, 1, 0.5}), each condition repeated over n=10 seeds. We report five findings. (i) Equity–accuracy dissociation: under attack the DEI degrades significantly more, and with far larger variance, than accuracy (Wilcoxon, Holm-corrected p=0.023); mean accuracy masks the complete loss of a diagnostic class. (ii) Personalisation resilience: personalised algorithms (HPFL, Ditto) preserve diagnostic equity markedly better than FedAvg. (iii) Restoration is defence- and adversary-dependent: at f =1 all robust aggregators restore equity fully; at f =2 (n=5) only the coordinate-wise Median restores it (p=0.002), while trimmed-mean is provably equivalent to no defence (breakdown point 1). (iv) A privacy–equity tradeoff: without defence, DP collapses diagnostic equity monotonically (DEI 0.91→0.02 as ε→0.5 for FedAvg), a cost invisible to and steeper than the accuracy loss; robust aggregation neutralises it. (v) An axiomatic foundation: the DEI as published violates Pareto monotonicity in 46% of conditions, and we propose the Atkinson–DEI, a welfare-economic power-mean generalisation that repairs this (0% violations) while preserving every empirical finding (ρ=0.962). We argue that diagnostic equity must be monitored and defended as a first-class admissibility criterion for the secondary use of health data.