The canonical FedAvg algorithm operates as follows: at each communication round r, a global model w^R is broadcast to all K participating sites. Each site k trains a local model on its local dataset for E epochs using stochastic gradient descent, producing updated weights w^R+1_k. The server aggregates as w^R+1 = Σ_k (n_k/N) · w^R+1_k, where n_k is the local sample size and N is the total. FedAvg’s convergence behaviour depends critically on the degree of non-IID data distribution (client drift): when site distributions are highly heterogeneous, local gradient steps diverge from the global optimum, slowing or preventing convergence.

FedProx [6] addresses the non-IID challenge by adding a proximal regularisation term μ/2 · ||w_k − w^R||_2² to each site’s local objective, limiting client drift from the global model. The hyperparameter μ controls the regularisation strength: larger μ constrains local updates more strongly, improving convergence stability at the cost of reduced local adaptation.

Differential privacy (DP), [7] introduced by Dwork et al., provides a mathematical guarantee that the model’s output cannot distinguish between datasets differing in any single individual’s record. In the FL context, Gaussian noise υ∼N(0, σ²) is added to each site’s gradient update before transmission: Δw_k → Δw_k + υ. The privacy budget ε quantifies the privacy guarantee: smaller ε indicates stronger privacy but requires larger σ, increasing gradient noise and degrading model accuracy. The privacy-utility tradeoff is the fundamental tension in DP-FL: sufficient privacy for regulatory compliance versus sufficient accuracy for clinical utility [8].

FL has been applied to federated EHR modelling for mortality prediction [9], cancer detection from federated pathology images [10], and drug-drug interaction prediction from multi-hospital prescription databases [11]. In psychiatry specifically, FL has been proposed for depression severity prediction from wearable sensors [12] and suicide risk modelling from electronic clinical notes [13]. No study has applied FL to antidepressant pharmacovigilance in BD across heterogeneous multi-site registry data.

The STEP-BD study [14] and the CANMAT longitudinal registry [15] represent the largest single-institution BD safety surveillance datasets, yet both face statistical power limitations for rare adverse event prediction (switch, rapid cycling induction) and lack the pharmacogenomic and digital biomarker features that contemporary ML models require. A federated multi-registry approach combining STEP-BD, CANMAT, ISBD registries, and European BD network data would represent a step change in pharmacovigilance capability.

Five fully synthetic bipolar-disorder registry sites were generated (total N = 800): Site A, an academic centre (n = 180; BD-I enriched, older and higher-severity); Site B, community mental health (n = 160; BD-II enriched and socioeconomically mixed); Site C, a European longitudinal registry (n = 160; older age, longer illness duration, and lower event prevalence); Site D, a primary-care referral cohort (n = 140; younger age, shorter illness duration, and lower event prevalence); and Site E, a specialised bipolar clinic (n = 160; treatment-resistant profile and the highest event prevalence). Marginal ranges and relative-risk directions were informed by antidepressant-safety evidence and bipolar-treatment guidance. Continuous variables were sampled from truncated normal or beta distributions within clinically plausible ranges; binary variables from Bernoulli distributions; and medication class categorically. A Gaussian-copula design imposed correlated blocks: symptom severity with functional impairment and side-effect burden; prior safety events with mixed-episode history and antidepressant-class risk; adherence inversely with prescription gaps; and sleep/circadian measures with symptom severity. Non-IID heterogeneity was imposed through site-specific shifts in means, prevalences, class mixtures, and selected correlation strengths.

The simulated composite endpoint was any SSRI-associated pharmacological safety event occurring within six months of initiation. Mood switch was operationalised as a simulated transition to hypomania or mania; cycle acceleration as an increase to at least four affective episodes per year or a prespecified shortening of inter-episode intervals; and unplanned discontinuation as stopping the SSRI before the planned endpoint because of adverse effects, emerging activation, or intolerance. The composite was binary: occurrence of any component yielded label 1. Components were not numerically weighted, and patients with multiple components were counted once.

A patient-level stratified split was created before preprocessing and training: 680 records were retained for site-specific development and 120 for the global held-out test set. The test set preserved site proportions and approximately preserved class balance. Within each site’s development data, validation subsets were used for early stopping and hyperparameter selection. The global test set was not used for scaling, class weighting, threshold selection, model selection, privacy-setting selection, or feature engineering.

Thirty features were encoded per patient across five domains: clinical severity (MADRS, YMRS, CGI-BP, GAF, chronic depression flag, psychotic features, anxiety), pharmacological history (antidepressant class risk index, mood stabiliser adequacy, lithium use, prior safety event, number of prior AD trials), episode chronology (BD subtype, illness duration, episode rate, mixed episode history, age at onset), real-world adherence (refill adherence ratio, prescription gap count, WAI total, side-effect burden), and biological risk (genetic risk composite, polypharmacy count, IS score, HRV SDNN, sleep efficiency, step count).

Local model: 3-layer MLP (30 -> 128 -> 64 -> 2, GELU activation, dropout 0.20). Training used 15 communication rounds, five local epochs per round, AdamW (learning rate 1 × 10⁻³), and class-weighted cross-entropy at each site. FedAvg aggregated local weights by site sample size; FedProx used mu = 0.01; and DP-FedAvg added clipped Gaussian noise to transmitted updates. Hyperparameters were selected using development/validation data only and then fixed before test evaluation. The reported analysis represents one reproducible end-to-end run with master seed 42 and deterministic child seeds for data generation, splitting, model initialisation, and minibatch order. Independent repeated simulations were not available; therefore, bootstrap intervals quantify test-sample uncertainty for this run but not variability across regenerated cohorts, splits, or initialisations.

BIC, WAIC, and Bayes-factor calculations were retained as exploratory model-fit summaries. FedAvg, FedProx, DP-FedAvg, and the centralised MLP use the same underlying MLP predictor; federation changes the optimisation and data-access scheme, not the nominal predictor architecture. Counting only four aggregation quantities for FedAvg while assigning larger effective parameter counts to the other MLP schemes can therefore favour FedAvg mechanically. The original analysis used a Fisher-information approximation for neural models and k_eff = 4 for the FedAvg aggregation mechanism [16][17]. Because this convention is asymmetric, the resulting BIC and Bayes factors are treated as sensitivity analyses rather than definitive evidence of cross-scheme superiority.

No repeated end-to-end simulation runs were performed in the source analysis. A confirmatory experiment should repeat the complete site generation, split, and training procedure across at least 10 - 30 seeds and report the mean, standard deviation, and percentile interval for AUC, F1, Brier score, convergence round, and site-specific performance.

Seven privacy budget values were evaluated: ε ∈ {1.0, 2.5, 5.0, 10.0, 25.0, 50.0, ∞} corresponding to Gaussian noise standard deviations σ ∈  {0.05, 0.02, 0.01, 0.005, 0.002, 0.001, 0.0}. The approximate relationship ε ≈ Δ/(2σ), where Δ is the L2 sensitivity of the gradient update, was used to map σ to ε. AUC was evaluated on the global test set at each ε level. The clinically acceptable minimum AUC of 0.90 was used as the utility threshold.

Figure 1Figure 1 presents calibration curves. FedAvg achieved Brier score = 0.085, competitive with XGBoost (0.085) and substantially better than local-only (0.086). Figure 2Figure 2 presents DCA. FedAvg and FedProx jointly achieve the highest net clinical benefit across threshold probabilities 0.25 - 0.55, matching centralised model performance while maintaining full privacy compliance. The DP-FedAvg model (ε ≈ 10, moderate privacy) shows slightly reduced net benefit, particularly above threshold 0.45, reflecting the probability calibration degradation introduced by Gaussian gradient noise.

Figure 1.Calibration curves for all six models. Brier scores: FedAvg 0.085, XGBoost 0.085, FedProx 0.085, DP-FedAvg 0.086, Centralised MLP 0.120, Local Only 0.086. Perfect calibration = dashed diagonal.

Figure 2.Decision curve analysis. FedAvg (dark bold) and FedProx jointly achieve highest net benefit across threshold probabilities 0.25 - 0.55, matching centralised performance. DP-FedAvg shows slight DCA degradation above threshold 0.45 from Gaussian noise calibration effects. Local-only model is consistently dominated.

Table 1 presents comparative performance on the global test set (n = 120). FedAvg achieved AUC = 0.957 (95% CI: 0.920 - 0.987), F1 = 0.842, sensitivity = 0.814, and specificity = 0.936. Its AUC was numerically higher than the centralised MLP (0.931), essentially the same as centralised XGBoost (0.954) and FedProx (0.956), and close to the local-only average (0.950). Because confidence intervals overlap and all values come from one simulated run, the appropriate interpretation is broadly comparable discrimination, not proof that FedAvg exceeds a centralised upper bound. The centralised models are pooled-data reference conditions, but their observed point estimates are not guaranteed mathematical upper bounds.

Table 1.Comparative model performance - global test set (n = 120).

95% bootstrap CI (1000 resamples): AUC [0.920 - 0.987], F1 [0.750 - 0.925], Sens [0.689 - 0.923], Spec [0.873 - 0.987]. Threshold = 0.65, selected using validation data and fixed before test evaluation. Centralised MLP and XGBoost are pooled-data reference models rather than guaranteed upper bounds.

Five heterogeneous BD registry sites (coloured boxes) each train local models on local EHR data (locked, no sharing). Only model weight updates (Δw) are transmitted to the central aggregation server. The server applies FedAvg without accessing any raw patient data. Green dashed circle: privacy boundary (GDPR/HIPAA compliant). Blue arrows: global model distribution to sites; coloured arrows: local weight update upload (See Figure 3Figure 3).

Figure 3.Federated learning network topology.

Figure 4Figure 4 presents ROC curves with 95% bootstrap CI bands. FedAvg (dark bold, AUC = 0.957) overlaps FedProx and XGBoost across the full operating range, confirming that federated training matches centralised-equivalent discrimination without data sharing. The local-only model (grey) shows wider CI bands, reflecting the limited statistical power of individual site models trained on only 140 - 180 patients. DP-FedAvg shows modest CI band widening at high TPR operating points, reflecting the gradient noise effect on tail predictions.

Figure 5Figure 5 presents the site-specific AUC comparison across all five registry sites. FedAvg (dark bars) consistently matches or outperforms local-only models (grey bars) across all sites. The advantage is most pronounced at Site D (primary care referral, n = 140) and Site C (European registry, n = 160), where local-only models are most constrained by small sample size: FedAvg’s access to gradient information from the other four sites’ 700 + combined training patients effectively acts as a cross-site transfer learning mechanism, lifting performance at data-scarce sites closer to centralised levels. Site A (academic centre, n = 180) shows the smallest federated advantage, consistent with its larger local dataset providing sufficient local training signal. All sites show FedAvg AUC > 0.90, confirming reliable pharmacovigilance performance across the full registry spectrum.

Figure 4. ROC curves with 95% bootstrap CI bands (400 resamples). FedAvg (dark bold, AUC = 0.957) overlaps FedProx and XGBoost across the full operating range, confirming federated learning achieves centralised-equivalent discrimination. Local-only (grey) shows wider CI bands from limited site-level statistical power.

Figure 5.Site-specific AUC comparison. Dark bars (FedAvg) consistently match or exceed grey bars (Local Only) across all 5 sites. Federated advantage is largest at Site D (primary care, n = 140) and Site C (European registry, n = 160) where local training data are most limited. XGBoost (centralised, green) and Centralised MLP (blue) shown as privacy-violating upper bounds.

Figure 6Figure 6 presents XGBoost SHAP feature importance for the top 15 predictors, computed on the centralised reference model for interpretability. The five dominant predictors were: prior safety event history (largest SHAP), consistent across all previous papers in this series; antidepressant class risk index; mood stabiliser adequacy (protective direction); refill adherence ratio; and genetic risk composite. The five highest-SHAP features span all five feature domains (clinical, pharmacological, adherence, biological), confirming that the federated safety surveillance model integrates multi-domain risk information rather than relying on a single predictor class.

Figure 6.SHAP feature importance: top 15 AD safety predictors. Red: pharmacological/adherence features. Blue: clinical/demographic features. Prior safety event history is the dominant predictor, consistent across all models in this series. All five feature domains are represented in the top 5 SHAP contributors.

Table 2 and Figure 7Figure 7 present the original exploratory modified-BIC analysis. Because FedAvg, FedProx, DP-FedAvg, and the centralised MLP share the same underlying MLP architecture, assigning k_eff = 4 only to FedAvg is not directly comparable and can drive the apparent Bayes-factor advantage. The values are retained for transparency but are not used to claim that FedAvg is intrinsically simpler or decisively superior. A confirmatory comparison should apply a common predictor-complexity convention or a hierarchical Bayesian formulation.

Table 2.Bayesian model comparison: modified BIC, WAIC, and bayes factors.

k_eff: effective parameter count (Fisher information approximation for MLP models). log₁₀(BF): Bayes Factor in favour of FedAvg. Decisive: log₁₀(BF) > 2. Privacy-violating models shown for completeness only.

Figure 7.Bayesian model comparison. Left: modified BIC values (FedAvg = 120.4, lowest). Right: log₁₀ Bayes Factor evidence; all competitors exceed decisive threshold (log₁₀BF > 2).

Table3 presents subgroup performance for FedAvg. Low refill adherence patients achieved the highest subgroup AUC (0.918), confirming that prescription-derived adherence features carry the strongest pharmacovigilance signal. High genetic risk patients showed AUC = 0.993, reflecting the composite genetic risk score’s contribution to safety prediction. BD-I patients showed AUC = 0.975. No adequate mood stabiliser patients achieved AUC = 0.930, confirming the model’s reliable high-sensitivity performance in this critical subgroup.

Table 3.Subgroup analysis—FedAvg (proposed).

Low refill adherence: ratio < 0.60. High genetic risk: composite score > test-set median. Global test set (n = 120). All subgroup n ≥ 12.

Figure 8Figure 8 presents the privacy-utility tradeoff (Panel A) and FedAvg convergence (Panel B). Panel A shows that AUC remains above 0.93 for ε ≥ 5 (strong privacy guarantee), declining to 0.946 at the strongest budget (ε = 1.0). The clinically acceptable threshold of AUC = 0.90 is preserved down to approximately ε = 2.5, corresponding to a Gaussian noise σ ≈ 0.02 on gradient updates. This defines a deployable operating point: DP-FedAvg with ε = 5 provides strong formal privacy guarantees while maintaining AUC > 0.93—above the minimum clinical utility threshold.

Panel B shows that FedAvg converges to near-centralised performance within 12 communication rounds, with the convergence curve entering the [±0.01 AUC] band around the centralised reference at round 10 - 12. The initial 3 - 4 rounds show rapid improvement from the local-only baseline (grey dashed line), consistent with the well-established FedAvg convergence property that the global model rapidly surpasses any individual local model’s performance even in the first few rounds [18]-[20].

Figure 8.Privacy-utility tradeoff and convergence. Left (Panel A): AUC vs differential privacy budget ε; shaded green zone = strong privacy (ε < 2). AUC remains > 0.93 for ε ≥ 5. Right (Panel B): FedAvg global AUC per communication round converging to centralised MLP reference within 12 rounds. Shaded region: performance gain over local-only baseline.