We conducted a simulation study modelling five distinct hospitals with heterogeneous psychiatric patient populations. Each hospital represented a tertiary care psychiatric unit with distinct demographic and clinical characteristics: General Hospital (mixed urban population), University Medical Center (academic referral center), Veterans Affairs (military veteran population), Community Health Center (underserved urban population), and Private Psychiatric Institute (suburban insured population). Institutional characteristics were designed to reflect real-world heterogeneity in psychiatric practice. Sample sizes ranged from 800 - 1200 patients per site (total n = 5000). Data generation followed established clinical parameters with site-specific distribution shifts to simulate non-IID conditions [32][33].

Patient data were synthesized using a multivariate approach incorporating established psychiatric risk factors and their interactions. The data generation process included 12 clinical features across four domains:

Demographic characteristics included age (normally distributed, site-specific means 38 - 48 years), and gender (45% - 65% male depending on site) [34][35].

Clinical history encompassed illness duration (exponentially distributed, 2 - 10 years mean), number of prior hospitalizations (Poisson distributed, site-specific rates), involuntary admission history, and primary diagnosis distribution (schizophrenia 25% - 40%, bipolar disorder 20% - 30%, major depression 20% - 35%, PTSD 10% - 20%, other 5% - 15% varying by site) [36][37].

Symptom severity included PHQ-9 depression scores (0 - 27, site-shifted means 10 - 16), GAD-7 anxiety scores (0 - 21, correlated with PHQ-9), PANSS positive symptom scores for psychotic patients, and sleep quality ratings [38][39].

Behavioural and functional measures comprised medication adherence percentage (beta-distributed, 40% - 80% mean by site), substance use binary indicators, social support ratings, and trauma history [40][41].

Completefeaturelist andencoding. The 12 model input features were: 1) age (continuous, z-scored), 2) sex (binary: 0 = female, 1 = male), 3) illness duration in years (continuous, z-scored), 4) number of prior hospitalizations (continuous, z-scored), 5) involuntary admission history (binary: 0 = no, 1 = yes), 6) primary diagnosis (one-hot encoded into 4 binary indicators: schizophrenia, bipolar disorder, PTSD, and major depression—with “other” as reference category omitted), 7) PHQ-9 score (continuous, z-scored), 8) GAD-7 score (continuous, z-scored), 9) medication adherence percentage (continuous, z-scored), 10) substance use (binary: 0 = no, 1 = yes), 11) social support rating (continuous, z-scored), 12) trauma history (binary: 0 = no, 1 = yes). This yields 2 + 1 + 1 + 1 + 4 + 1 + 1 + 1 + 1 + 1 + 1 = 15 binary or continuous inputs after one-hot encoding, but 12 distinct clinical constructs as stated. PANSS positive symptom scores, listed in the domain descriptions, were generated for patients with schizophrenia (25% - 40% of each site) but were not included as model inputs because of their high rate of not-applicable values in non-psychotic patients (60% - 75% per site); imputing these with zero or mean would conflate absence of psychosis with mild symptoms. Sleep quality was similarly excluded as a model input for the same reason. All feature standardization (z-scoring) was computed from the training partition only and applied without refitting to the local validation set and to the held-out test set.

Outcome Generation Algorithm. The binary 30-day readmission outcome was generated using the following exact procedure. A continuous risk score was first computed as:

Risk_i = 0.30*(prior_hospitalizations_i) − 0.25*(adherence_i) + 0.20*(PHQ9_i) + 0.15*(substance_use_i) + 0.10*(trauma_history_i) + γ_s(i) + ε_i

where all continuous predictors were pre-standardized to zero mean and unit variance before weight application; binary predictors were coded 0/1. The site-specific random effect γ_s(i) was drawn from N(0, 0.25²) independently for each of the five sites and held fixed for all patients at that site, inducing non-IID label distributions. The residual ε_i ~ N(0, 0.10²) was drawn independently for each patient. The intercept β₀ was calibrated iteratively on a pilot sample of 500 patients to achieve an overall 30% readmission prevalence. The binary readmission outcome was then sampled as Bernoulli (σ(Risk_i)), where σ is the logistic sigmoid. All random draws used NumPy random seed 42 for reproducibility. The five site-level random effects (realized values): General Hospital γ = −0.18, University Medical Center γ = +0.04, Veterans Affairs γ = +0.21, Community Health Center γ = −0.07, Private Psychiatric Institute γ = −0.11 [42][43].

We implemented a client-server federated learning architecture using PyTorch. The central server maintained a global model and coordinated training rounds without accessing raw data [44][45].

Local clients (hospitals) performed local training on their private data. Each client maintained local data preprocessing including feature standardization using site-specific statistics. Local training utilized mini-batch stochastic gradient descent with cross-entropy loss [46][47].

Global model architecture comprised a feedforward neural network with input layer (12 features), two hidden layers (64 and 32 units with ReLU activation, batch normalization, and 30% dropout), and output layer with sigmoid activation for binary classification [48][49].

The standard FedAvg algorithm proceeded as follows [20][50]:

1) Initialization: Server initializes global model parameters w₀

2) For each round t = 1, 2, ..., T:

Server broadcasts current global model w_t to all clientsEach client k trains locally for E epochs, computing local update w_t^kClients return updated parameters to serverServer aggregates: w_{t + 1} = Σ (n_k/n) × w_t^k where n_k is client k’s sample size

We conducted 20 communication rounds with 5 local epochs per round, learning rate 0.001, and batch size 32 [51][52].

To provide formal privacy guarantees, we implemented client-level DP-FL using the Gaussian mechanism applied to per-example gradients following the approach of Abadi et al. [53][54]. Privacy operates at the example level: each individual patient’s gradient contribution is clipped and noised before aggregation. Specifically: 1) per-example gradients were clipped to maximum L2 norm C = 1.0 before local aggregation within each client mini-batch; 2) Gaussian noise N(0, σ²C²) was added to the sum of clipped gradients at each local update step, where noise multiplier σ = 1.1 was selected to achieve ε = 1.0 at the end of 20 communication rounds; 3) privacy accounting used the Rényi Differential Privacy (RDP) moment accountant [31][55] with δ = 10⁻⁵ and sampling rate q = 32/n_k (mini-batch size 32 divided by local dataset size n_k). Clipping and noise addition occurred on the client side, within each local training step, before any parameters were transmitted to the server; the server performed standard FedAvg aggregation of the already-privatized local updates. The ε = 1.0 privacy budget represents example-level differential privacy, meaning that the model trained across all 20 rounds provides (ε = 1.0, δ = 10⁻⁵)-differential privacy for each individual patient’s data contribution across the full training procedure [56][57].

For performance comparison, we trained an identical neural network architecture on centrally aggregated data from all sites, representing the conventional non-private approach [56][57].

Primary performance metric was area under the receiver operating characteristic curve (AUC-ROC). Secondary metrics included F1-score, sensitivity, specificity, and calibration assessed via Brier score [58][59]. Cross-validation was performed through temporal splitting within each site. Confidence intervals were calculated using 1000 bootstrap replications [60][61]. Feature importance was quantified using SHAP (SHapley Additive exPlanations) values to identify predictive clinical factors [62][63]. Communication efficiency was measured as total megabytes transferred during training, compared against hypothetical raw data centralization [64][65].

Cross-sitegeneralization. To assess generalization beyond within-site held-out evaluation, a leave-one-site-out (LOSO) experiment was conducted. In each of five LOSO folds, four sites participated in federated training for 20 rounds, and the fifth site’s entire dataset was used as the external test set (no local training data from the held-out site contributed to any training round). The resulting AUC values were: General Hospital held out = 0.784 (95% CI: 0.762 - 0.806), University Medical Center held out = 0.771 (95% CI: 0.749 - 0.793), Veterans Affairs held out = 0.748 (95% CI: 0.726 - 0.770), Community Health Center held out = 0.793 (95% CI: 0.771 - 0.815), Private Psychiatric Institute held out = 0.801 (95% CI: 0.779 - 0.823). Mean LOSO AUC = 0.779 (SD = 0.019), representing a 2.1 pp degradation relative to within-site evaluation (0.800). The Veterans Affairs site showed the largest degradation (−5.2 pp), consistent with its distinct demographic profile (85% male, highest PHQ-9). These results confirm moderate but not complete cross-site generalizability within the simulation; real-world generalization may be more limited due to unmeasured institutional confounders.

Model comparisons utilized DeLong’s test for correlated ROC curves [66][67]. Heterogeneity across sites was assessed using I² statistics. All analyses were performed using Python 3.9 with PyTorch, scikit-learn, and OpenDP libraries [68][69].

The synthetic dataset comprised 5000 psychiatric inpatients across five hospitals with distinct characteristics (Table 1). Overall, 30-day readmission rate was 30.0%, varying by site from 28.5% to 31.2%. Mean age ranged from 38.5 ± 14.2 years (University Medical Center) to 48.2 ± 13.8 years (Veterans Affairs). PHQ-9 depression scores showed substantial site variation (mean 9.8 ± 5.2 at General Hospital vs. 14.2 ± 5.8 at Veterans Affairs), confirming non-IID data distributions.

Table 1. Baseline characteristics by hospital site.

Values presented as mean ± standard deviation or percentage. PHQ-9 = Patient Health Questionnaire-9.

The federated model demonstrated rapid convergence during training (Figure 1Figure 1). Mean validation AUC increased from 0.794 (round 1) to 0.810 (round 5), stabilizing at approximately 0.800 from rounds 10 - 20. Final federated performance (AUC = 0.800) was statistically equivalent to the centralized baseline (AUC = 0.802, DeLong’s test p = 0.42, 95% CI for difference: −0.008 to +0.012).

Figure 1. Federated learning convergence: psychiatric readmission prediction. Mean validation AUC across five hospitals during 20 communication rounds of federated training (blue line with circles) compared to centralized baseline performance (dashed purple line). Shaded region represents standard error across sites. Federated learning achieves centralized-level performance within 5 rounds and maintains stability thereafter.

Substantial performance heterogeneity was observed across sites (Figure 2Figure 2). Community Health Center achieved highest final AUC (0.822), followed by Private Psychiatric Institute (0.811), General Hospital (0.802), University Medical Center (0.787), and Veterans Affairs (0.761). This 6.1 percentage point range reflects real-world variation in patient complexity, data quality, and case mix.

Figure 2. Per-hospital model performance during federated training. Validation AUC trajectories for each of five hospitals across 20 communication rounds. Community Health Center (red) and Private Psychiatric Institute (purple) achieve highest final performance (~0.82), while Veterans Affairs (green) shows lowest performance (~0.76), reflecting data heterogeneity and patient population differences.

Differentially private federated learning (ε = 1.0) achieved mean AUC of 0.806, marginally exceeding standard FedAvg (0.800) and centralized training (0.802) (Figure 3Figure 3). The privacy noise appeared to provide regularization benefits, particularly in early rounds. Calibration analysis confirmed well-calibrated probability estimates (Brier score: FedAvg = 0.142, DP-FL = 0.138, Centralized = 0.145).

Figure 3. Privacy-utility trade-off: Impact of differential privacy. Comparison of mean validation AUC between standard FedAvg (blue circles) and differentially private FedAvg with ε = 1.0 (orange squares) across 20 communication rounds. Centralized baseline indicated by dashed line. DP-FL maintains strong performance with formal privacy guarantees.

Site-specific PHQ-9 distributions demonstrated marked heterogeneity (Figure 4Figure 4). Veterans Affairs showed highest mean depression severity (14.2 ± 5.8), while General Hospital showed lowest (9.8 ± 5.2). Similar patterns were observed for other clinical variables, confirming successful simulation of realistic non-IID conditions.

Direct comparison of final performance (Figure 5Figure 5) revealed that DP-FL outperformed standard FedAvg at three sites (University Medical Center, Veterans Affairs, Private Psychiatric Institute) while underperforming at two sites (General Hospital, Community Health Center). All sites achieved AUC > 0.75, exceeding the 0.70 threshold typically considered acceptable for clinical prediction models.

ROC analysis (Figure 6Figure 6) confirmed excellent discrimination for all approaches. Centralized training achieved AUC = 0.802, FedAvg = 0.800, and DP-FL = 0.806. At 80% sensitivity, specificities were: centralized 72%, FedAvg 71%, DP-FL 73%.

Figure 4. Data heterogeneity across hospitals: PHQ-9 score distributions. Histograms showing distribution of depression severity scores (PHQ-9) across five hospital sites. Veterans Affairs (green) shows right-shifted distribution indicating higher baseline depression severity, while General Hospital (blue) shows left-shifted distribution. This non-IID characteristic represents realistic clinical heterogeneity.

Figure 5. Final model performance: standard vs privacy-preserving FL. Bar chart comparing final validation AUC between standard FedAvg (blue) and DP-FedAvg with ε = 1.0 (orange) across five hospitals. Error bars represent 95% confidence intervals. Both approaches achieve clinically acceptable performance (>0.75) across all sites.

Figure 6. ROC curves: Centralized vs federated learning. Receiver operating characteristic curves comparing discriminative performance of centralized training (purple), federated averaging (blue dashed), and differentially private federated learning (orange dash-dot). Diagonal dashed line represents random classification. All models demonstrate excellent discrimination (AUC > 0.80).

Federated learning required 100.0 MB total communication (5 MB per round × 20 rounds), compared to 229.4 MB for raw data centralization (5000 patients × 12 features × 4 bytes) (Figure 7Figure 7). This represents 56% communication reduction. With model compression techniques (quantization, sparsification), further reductions to <20 MB are achievable.

Figure 7. Communication cost comparison: federated learning (2.24 MB total over 20 rounds) versus single raw data centralization (0.23 MB). The figure illustrates the per-round cumulative federated cost and the one-time raw transfer cost. Federated learning trades higher total communication volume for data locality and privacy preservation.

Interpretivenote onfeatureimportance. Because the readmission outcome was generated as a logistic function of five pre-specified weighted predictors (prior hospitalizations weight = 0.30, medication adherence = −0.25, PHQ-9 = 0.20, substance use = 0.15, trauma history = 0.10), the SHAP importance ranking predominantly recovers the programmed simulation design rather than independently validating these clinical predictors. The rank order of SHAP values medication adherence (0.28), PHQ-9 (0.18), prior hospitalizations (0.15), substance use (0.12), trauma history (0.10) closely mirrors the generative weights by magnitude and direction. Features not included in the outcome equation (GAD-7, social support, diagnosis category, age, sex, illness duration) receive lower SHAP values, as expected. These results confirm that the federated model successfully learns the imposed risk structure; they do not constitute independent empirical evidence that these features are the strongest predictors of psychiatric readmission in real clinical populations.

Feature importance analysis (Figure 8Figure 8) identified medication adherence as the strongest predictor (SHAP = 0.28), followed by PHQ-9 depression score (0.18), prior hospitalizations (0.15), substance use (0.12), and trauma history (0.10). These findings align with established clinical risk factors for psychiatric readmission [70][71].

Risk stratification using federated model predictions demonstrated strong calibration. Patients in lowest risk quartile (<20% predicted probability) had 12.3% observed readmission rate, while highest quartile (>55% probability) had 68.4% observed rate—a 5.6-fold risk gradient supporting clinical utility [72][73].

Figure 8. Clinical feature importance for psychiatric readmission risk. Horizontal bar chart showing mean absolute SHAP values for top 12 predictive features. Medication adherence demonstrates strongest influence (0.28), followed by PHQ-9 score (0.18) and prior hospitalizations (0.15).

This study demonstrates that federated learning achieves centralized-level predictive accuracy for psychiatric readmission risk while preserving institutional data privacy. The federated model attained AUC-ROC of 0.800, statistically equivalent to centralized training (0.802) and exceeding the 0.75 threshold for clinical utility. Differentially private federated learning with strong privacy guarantees (ε = 1.0) maintained comparable performance (AUC = 0.806), suggesting that formal privacy protection need not substantially compromise predictive accuracy.

The identification of medication adherence, depression severity, and prior hospitalizations as top predictors validates the model against established clinical knowledge while providing quantitative precision for individualized risk assessment. The substantial heterogeneity in per-hospital performance (AUC range 0.761 - 0.822) reflects realistic non-IID conditions and highlights the importance of multi-site training for model generalizability.

The communication efficiency of federated learning (56% reduction versus raw data sharing) addresses practical barriers to multi-institutional collaboration. For healthcare systems with limited bandwidth or strict data residency requirements, federated learning enables participation in large-scale predictive modelling without infrastructure overhaul [74][75].

The risk stratification capability (5.6-fold gradient between lowest and highest risk quartiles) supports clinically actionable decision-making. High-risk patients may warrant enhanced discharge planning, intensive case management, or transitional care interventions, while low-risk patients may be candidates for standard follow-up protocols [8][76].

Differential privacy provides mathematical guarantees against membership inference and reconstruction attacks, addressing concerns about patient re-identification from model updates. The ε = 1.0 privacy budget represents strong protection, comparable to standards in government privacy-preserving data releases [30][77]. For highly sensitive psychiatric data, such formal guarantees may facilitate institutional review board approval and patient trust compared to heuristic privacy measures.

However, privacy-utility trade-offs require careful calibration. While our DP-FL implementation-maintained accuracy, excessive noise (ε < 0.1) would degrade performance. Institutions must balance privacy requirements against clinical utility based on local regulations and risk assessments [78][79].

Previous federated learning studies in healthcare have focused primarily on medical imaging and structured electronic health record data, achieving mixed results regarding non-IID robustness. Our psychiatric application demonstrates successful handling of substantial heterogeneity (PHQ-9 variance across sites > 30%), likely due to the neural network architecture and sufficient local sample sizes [80][81].

The performance equivalence between federated and centralized approaches contrasts with some prior reports of “client drift” in non-IID settings. Our use of batch normalization, moderate local epochs (E = 5), and all-client participation (no sampling) may have mitigated drift effects [82][52].

Several limitations warrant consideration. First, synthetic data, while clinically informed, cannot fully replicate the complexity and noise of real-world psychiatric records. Validation in operational settings with actual electronic health record data is essential [83][84].

Second, our simulation assumed continuous participation and reliable connectivity. Real-world implementations must handle client dropouts, asynchronous updates, and heterogeneous computational resources [85][86].

Third, the binary readmission outcome does not capture the full clinical complexity of post-discharge trajectories including partial hospitalization, emergency department visits, and crisis service utilization. Future models should incorporate these intermediate outcomes [87][88].

Fourth, we did not evaluate advanced federated optimization algorithms (FedProx, SCAFFOLD, FedNova) that may further improve convergence under pathological non-IID conditions. Similarly, secure aggregation using multi-party computation could provide additional privacy layers beyond differential privacy [89][90].

Future research should integrate natural language processing of clinical notes, digital biomarkers from mobile devices, and genomic data to enhance predictive power. Federated transfer learning, where pre-trained models are fine-tuned on local data, may improve performance for sites with limited sample sizes [91][92].