To enable controlled evaluation of federated learning under realistic yet privacy-preserving conditions, we construct a synthetic multi-hospital cohort comprising five hospitals, each contributing 1000 subjects (N = 5000). The synthetic design allows explicit control over population heterogeneity, outcome prevalence, and feature-label relationships, while avoiding the ethical and regulatory constraints associated with real clinical data [60]-[64].

Each subject is characterized by 10 predictive features representing established suicide risk and protective factors, grouped as follows:

(i) Demographics: age, gender.

(ii) Clinical severity: depression_score, anxiety_score;

(iii) Social determinants: social_support, life_stressors;

(iv) Clinical history: past_attempt, family_history; and

(v) Protective factors: coping_skills, treatment_adherence.

To explicitly model inter-hospital heterogeneity, feature distributions are systematically shifted as a function of hospital identity and a fixed heterogeneity parameter (set to 0.3). Hospitals with higher indices exhibit increased mean depression and anxiety scores alongside reduced social support and treatment adherence, thereby inducing site-specific risk profiles. These controlled distributional shifts result in non-independent and non-identically distributed (non-IID) data across hospitals and are illustrated in Figures 1(a)-(c).

The binary outcome variable, high-risk, is generated using a logistic risk formulation that integrates the above features with additive Gaussian noise to emulate unobserved confounding and measurement variability. Risk-increasing factors (e.g., symptom severity, prior suicide attempts, psychosocial stressors) contribute positively to the log-odds, while protective factors exert negative effects.

Observedprevalence: In the reported experimental configuration, the synthetic cohort exhibits a high overall prevalence of high-risk cases (91.16%), with hospital-specific prevalence ranging from 0.85 to 0.97. While intentionally extreme, this setting enables stress-testing of model behaviour under severe class imbalance and highlights the limitations of standard evaluation metrics such as accuracy. As discussed in later sections, this prevalence substantially influences precision-recall characteristics, confusion matrices, and threshold-dependent performance interpretation.

The high prevalence configuration (≈91%) does not reflect real-world suicide incidence rates. Instead, it was intentionally selected to stress-test federated convergence behaviour under extreme label skew and to examine metric sensitivity in majority-positive regimes. Future work will explore clinically realistic prevalence levels (e.g., 5% - 20%) to assess model robustness under minority-event conditions.

The binary suicide-risk outcome is generated using an explicit probabilistic risk model designed to reflect established clinical associations between individual-level factors and suicide risk. For each synthetic subject, a latent risk score is first computed as a linear combination of risk-increasing and protective variables, expressed in log-odds space. Specifically, clinical severity indicators including higher depression and anxiety scores contribute positively to the log-odds of high risk. Adverse social factors, such as reduced social support and an increased number of life stressors, further elevate risk. Historical vulnerability markers, namely a prior suicide attempt and a positive family history of suicidal behaviour, act as strong multiplicative risk contributors, consistent with their well-documented predictive value in clinical settings. In contrast, protective factors, including stronger coping skills and better treatment adherence, exert negative effects on the log-odds, partially mitigating overall risk. To account for unobserved confounding, measurement variability, and stochastic influences present in real-world clinical data, additive Gaussian noise is incorporated into the risk formulation [65]-[73]. The resulting latent score is transformed into a calibrated probability via the logistic (sigmoid) function. The final binary label, high-risk, is assigned when the estimated probability exceeds a threshold of 0.5, yielding a clear and reproducible decision rule for outcome generation.

Importantly, the underlying logistic risk function and coefficient structure were identical across all hospitals. Inter-hospital variability was introduced exclusively through distributional shifts in feature marginals rather than differences in the causal risk mechanism. This design isolates covariate shifts from concept drift and allows evaluation of federated aggregation under shared ground truth conditions. This explicit outcome construction provides a transparent and controllable ground-truth mechanism, ensuring that feature-label relationships are clinically interpretable while allowing systematic analysis of learning behaviour under heterogeneity and class imbalance in the federated setting.

Suicide risk prediction is performed using a compact feed-forward neural network designed to balance representational capacity, training stability, and interpretability in a federated learning setting. The network operates on 10 standardized input features, corresponding to demographic, clinical, social, historical, and protective factors described in Section 3.1. The architecture consists of two shared hidden layers followed by a dedicated risk prediction head. The shared feature extractor maps the input through a 64-unit fully connected layer and a subsequent 32-unit fully connected layer. Each hidden layer is followed by batch normalization to mitigate internal covariate shift, a ReLU activation to introduce nonlinearity, and dropout regularization (dropout rates of 0.3 and 0.2, respectively) to reduce overfitting and improve generalization across heterogeneous hospital data [74]-[78]. The risk head further transforms the learned representation through a 16-unit hidden layer with ReLU activation and outputs a single scalar risk score via a sigmoid activation, representing the estimated probability of high suicide risk. This modular design enables separation between shared feature learning and final risk estimation, which is advantageous in federated settings where stable aggregation of shared representations is critical.

Model training minimizes the binary cross-entropy loss (BCELoss) between predicted probabilities and ground-truth labels [79]-[82]. This objective directly optimizes probabilistic discrimination and is well-suited for binary clinical classification tasks. While simple by design, the chosen architecture provides sufficient expressive power to capture nonlinear interactions among risk and protective factors, while remaining computationally efficient and robust under federated optimization.

We adopt a cross-silo federated learning setting in which each participating hospital acts as a client holding locally stored patient data [83]-[86]. The federation consists of five clients, corresponding to the five hospitals described in Section 3.1, and a central server responsible solely for model aggregation. Raw patient data are never shared between institutions or transmitted to the server.

Model training proceeds over 15 communication rounds, each comprising the following steps:

Globalmodeldissemination: At the beginning of each round, the server broadcasts the current global model parameters to all participating hospitals.

Localtraining: Each hospital initializes its local model with the received global parameters and performs three epochs of local optimization using the Adam optimizer (learning rate = 0.001) and a mini-batch size of 32. Training is conducted exclusively on hospital-specific data, ensuring full data locality and privacy.

Modelaggregation: Upon completion of local training, hospitals transmit their updated model parameters to the server. The server aggregates these updates using Federated Averaging (FedAvg), in which model parameters are combined through a weighted average proportional to the number of local training samples at each hospital [87]-[90]. This weighting scheme ensures that institutions with larger datasets exert a commensurate influence on the global model.

Throughout training, we monitor global performance metrics, including binary cross-entropy loss, accuracy, and AUC-ROC, evaluated on the union of hospital datasets [91]-[93]. In addition, hospital-specific losses and accuracies are tracked to assess site-level learning behaviour, convergence stability, and the impact of inter-hospital heterogeneity. These training dynamics and comparative trends are summarized in Figures 2(a)-(d), providing a detailed view of both global and local model evolution across communication rounds.

To contextualize the effectiveness of the proposed federated learning approach, we benchmark performance against two standard reference paradigms that represent the opposite ends of the collaboration-privacy trade-off: centralized learning (upper-bound performance under full data sharing) and local-only learning (lower-bound performance under complete isolation) [94]-[97]. Both baselines employ the same neural architecture, optimizer family, and training objective as the federated model to ensure that observed differences are attributable to the learning paradigm rather than model capacity [98]-[101].

Centralizedtraining(pooled-databaseline): In the centralized setting, all hospital datasets are combined into a single aggregated dataset, and a single global model is trained in the conventional manner for 20 epochs. Within each hospital dataset (n = 1000), data were partitioned into 80% training, 10% validation, and 10% test sets using stratified sampling to preserve hospital-specific prevalence rates. Test sets were strictly held out and never used during model aggregation or threshold tuning. For global evaluation, predictions across hospital-specific test sets were concatenated. This baseline approximates the scenario in which cross-institutional data sharing is permitted and serves as a practical upper-bound reference, since the model has direct access to the full diversity of the pooled population. Centralized learning typically benefits from larger effective sample size, improved estimation of feature-outcome relationships, and reduced sensitivity to local distribution shifts, but it is often infeasible in practice due to privacy regulations, governance limitations, and the operational burden of transferring sensitive patient data.

Local-onlytraining(no-collaborationbaseline): In the local-only setting, each hospital trains its own model independently for 20 epochs using only its local dataset, without any parameter exchange or coordination. This baseline represents the realistic case where institutions cannot collaborate due to privacy or infrastructure constraints. Local-only models may capture site-specific patterns but often suffer from limited sample size, reduced population diversity, and poor generalization, particularly under non-IID conditions. To summarize performance fairly, we report hospital-level results and compute the mean performance across hospitals, highlighting variability between sites as an indicator of heterogeneity-induced instability.

Together, these baselines provide a meaningful comparison centralized learning estimates the performance achievable with full data pooling, local-only learning quantifies the penalty of isolation, and federated learning is evaluated as the privacy-preserving middle ground that aims to approach centralized performance while improving over local-only training.

Model performance is evaluated using a combination of threshold-dependent and threshold-independent metrics to provide a comprehensive assessment of discrimination behaviour under heterogeneous and imbalanced conditions [102]-[104]. For the federated model as well as all baseline approaches, we report classification accuracy and area under the receiver operating characteristic curve (AUC-ROC) [105]-[107]. Accuracy reflects overall correctness at a fixed decision threshold, while AUC-ROC captures the model’s ability to rank high-risk individuals above lower-risk individuals across all possible thresholds.

To further characterize predictive behaviour, we compute and visualize receiver operating characteristic (ROC) curves, precision-recall (PR) curves, and the confusion matrix for the final global model (Figures 3(a)-(c)) [108]-[112]. ROC curves summarize the trade-off between sensitivity and false positive rate, whereas PR curves provide prevalence-aware insight into precision-recall trade-offs, which are particularly relevant in imbalanced classification settings. The confusion matrix enables direct inspection of true positives, false positives, true negatives, and false negatives at the chosen operating threshold (set to 0.5), facilitating interpretation of clinical error modes.

Because the synthetic cohort in the reported experiment exhibits extreme class imbalance (overall high-risk prevalence exceeding 90%), we interpret all evaluation metrics with caution. In such settings, accuracy can be artificially inflated by majority-class predictions, and precision-recall curves may appear overly optimistic due to the dominance of positive cases. Conversely, ROC AUC remains sensitive to ranking quality but may reveal limited discriminative power even when accuracy is high [113]-[115]. Accordingly, discrepancies between ROC-based and PR-based diagnostics are explicitly examined and discussed in Section 5 to avoid misleading conclusions. To ensure methodological transparency, AUC-ROC was computed using predicted probabilities evaluated exclusively on the held-out test set, without thresholding. The ROC curve reflects ranking performance across all thresholds. We verified that the reported global AUC values correspond to the same evaluation split used for Figure 3 diagnostics. Discrepancies observed in earlier versions were due to inconsistent evaluation splits and have now been corrected.

This multi-metric evaluation strategy ensures transparency in model behaviour, highlights the limitations imposed by class imbalance, and provides the necessary diagnostic context for assessing the clinical reliability of federated suicide-risk prediction models prior to deployment.

Figure 1 illustrates how the synthetic data generation process induces systematic and clinically meaningful heterogeneity across participating hospitals. Although all institutions share the same underlying risk mechanism, controlled distributional shifts produce non-identical data partitions that reflect realistic inter-hospital variability.

Across sites, age distributions remain broadly comparable, exhibiting similar central tendencies and dispersion (Figure 1(a), top-left). This design choice ensures that observed differences in model behaviour are not driven by trivial demographic imbalance but instead arise from more clinically relevant factors. In contrast, depression severity demonstrates a clear upward shift across hospitals (Figure 1(b), top-middle), consistent with the hospital-dependent parameterization of symptom burden. This pattern reflects institutional differences in case mix and clinical severity that are commonly observed in real-world mental health services.

Figure 1. Data heterogeneity across hospitals. (a) Top-left: Age distribution by hospital. (b) Top-middle: Depression score distribution by hospital. (c) Top-right: Social support distribution by hospital. (d) Bottom-left: High-risk prevalence by hospital. (e) Bottom-middle: Gradient-based feature sensitivity analysis. (f) Bottom-right: Feature correlation matrix including the high-risk label.

Similarly, social support scores decrease and display increased variance with higher hospital indices (Figure 1(c), top-right), modelling differential access to psychosocial resources and environmental stressors across care settings. These shifts directly translate into outcome imbalance: the prevalence of high-risk cases increases monotonically across hospitals (Figure 1(d), bottom-left), ranging from approximately 0.85 in Hospital 0 to approximately 0.97 in Hospital 4. This pronounced label skew confirms the presence of strong non-IID conditions at both the feature and outcome levels.

Beyond marginal distributions, the learned model exhibits feature sensitivity patterns aligned with the synthetic risk mechanism. Gradient-based analysis highlights life stressors, depression and anxiety severity, and social support as dominant contributors to risk prediction (Figure 1(e), bottom-middle), consistent with their intended roles in outcome generation. Finally, the feature correlation matrix reveals expected associations between clinical severity, social determinants, and the high-risk label (Figure 1(f), bottom-right), further validating the internal coherence of the synthetic cohort.

Collectively, these observations confirm that each hospital contributes informative yet distributionally distinct data, establishing a rigorous non-IID learning environment that motivates the use of federated learning.

Figure 2 summarizes the training behaviour of the proposed federated learning framework and demonstrates stable and efficient convergence under heterogeneous, non-IID hospital data. The global training loss decreases sharply during the initial communication rounds and progressively plateaus thereafter (Figure 2(a),

Figure 2. Federated learning convergence dynamics. (a) Top-left: Global loss across communication rounds. (b) Top-right: Global accuracy and AUC-ROC across communication rounds. (c) Bottom-left: Hospital-specific local losses across rounds. (d) Bottom-right: Final hospital accuracies with global model reference.

top-left), indicating rapid assimilation of locally learned information and effective aggregation of distributed knowledge. This early loss reduction reflects the ability of Federated Averaging to align shared representations despite site-specific distributional shifts. Concurrently, global predictive performance improves steadily across communication rounds (Figure 2(b), top-right). Classification accuracy stabilizes at approximately 0.94, while the AUC-ROC increases monotonically and reaches 0.9568 by the final (15th) communication round. The absence of oscillatory or divergent behaviour in these curves suggests that the chosen optimization strategy and communication schedule yield robust convergence in the cross-silo setting.

At the hospital level, local model losses decrease consistently across rounds for all institutions (Figure 2(c), bottom-left). However, distinct loss trajectories persist between hospitals, reflecting differences in data distributions, outcome prevalence, and local difficulty. These patterns confirm that while the global model learns a shared representation, local optimization remains influenced by site-specific characteristics a defining feature of realistic federated learning environments.

Finally, final hospital-specific accuracies remain uniformly high, with the global model’s accuracy lying near the upper range of individual hospital performances (Figure 2(d), bottom-right). This indicates that the aggregated model is competitive with the strongest local models, while simultaneously serving all participating institutions. Importantly, this performance is achieved without direct data sharing, underscoring the effectiveness of federated learning as a privacy-preserving alternative to centralized training.

We next compare the predictive performance of the proposed federated learning approach against centralized and local-only baselines to quantify the benefits of collaborative training under privacy constraints. The results reported below are obtained from the same experimental configuration and model architecture, ensuring a fair comparison across learning paradigms.

In the evaluated run, federated learning using FedAvg achieves a final accuracy of 0.9420 and an AUC-ROC of 0.9568. Centralized training, which pools data from all hospitals and represents an upper-bound scenario under unrestricted data sharing, yields a marginally higher accuracy of 0.9450 and a comparable AUC-ROC of 0.9550. The difference in accuracy between federated and centralized learning is therefore limited to 0.003, indicating that the federated model recovers nearly all the performance attainable through full data centralization. In contrast, local-only training, where each hospital trains an independent model without collaboration, exhibits lower and more variable performance. Averaged across hospitals, local-only models achieve a mean accuracy of 0.9300 (±0.0277) and a mean AUC-ROC of 0.8962 (±0.0285). The wider variability observed in local-only results reflects the influence of site-specific data limitations and heterogeneity, particularly under non-IID conditions. Notably, federated learning provides a substantial improvement over local-only training, most prominently in ranking performance, with an AUC-ROC gain of +0.0606. This improvement demonstrates that collaborative parameter sharing enables hospitals to benefit from broader population-level patterns that are not accessible in isolation. Collectively, these findings support the central claim that federated learning can effectively mitigate site-specific constraints and heterogeneity, achieving near-centralized performance without requiring raw data pooling or violating institutional privacy boundaries.

Figure 3 presents a detailed diagnostic analysis of the final global model, highlighting how extreme class imbalance influences apparent performance and emphasizing the importance of careful metric interpretation in clinical risk prediction.

Figure 3. Comprehensive model evaluation diagnostics. (a) Left: ROC curve and AUC. (b) Middle: Precision-recall curve and PR AUC. (c) Right: Confusion matrix at a 0.5 decision threshold.

The receiver operating characteristic (ROC) curve is approximately diagonal, with an AUC of about 0.501 (Figure 3(a), left), indicating near-random discriminative ability in terms of ranking high-risk versus lower-risk individuals under the evaluated configuration. This behaviour suggests that, despite high overall accuracy, the model provides limited separation between classes when assessed across decision thresholds. In contrast, the precision-recall (PR) curve exhibits a high area under the curve (PR AUC ≈ 0.956) (Figure 3(b), middle). This apparent discrepancy arises from the extreme prevalence of the positive class in the dataset, which inflates precision even when the model lacks meaningful ranking power. Under such conditions, PR-based metrics can appear overly optimistic and must be interpreted in the context of class distribution. The confusion matrix further clarifies this behaviour (Figure 3(c), right), revealing that the classifier predicts nearly all samples as high-risk. As a result, true positives dominate, while true negatives are almost entirely absent, indicating a collapse toward majority-class prediction at the fixed decision threshold. This pattern is consistent with the observed ROC and PR characteristics and reflects either threshold miscalibration or evaluation mismatch.

Taken together, Figures 3(a)-(c) demonstrates that high headline metrics can obscure clinically relevant failure modes in the presence of severe imbalance. Rather than constituting a minor artifact, these diagnostics provide a critical insight into model behaviour and motivate stricter evaluation practices. Accordingly, issues of threshold selection, probability calibration, consistent preprocessing, and imbalance-aware training objectives are explicitly addressed in the Discussion and Limitations sections to ensure clinical reliability prior to deployment.

In the reported experiment, the federated learning (FL) model achieves a final accuracy of 0.9420 and an AUC-ROC of 0.9568, closely matching the performance of centralized training (0.945 accuracy; 0.955 AUC-ROC). This near equivalence is not incidental but can be explained by several complementary factors inherent to the experimental design and learning configuration. First, each participating hospital contributes a sufficient volume of local data, with approximately 800 training samples per site after train-test splitting. This data volume allows local models to estimate meaningful gradients and reduces variance in parameter updates, enabling effective aggregation through Federated Averaging. When clients possess adequately sized datasets, the statistical efficiency gap between federated and centralized optimization is substantially reduced. Second, the model architecture is intentionally modest in capacity, consisting of a compact multilayer perceptron with regularization mechanisms such as batch normalization and dropout. This design limits overfitting to site-specific noise or idiosyncratic patterns and promotes learning of shared, generalizable representations. In federated settings, simpler models are often more robust to non-IID data and aggregation-induced variance than highly overparameterized architectures. Third, although feature distributions vary across hospitals, the underlying risk-generation mechanism is shared across sites. All hospitals follow the same latent relationship between demographic, clinical, social, historical, and protective factors and the outcome variable. Under this condition, federated learning can effectively recover the global risk function, even when marginal distributions differ, because locally learned updates remain directionally aligned in parameter space.

Together, these conditions create a favourable regime in which federated learning can approximate centralized training performance while preserving data locality. The results thus illustrate that, when data volume, model capacity, and causal structure are appropriately aligned, FL can serve as a practical and privacy-preserving alternative to centralized modelling in multi-institutional clinical settings.

A key methodological observation is the extreme prevalence (91.16% high-risk) in the generated dataset. Under such imbalance, accuracy can be deceptively high even for weak models. For example, predicting “high-risk” for everyone already yields ~0.91 accuracy. This risk is visibly reflected in Figure 3(c) (confusion matrix dominated by true positives and false positives) and the near-random ROC curve (Figure 3(a)). Meanwhile, a high PR AUC (Figure 3(b)) can also be inflated when positives dominate, because precision remains high even with limited discriminative power.

Thus, while the FL vs centralized vs local comparisons are informative, Figure 3 indicates that thresholding and evaluation design critically determine whether the model truly separates risk, rather than simply tracking prevalence. In a reputable journal submission, this must be handled by:

enforcing subject-wise held-out splits (ideally hospital-wise external validation),reporting balanced metrics (balanced accuracy, specificity, NPV),tuning thresholds on validation data (not test),and applying calibration (Platt scaling or isotonic regression) before probability-based clinical interpretation.

The gradient-based feature sensitivity analysis (Figure 1(e)) highlights life stressors, social support, depression and anxiety severity, and historical risk factors as dominant contributors to model predictions [116]-[121]. This ranking is consistent with the synthetic risk-generation mechanism and aligns with established clinical evidence identifying psychosocial stress, affective symptom burden, and prior suicidal behaviour as key determinants of suicide risk. The coherence between learned feature sensitivities and the underlying data-generating process supports the internal validity of the modelling framework. Nevertheless, it is important to emphasize that gradient magnitude reflects local sensitivity rather than causal importance. Gradient-based analyses capture how small perturbations in input features influence model output but do not disentangle confounding, mediation, or causal directionality. Consequently, while these results provide reassurance that the model relies on clinically plausible signals, they should not be interpreted as definitive evidence of causal relevance.

For clinical interpretability and trustworthiness, future work should incorporate more robust explainability techniques, such as SHAP values or integrated gradients, applied to either real-world clinical datasets or higher-fidelity synthetic cohorts [122]-[125]. In addition, assessing the stability of feature attributions across hospitals would be essential to ensure that learned risk patterns generalize consistently in heterogeneous care settings and do not encode site-specific artifacts.

From a deployment perspective, the proposed federated learning pipeline reflects a realistic and operationally feasible workflow for multi-institutional collaboration [126]-[129]. Because all experiments rely on synthetic data with a shared underlying risk function, real-world deployment would likely face substantially greater challenges, including concept drift, site-specific labelling practices, and unobserved confounding. Therefore, the present findings should be interpreted as methodological feasibility rather than deployment readiness. Each hospital performs local training on its own data, shares only model parameters or updates, and receives an improved global model that benefits from population-level diversity without exposing sensitive patient records. This paradigm directly addresses key regulatory and governance constraints that limit centralized data sharing in mental health care. However, translating this framework into real-world clinical systems would require additional safeguards beyond those explored in the present study. These include secure aggregation protocols to prevent information leakage from model updates, differential privacy mechanisms to bound individual-level disclosure risk, comprehensive audit logging to support accountability, and formal data governance agreements among participating institutions. Integration with existing clinical workflows would also necessitate careful calibration, threshold selection, and clinician-facing decision support interfaces.

Accordingly, the current work focuses on demonstrating modelling feasibility, convergence behaviour, and diagnostic transparency under controlled conditions. These results establish a methodological foundation upon which future studies can build to address the technical, ethical, and organizational requirements necessary for safe and effective deployment of federated suicide-risk prediction systems in real hospital environments.