Federated learning enabled privacy-preserving data access for predicting 30-day mortality in acute myocardial infarction

Federated learning enabled privacy-preserving data access for predicting 30-day mortality in acute myocardial infarction | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Federated learning enabled privacy-preserving data access for predicting 30-day mortality in acute myocardial infarction Koutarou Matsumoto, Yuta Nakamura, Masahiro Kamouchi, Ewout Steyerberg This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7454748/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Background Federated learning may reduce privacy risks by allowing each institution to retain its data while performing distributed prediction model training and validation. This study evaluated the performance of federated learning approaches in predicting 30-day mortality in patients with acute myocardial infarction (AMI). Methods We analyzed data from 40,830 patients with AMI across 16 regions in the GUSTO-I trial. Logistic regression models were developed using three approaches: (1) federated learning— each institution trained a local model on its own data and transmitted regression coefficients to a central server for aggregation; (2) centralized learning—individual patient data were centrally available for analysis; and (3) local modeling—training of 16 local models. Each approach included logistic models without regularization and those with L1, L2, and Elastic Net regularization. Model performances were evaluated using the area under the receiver operating characteristic curve (AUROC) and calibration metrics. Results When applied within their respective development regions using stratified five-fold cross-validation, the models achieved AUROC values ranging from 0.733 to 0.846, with local models consistently underperforming compared to the federated learning and centralized models. Applying local models to other regions led to substantial performance degradation, with some exhibiting markedly poor discrimination and calibration. Federated learning and centralized models exhibited stable performance across regions. The AUROC of the federated learning model was very similar to that of the centralized model (0.847 vs. 0.847) and demonstrated stable calibration. These findings were further supported by the similarity in the regression coefficients between the federated learning and centralized models, while coefficients varied by region. Conclusion Federated learning enables privacy-preserving utilization of regional data while maintaining nearly identical predictive performance as centralized models. Further implementation is recommended for multi-institutional settings under data-sharing constraints. Trial registration: Not applicable; this is a secondary analysis of the GUSTO-I randomized trial (enrollment 1990–1993) with no new participant enrollment or intervention assignment. federated learning acute myocardial infarction clinical prediction model clinical decision-making mortality prediction Figures Figure 1 Figure 2 Figure 3 Figure 4 1. Background With recent advancements in machine learning technology, there is an increased expectation from clinical prediction models to perform as decision-support tools in medical practice [ 1 ]. Developing high-accuracy predictive models requires large and diverse datasets. However, the amount of data available within a single medical institution or region is inherently limited. To overcome this limitation, several studies have sought to aggregate data from multiple institutions or regions to build more comprehensive predictive models. However, data sharing presents a significant risk of privacy breaches, as medical records contain highly sensitive personal information, making large-scale data collection across multiple institutions and regions challenging. Moreover, subsequent to the development and deployment of a model, its performance may degrade over time, necessitating periodic retraining and continuous data collection [ 2 ]. Therefore, enabling predictive modeling through data integration requires a framework that facilitates ongoing data collection, while minimizing the risk of medical information leakage, also for cross-border data sharing. To address these issues, federated learning, a form of distributed learning proposed originally by Google, has attracted considerable attention in recent years [ 3 ]. Federated learning allows each medical or research institution to train models locally within their respective environments, while sharing only the learned model parameters to construct a global model. This approach enables the development of high-performance predictive models without directly sharing raw medical data, making it a promising solution in the healthcare domain. The effectiveness of federated learning has been demonstrated in various applications, including the detection of COVID-19-related CT abnormalities, prediction of oxygen therapy requirements, classification of melanoma cases, postoperative recurrence risk prediction in patients with advanced gastric cancer, and mortality risk assessment in intensive care units [ 4 – 8 ]. Most applications of federated learning in healthcare have focused on unstructured data, such as medical imaging; however, its applicability to prediction with structured clinical data has not been extensively validated [ 9 ]. Moreover, as clinical prediction models are disease-specific, the applicability of federated learning has been limited to a select number of conditions. This study aimed to evaluate the feasibility of federated learning from two perspectives. First, we evaluated the predictive performance of federated learning as compared to that of centralized learning. In particular, we examined whether similar performance holds when applying advanced logistic regression modeling with L1 and L2 regularization. Second, we assessed the extent to which a global model outperforms local models. 2. Methods 2.1. Study design and participants In this study, we used data from the GUSTO-I trial, which was specifically designed to evaluate four treatment strategies for AMI [ 10 ]. The GUSTO-I trial enrolled 41,021 patients admitted to 1,081 hospitals in 15 countries during 1990–1993, all of whom provided informed consent. Among these participants, 40,830 patients with known 30-day vital status were included in this analysis [ 11 ]. As a large and ethnically diverse dataset, the GUSTO-I database has been widely used in various clinical prediction studies [ 11 – 22 ]. Using this dataset, we developed and validated prediction models for 30-day mortality. The modeling process was conducted in accordance with the TRIPOD + AI statement [ 1 ]. 2.2. Clinical outcomes and predictors The clinical outcome was defined as 30-day mortality following hospitalization for AMI. Seventeen candidate predictors, identified in prior studies, were available for analysis—four continuous and 13 categorical—as summarized in Table 1 [ 11 , 12 ]. Table 1 Predictors and data types Candidate predictors used for model development. Continuous variables were analyzed on their native scales; categorical variables were coded as binary (yes/no) or ordinal as indicated. Predictor Data type Age (years) Continuous variable Height (cm) Weight (kg) Number of ECG leads (count) Killip Classification: Class I: No signs of heart failure Class II: Mild to moderate heart failure Class III: Pulmonary edema Class IV: Cardiogenic shock Categorical variable (ordinal scale) Female sex Categorical variable (nominal scale) Diabetes Hypotension (systolic blood pressure 80 bpm) Anterior infarct location Previous MI Hypertension history Hypercholesterolemia Previous angina pectoris Family history of MI Time to relief of chest pain > 1 h Smoking History: 1: Never smoker 2: Former smoker 3: Current smoker Categorical variable (ordinal scale) ECG, electrocardiogram; MI, myocardial infarction; bpm, beats per minute; mmHg, millimeters of mercury. 2.3. Model development Previous studies have reported that flexible nonlinear approaches, such as neural networks, did not outperform logistic regression models in terms of predictive accuracy when applied to the GUSTO-I trial dataset [ 12 ]. Similarly, studies using other large-scale cardiovascular disease databases have concluded that machine learning approaches offered no clear advantage in predicting short-term mortality [ 23 ]. Based on these findings, this study primarily employed logistic regression models incorporating four approaches: without regularization, L1 regularization, L2 regularization, and Elastic Net. 2.3.1. L1 regularization method The L1 regularization method (L1), also known as the least absolute shrinkage and selection operator (LASSO), is commonly used for variable selection. By adding the sum of the absolute values of the regression coefficients to the loss function of logistic regression, L1 induces sparsity, meaning that some regression coefficients shrink to exactly zero. Consequently, it allows for both feature selection and coefficient shrinkage simultaneously. The L1 estimator \(\:{\widehat{\beta\:}}_{L1}\) is obtained by minimizing the following objective function [ 24 ]: $$\:{\widehat{\beta\:}}_{L1}=\text{arg}\underset{\beta\:}{\text{m}\text{i}\text{n}}\left\{-{\sum\:}_{i=1}^{n}\left[{Y}_{i}\text{l}\text{o}\text{g}\left({\:\pi\:}_{i}\right)+\left(1-{Y}_{i}\right)\text{l}\text{o}\text{g}\left(1-{\pi\:}_{i}\right)\right]+\lambda\:{\sum\:}_{j=1}^{p}\left|{\beta\:}_{j}\right|\right\},$$ where \(\:{Y}_{i}\) is the binary outcome variable for the \(\:i\) -th case, and \(\:{X}_{i}={\left({X}_{i1},\:{X}_{i2},\:\dots\:,\:{X}_{ip}\right)}^{T}\) represents the predictor variables for the \(\:i\) -th case. The probability of mortality given \(\:{X}_{i}\) is modeled as $$\:{\pi\:}_{i}=\frac{1}{{1+\text{e}\text{x}\text{p}(-(\beta\:}_{0}+\sum\:_{j=1}^{p}{\beta\:}_{j}{X}_{ij}\left)\right)},$$ where \(\:\lambda\:>0\) is the regularization parameter that controls the complexity of the model. 2.3.2. L2 regularization method The L2 regularization method (L2), also known as Ridge regression, incorporates the sum of the squared regression coefficients into the loss function of logistic regression. Unlike L1, L2 does not perform feature selection because it shrinks the regression coefficients toward zero without making them exactly zero. Instead, it distributes the regularization effect across all features, preventing an excessive influence from any single predictor. The L2 estimator \(\:{\widehat{\beta\:}}_{L2}\) is obtained by minimizing the following objective function [ 25 , 26 ]: $$\:{\widehat{\beta\:}}_{L2}=\text{arg}\underset{\beta\:}{\text{min}}\left\{-{\sum\:}_{i=1}^{n}\left[{Y}_{i}\text{l}\text{o}\text{g}\left({\:\pi\:}_{i}\right)+\left(1-{Y}_{i}\right)\text{l}\text{o}\text{g}\left(1-{\pi\:}_{i}\right)\right]+\lambda\:{\sum\:}_{j=1}^{p}{\beta\:}_{j}^{2}\right\}$$ 2.3.3. Elastic Net regularization method Elastic Net constructs a loss function that combines both L1 and L2 regularization, introducing a mixing parameter \(\:\alpha\:\) that adjusts the balance between the two penalties. This approach simultaneously enables feature selection and coefficient shrinkage, mitigating the issue in which LASSO tends to select only one of a set of highly correlated variables, whereas Ridge retains all features. The Elastic Net estimator \(\:{\widehat{\beta\:}}_{elastic}\) is obtained by minimizing the following function [ 27 ]: $$\:{\widehat{\beta\:}}_{elastic}=\text{arg}\underset{\beta\:}{\text{min}}\left\{-{\sum\:}_{i=1}^{n}\left[{Y}_{i}\text{l}\text{o}\text{g}\left({\:\pi\:}_{i}\right)+\left(1-{Y}_{i}\right)\text{l}\text{o}\text{g}\left(1-{\pi\:}_{i}\right)\right]+\lambda\:{\sum\:}_{j=1}^{p}\left(\alpha\:{\beta\:}_{j}^{2}+\left(1-\alpha\:\right)\left|{\beta\:}_{j}\right|\right)\right\},$$ where \(\:\alpha\:\in\:\:\left[0,\:1\right]\) determines the relative contribution of L1 and L2 regularization. Setting \(\:\alpha\:=1\) corresponds to pure Ridge regression, whereas \(\:\alpha\:=0\) corresponds to pure LASSO. Intermediate values of \(\:\alpha\:\) provide a trade-off between feature selection and coefficient stability. The regularization parameter \(\:\lambda\:\) was selected within the range of 10 − 3 to 10 3 using five-fold cross-validation, where the value that achieved the highest area under the receiver operating characteristic curve (AUROC) on the validation dataset was chosen. For Elastic Net, in addition to the regularization parameter \(\:\lambda\:\) , the mixing parameter \(\:\alpha\:\) was selected from three candidate values: 0.1, 0.5, and 0.9, by identifying the optimal combination. Furthermore, all predictor variables were standardized before being input into the models. 2.4. Federated learning algorithm In federated learning, the model update process is performed iteratively between the clients, who train the models and update their parameters using local data from their respective regions, and the server, which aggregates the regression coefficients updated by the clients to construct and distribute a global model. The updating process follows the following steps: The server randomly selects a subset of clients and distributes the global model. Each client updates the global model using their respective local data and sends the updated model back to the server. The server aggregates the regression coefficients updated by the clients and utilizes them to generate a new global model. In this study, we employed Federated Averaging (FedAvg), a fundamental algorithm in federated learning, to aggregate the regression coefficients. In FedAvg, the regression coefficients are aggregated using a weighted average based on the sample size of each client [ 3 ]. The global model is updated using the following weighted aggregation formula: $$\:{w}_{t+1}\leftarrow\:\sum\:_{k\in\:{S}_{t}}\frac{{n}_{k}}{n}{w}_{t+1}^{\left(k\right)},\:\:\:\:\:n=\sum\:_{k\in\:{S}_{t}}{n}_{k}$$ , where \(\:t\) denotes the round number for updating the regression coefficients, \(\:{S}_{t}\) represents the set of clients selected in round \(\:t\) , \(\:n\) is the total number of samples across all clients, \(\:{n}_{k}\) corresponds to the number of samples held by the \(\:k\) -th client, \(\:{w}_{t+1}^{\left(k\right)}\) denotes the regression coefficients of the model updated by client \(\:k\) using its local dataset in round \(\:t+1\) , and \(\:{w}_{t+1}\) represents the regression coefficients of the global model at round \(\:t+1\) . In this study, the total number of update rounds for the regression coefficients was set to ten. Although federated learning typically selects a random subset of clients in each round for model aggregation, this approach results in an unstable convergence. To address this issue, we incorporated the regression coefficients from all 16 clients (regions) in each round for model aggregation. 2.5. Model evaluation metrics and procedures We evaluated discriminative performance using the AUROC, and assessed calibration via the calibration slope and intercept (calibration-in-the-large). Although the area under the precision–recall curve (AUPRC) is sometimes recommended for class-imbalanced outcomes such as mortality, it ignores true negatives, is sensitive to outcome prevalence, and is less straightforward to compare across populations; moreover, because precision equals positive predictive value, it partially reflects threshold-dependent clinical utility rather than pure ranking-based discrimination, thereby limiting its value as a primary evaluation metric for clinical prediction models [ 28 ]. Accordingly, we report AUROC and do not report AUPRC in this study. First, for within-region validation, we performed stratified five-fold cross-validation to develop and validate local models within each region. The data were stratified by outcome status to ensure a consistent outcome ratio across folds. In addition, the centralized and federated learning models, trained using all available data, were evaluated on the test set of each fold and compared with the local models. To ensure full formal consistency, the centralized and federated models should ideally be trained with exclusion of the one-fifth not used for training by the local models. One-fifth of 16 regions amounts to only about 1.25% of the total data. Indeed, preliminary analyses showed negligible differences in performance when using a simpler approach that trained centralized and federated models on the entire dataset. Therefore, for within-region validation, we report the validation results obtained using centralized and federated models trained on the full dataset. Next, for between-region validation to assess variability across regions, we applied locally developed models to other regions and compared their predictive performances with those of the centralized and federated models. For this evaluation, the global models were developed by excluding the region used for validation—that is, each model was trained on data from all 15 other regions. For this evaluation, point estimates and 95% confidence intervals were calculated for each target region. The confidence intervals were derived from 1,000 bootstrap resamples. 2.6. Model interpretability First, we computed the standardized regression coefficients for each model. Rather than presenting them individually, we performed principal component analysis (PCA)—a dimensionality-reduction technique—on the coefficient matrix (models × predictors) to because direct inspection of full coefficient vectors is high-dimensional and obscures between-model similarities. We then plotted the first two principal components to visualize the relative similarity among the models. 2.7. Analytical software and packages All analyses were conducted using Python (version 3.8.10). Model development and evaluation were performed using scikit-learn, whereas federated learning was implemented using the Flower framework. The statistical code is provided in the Supplemental Methods section of the Supplemental Material. 3. Results 3.1. Baseline characteristics In the GUSTO dataset, 2,851 (7.0%) of 40,830 patients died within 30 days. Region 16 had the fewest cases (1,231 patients), whereas Region 12 had the most cases (4,352 patients). Among all regions, Region 13 had the lowest (5.3%), and Region 6 had the highest mortality rate (8.4%). Although no significant differences were observed in terms of age or sex, certain regions exhibited notable variations in the prevalence of risk factors and medical histories (Table S1 ). 3.2. AUROCs in development regions Tables 2 and S2 present the mean and standard deviation of the AUROC values for the local models developed within each region, as well as for the centralized and federated learning models, evaluated on the test data using stratified five-fold cross-validation. Except for Region 10, the AUROC of the centralized and federated learning models exceeded those of the local models across all regions. Notably, in Region 16, the AUROC of the centralized and federated learning models was more than 0.04 higher than that of the cross-validated local model. The centralized and federated learning models achieved the highest AUROC of 0.847 in Region 1, whereas the lowest AUROC of 0.779 was observed in Region 16. This trend remained consistent, regardless of the regularization application (L1, L2, or Elastic Net). Moreover, the AUROC values for the validation of the centralized and federated learning models were nearly identical. Table 2 Cross-validated AUROC comparison of local, centralized, and federated L1-regularized logistic regression models Mean (SD) AUROC across stratified 5-fold cross-validation within each region. Local models were trained and validated within their development region using five folds. Centralized and federated global models were trained on the full dataset and evaluated on the same held-out folds for comparability. L1 denotes the lasso penalty. Higher AUROC indicates better discrimination. Results for unpenalized, L2 (ridge), and Elastic Net models are reported in Table S2. Region, n Event (%) Local Centralized global FL global Region 1, n = 2188 6.2 0.846 (0.048) 0.847 (0.044) 0.847 (0.044) Region 2, n = 2952 7.8 0.813 (0.044) 0.817 (0.043) 0.817 (0.043) Region 3, n = 2030 8.2 0.813 (0.038) 0.828 (0.041) 0.828 (0.041) Region 4, n = 2876 7.5 0.832 (0.022) 0.837 (0.023) 0.836 (0.022) Region 5, n = 1909 7.0 0.821 (0.036) 0.823 (0.035) 0.824 (0.036) Region 6, n = 1585 8.4 0.773 (0.047) 0.790 (0.032) 0.790 (0.032) Region 7, n = 3150 6.7 0.807 (0.034) 0.815 (0.027) 0.814 (0.027) Region 8, n = 2916 6.4 0.826 (0.041) 0.834 (0.047) 0.834 (0.047) Region 9, n = 3123 7.2 0.829 (0.019) 0.830 (0.022) 0.831 (0.022) Region 10, n = 1717 5.5 0.811 (0.048) 0.809 (0.032) 0.810 (0.031) Region 11, n = 2491 7.7 0.830 (0.034) 0.833 (0.038) 0.832 (0.037) Region 12, n = 4352 6.8 0.826 (0.034) 0.831 (0.032) 0.830 (0.031) Region 13, n = 2297 5.3 0.821 (0.066) 0.836 (0.047) 0.835 (0.049) Region 14, n = 3437 7.6 0.808 (0.041) 0.817 (0.046) 0.817 (0.046) Region 15, n = 2576 6.0 0.786 (0.036) 0.803 (0.036) 0.803 (0.037) Region 16, n = 1231 8.0 0.733 (0.071) 0.779 (0.086) 0.779 (0.085) AUROC: area under the receiver operating characteristic curve; n: number of patients in each region; Local: model trained on its own development region; Centralized global: global model trained on pooled data; FL global: global model developed with federated learning. The data are presented as the mean (standard deviation) of the AUROC on the validation data in a stratified 5-fold cross-validation for each region. 3.3. Performance in other regions Figure 1 presents the AUROC values for L1 models trained in each region and applied to other regions, as well as for centralized L1 models trained on pooled data and federated L1 models. Overall, both the centralized and federated learning models outperformed the local models in terms of external AUROC, and this trend remained consistent regardless of the application of regularization (Fig. 2 , Figure S1 to 3). However, the performance of the local models varied considerably. Notably, the model developed using Region 10 exhibited a substantial decrease in discrimination when applied to other regions. Figures 2 and 3 show the calibration slope and intercept for each approach, respectively. In particular, the model developed using Region 16 showed substantial deviations in the slope and intercept (Figs. 2 and 3 , Figures S4 to 9). Compared with the local L1 models, the centralized and federated L1 models exhibited more stable calibration. Results were similar with other modeling strategies (unpenalized, L2, or Elastic Net). 3.4. Standardized regression coefficients of each model The centralized models trained on pooled data and the federated learning models exhibited similar standardized regression coefficient distributions according to PCA (Fig. 4 ). In contrast, certain regions, such as Regions 10 and 16, displayed quite distinct coefficient distributions, deviating from those observed in other regions. 4. Discussion This comparative study confirmed the promise of federated learning approaches for prediction model development and validation. We compared local models with global models, including a centralized model trained on pooled data and a federated learning model, on the following scenarios: (1) application within their respective development regions and (2) application of models developed in one region to other regions. The results showed that the discriminatory performances and calibrations of the centralized and federated learning models were nearly identical, which was further supported by the similarities in their regression coefficients. This result was found for unpenalized and penalized estimation approaches. Additionally, in the local cross-validation, the global models outperformed the local models in most regions. Moreover, when the local models were applied to other regions, substantial variability was observed, with some regional models exhibiting markedly poor discrimination and calibration. 4.1 Predictive performance for the GUSTO-I dataset Multiple algorithms were previously compared to unpenalized logistic regression in the GUSTO dataset, including various nonlinear and flexible models. The unpenalized logistic regression model achieved the highest discrimination performance, with an AUROC of 0.820 [ 12 ]. Therefore, we adopted logistic regression modeling for the analysis in this study. The advanced logistic regression models incorporating L1 and L2 regularization showed minimal differences in discrimination performance compared to the unregularized model, suggesting that conventional maximum likelihood estimation may be sufficient in this setting with relatively large sample sizes by region. Another study compared multiple logistic regression models and confirmed that the model developed using the GUSTO-I dataset achieved an AUROC of approximately 0.82 [ 16 ]. In the same study, models developed in other cohorts showed slightly lower discriminative performance, with AUROCs ranging from 0.76–0.78 when applied to the GUSTO-I dataset, with some improvement by re-estimating the regression coefficients. Similarly, in our study, the L1 model developed using Region 16 of the GUSTO dataset achieved a high AUROC of 0.849 (0.812–0.882) when applied to Region 1. However, it exhibited poor calibration. These findings further underscore the importance of caution when transporting local models to different geographical regions. 4.2 Utility of Federated Learning If the sample size is large, using a model developed in a specific region within that same region is the most rational choice at the practical implementation stage of clinical prediction models given its superior accuracy. This is because the model optimally reflects the characteristics of the data from the development region. However, securing a sufficient sample size is often challenging for a specific region or hospital. In our comparison of local and global models, the local models failed to outperform the global models in terms of the AUROC on the test data. Furthermore, when applying local models outside their development regions, factors such as covariate shift, target shift, and concept drift may lead to a decline in predictive performance, necessitating careful consideration of these risks [ 29 ]. To address the challenges associated with the limitations of applying local models beyond their development regions, the TRIPOD + AI guidelines recommend reporting the impact of heterogeneity on predictive performance, and emphasize that reports should ideally include information from diverse geographic regions [ 1 ]. As demonstrated in this study, constructing prediction models using data from multiple regions may enable stable accuracy across different regions. Privacy constraints may however hamper the continuous collection of clinical data from multiple institutions across national borders. Federated learning, which implies sharing only model parameters instead of raw data, offers a promising approach for mitigating privacy risks. The performance of the federated learning models was comparable to that of the centralized models trained on pooled data, which is consistent with the findings of previous studies [ 4 – 8 ]. Overall, our results for predicting mortality in patients with AMI confirm that federated learning has huge potential for the pipeline of development, validation, and updating of prediction models while preserving data privacy [ 2 ]. 4.3 Limitations In this study, the FedAvg approach was adopted for federated learning, although variants can be considered. In addition, the GUSTO-I data were obtained from a randomized controlled trial with pre-specified data collection and strict definitions. This may have contributed to limited heterogeneity between locally developed models. Federated learning with observational data may show larger heterogeneity, and hence, more potential for local learning methods. 5. Conclusion Federated learning can achieve predictive performance similar to that of a model trained on centralized data. Both federated and centralized global models may exhibit superior predictive performance compared to models developed using data from a single setting. Federated learning allows the development of prediction models while preserving data privacy and eliminating the need for direct data sharing, making it an essential technology for the cross-border use of medical data. Abbreviations AI artificial intelligence AMI acute myocardial infarction AUPRC area under the precision–recall curve AUROC area under the receiver operating characteristic curve COVID-19 coronavirus disease 2019 CT computed tomography FedAvg Federated Averaging GUSTO-I Global Utilization of Streptokinase and Tissue Plasminogen Activator for Occluded Coronary Arteries (trial) L1 L1 regularization (lasso penalty) L2 L2 regularization (ridge penalty) LASSO least absolute shrinkage and selection operator PCA principal component analysis TRIPOD + AI Transparent Reporting of a multivariable prediction model for Individual Prognosis Or Diagnosis + Artificial Intelligence Declarations Ethics approval and consent to participate Not applicable. This study is a secondary analysis of the publicly available, de-identified GUSTO-I randomized trial dataset (enrollment 1990–1993); no new participant recruitment or intervention assignment was undertaken. The original trial obtained ethics approval at participating centers with informed consent from all participants (see primary trial publications). Clinical trial number Not applicable. Consent for publication Not applicable. This manuscript contains no individual person’s data in any form (including images, videos, or identifiable details). Availability of data and materials The GUSTO-I dataset is publicly available from the Duke Clinical Research Institute: It can be loaded into R using the following command: load(url("http://hbiostat.org/data/repo/gusto.rda")). Competing interest None. Funding This study was supported by a Grant-in-Aid for Scientific Research (JSPS KAKENHI Grant Number: JP25H01083) from the Japanese Society for the Promotion of Science (JSPS). CRediT authorship contribution statement Koutraou Matsumoto : Writing – original draft, Methodology, Software, Formal analysis, Data curation, Conceptualization. Yuta Nakamura : Software, Formal analysis, Data curation. 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Performance evaluation of predictive AI models to support medical decisions: overview and guidance. arXiv. 2024;2412.10288 https://doi.org/10.48550/arXiv.2412.10288 Sahiner B, Chen W, Samala RK, Petrick N. Data drift in medical machine learning: Implications and potential remedies. Br J Radiol. 2023;96:20220878. https://doi.org/10.1259/bjr.20220878 Additional Declarations No competing interests reported. Supplementary Files supplementalmaterial.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7454748","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":513742005,"identity":"52e7bf3d-3911-4584-960b-4c7bba9613eb","order_by":0,"name":"Koutarou 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09:25:59","extension":"html","order_by":17,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":114432,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7454748/v1/722c2af6e4c95a59fd366950.html"},{"id":91834369,"identity":"0316ea51-76d1-4203-a39f-0cc779d78258","added_by":"auto","created_at":"2025-09-22 09:26:04","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":436568,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eAUROCs of local, centralized, and federated learning models using L1-regularized logistic regression in validation regions.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAUROC: area under the receiver operating characteristic curve; Centralized: global model trained on pooled data minus the validation region; FL: global model developed with federated learning minus the validation region. Point estimates and 95% confidence intervals of AUROCs for region-specific, centralized, and federated learning models developed using L1-regularized logistic regression are presented by validation region. The confidence intervals were calculated based on 1000 bootstrap iterations. The model developed for Region 10 is represented in red across the plots.\u003c/p\u003e","description":"","filename":"fig1.tif.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7454748/v1/26fdfee9257eb9541a32e959.jpg"},{"id":91834368,"identity":"3a974b77-3317-4fd8-bf8d-f92ef8fb3522","added_by":"auto","created_at":"2025-09-22 09:26:04","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":440775,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCalibration slopes of local, centralized, and federated learning models using L1-regularized logistic regression.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eCentralized: model trained on pooled data; FL: federated learning. Point estimates and 95% confidence intervals of calibration slopes for region-specific, centralized, and federated learning models developed using L1-regularized logistic regression are presented by validation region. The confidence intervals were calculated based on 1000 bootstrap iterations. The model developed for Region 16 is represented in red across the plots.\u003c/p\u003e","description":"","filename":"fig2.tif.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7454748/v1/337bc641bd8ee99929b7a829.jpg"},{"id":91834371,"identity":"ded2a324-7e5d-44b3-be4c-fc7d28ef4ea4","added_by":"auto","created_at":"2025-09-22 09:26:04","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":251835,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCalibration intercepts of local, centralized, and federated learning models using L1-regularized logistic regression.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eCentralized: model trained on pooled data; FL: federated learning. Point estimates and 95% confidence intervals of calibration intercepts for region-specific, centralized, and federated learning models developed using L1-regularized logistic regression are presented by validation region. The confidence intervals were calculated based on 1000 bootstrap iterations. The model developed in Region 16 is represented in red across the plots.\u003c/p\u003e","description":"","filename":"fig3.tif.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7454748/v1/c4ad60d66ec538d392a4037f.jpg"},{"id":91834399,"identity":"67f3ced8-3730-456a-a384-e2c0358db9bb","added_by":"auto","created_at":"2025-09-22 09:26:08","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":176267,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFirst and second principal components of the standardized regression coefficients for each model.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFL: global model developed with federated learning; Centralized: global model trained on all pooled data. A scatter plot of the first and second principal components was obtained by applying principal component analysis (PCA) to the standardized regression coefficients of each model. The vertical and horizontal axes correspond to the first and second principal components, respectively. Red squares represent FL, blue triangles represent the Centralized models, and black triangles represent the models developed in each region.\u003c/p\u003e","description":"","filename":"fig4.tif.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7454748/v1/3d7e0a1b57eec5efbe081532.jpg"},{"id":108131880,"identity":"9c09cb32-96ac-4f2a-9c48-5f3f5f1a8cc7","added_by":"auto","created_at":"2026-04-29 16:26:05","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1632057,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7454748/v1/216facd8-db5c-4780-b8a6-8e164e619534.pdf"},{"id":91834394,"identity":"c8c42e54-f6ec-4cb6-9c89-32ce0ffc8af9","added_by":"auto","created_at":"2025-09-22 09:26:07","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":5177335,"visible":true,"origin":"","legend":"","description":"","filename":"supplementalmaterial.docx","url":"https://assets-eu.researchsquare.com/files/rs-7454748/v1/9c9e3c3ddfeaeb91fe3694fe.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Federated learning enabled privacy-preserving data access for predicting 30-day mortality in acute myocardial infarction","fulltext":[{"header":"1. Background","content":"\u003cp\u003eWith recent advancements in machine learning technology, there is an increased expectation from clinical prediction models to perform as decision-support tools in medical practice [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Developing high-accuracy predictive models requires large and diverse datasets. However, the amount of data available within a single medical institution or region is inherently limited. To overcome this limitation, several studies have sought to aggregate data from multiple institutions or regions to build more comprehensive predictive models.\u003c/p\u003e\u003cp\u003eHowever, data sharing presents a significant risk of privacy breaches, as medical records contain highly sensitive personal information, making large-scale data collection across multiple institutions and regions challenging. Moreover, subsequent to the development and deployment of a model, its performance may degrade over time, necessitating periodic retraining and continuous data collection [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Therefore, enabling predictive modeling through data integration requires a framework that facilitates ongoing data collection, while minimizing the risk of medical information leakage, also for cross-border data sharing.\u003c/p\u003e\u003cp\u003eTo address these issues, federated learning, a form of distributed learning proposed originally by Google, has attracted considerable attention in recent years [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Federated learning allows each medical or research institution to train models locally within their respective environments, while sharing only the learned model parameters to construct a global model. This approach enables the development of high-performance predictive models without directly sharing raw medical data, making it a promising solution in the healthcare domain.\u003c/p\u003e\u003cp\u003eThe effectiveness of federated learning has been demonstrated in various applications, including the detection of COVID-19-related CT abnormalities, prediction of oxygen therapy requirements, classification of melanoma cases, postoperative recurrence risk prediction in patients with advanced gastric cancer, and mortality risk assessment in intensive care units [\u003cspan additionalcitationids=\"CR5 CR6 CR7\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Most applications of federated learning in healthcare have focused on unstructured data, such as medical imaging; however, its applicability to prediction with structured clinical data has not been extensively validated [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Moreover, as clinical prediction models are disease-specific, the applicability of federated learning has been limited to a select number of conditions.\u003c/p\u003e\u003cp\u003eThis study aimed to evaluate the feasibility of federated learning from two perspectives. First, we evaluated the predictive performance of federated learning as compared to that of centralized learning. In particular, we examined whether similar performance holds when applying advanced logistic regression modeling with L1 and L2 regularization. Second, we assessed the extent to which a global model outperforms local models.\u003c/p\u003e"},{"header":"2. Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1. Study design and participants\u003c/h2\u003e\u003cp\u003eIn this study, we used data from the GUSTO-I trial, which was specifically designed to evaluate four treatment strategies for AMI [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. The GUSTO-I trial enrolled 41,021 patients admitted to 1,081 hospitals in 15 countries during 1990\u0026ndash;1993, all of whom provided informed consent. Among these participants, 40,830 patients with known 30-day vital status were included in this analysis [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. As a large and ethnically diverse dataset, the GUSTO-I database has been widely used in various clinical prediction studies [\u003cspan additionalcitationids=\"CR12 CR13 CR14 CR15 CR16 CR17 CR18 CR19 CR20 CR21\" citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Using this dataset, we developed and validated prediction models for 30-day mortality. The modeling process was conducted in accordance with the TRIPOD\u0026thinsp;+\u0026thinsp;AI statement [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e].\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2. Clinical outcomes and predictors\u003c/h2\u003e\u003cp\u003eThe clinical outcome was defined as 30-day mortality following hospitalization for AMI. Seventeen candidate predictors, identified in prior studies, were available for analysis\u0026mdash;four continuous and 13 categorical\u0026mdash;as summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003e\u003cb\u003ePredictors and data types\u003c/b\u003e Candidate predictors used for model development. Continuous variables were analyzed on their native scales; categorical variables were coded as binary (yes/no) or ordinal as indicated.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"2\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePredictor\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eData type\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAge (years)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\" morerows=\"3\" rowspan=\"4\"\u003e\u003cp\u003eContinuous variable\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHeight (cm)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eWeight (kg)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNumber of ECG leads (count)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eKillip Classification:\u003c/p\u003e\u003cp\u003eClass I: No signs of heart failure\u003c/p\u003e\u003cp\u003eClass II: Mild to moderate heart failure\u003c/p\u003e\u003cp\u003eClass III: Pulmonary edema\u003c/p\u003e\u003cp\u003eClass IV: Cardiogenic shock\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCategorical variable\u003c/p\u003e\u003cp\u003e(ordinal scale)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFemale sex\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\" morerows=\"10\" rowspan=\"11\"\u003e\u003cp\u003eCategorical variable\u003c/p\u003e\u003cp\u003e(nominal scale)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDiabetes\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHypotension (systolic blood pressure\u0026thinsp;\u0026lt;\u0026thinsp;100 mmHg)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTachycardia (pulse\u0026thinsp;\u0026gt;\u0026thinsp;80 bpm)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAnterior infarct location\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePrevious MI\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHypertension history\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHypercholesterolemia\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePrevious angina pectoris\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFamily history of MI\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTime to relief of chest pain\u0026thinsp;\u0026gt;\u0026thinsp;1 h\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSmoking History:\u003c/p\u003e\u003cp\u003e1: Never smoker\u003c/p\u003e\u003cp\u003e2: Former smoker\u003c/p\u003e\u003cp\u003e3: Current smoker\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCategorical variable (ordinal scale)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eECG, electrocardiogram; MI, myocardial infarction; bpm, beats per minute; mmHg, millimeters of mercury.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e2.3. Model development\u003c/h2\u003e\u003cp\u003ePrevious studies have reported that flexible nonlinear approaches, such as neural networks, did not outperform logistic regression models in terms of predictive accuracy when applied to the GUSTO-I trial dataset [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Similarly, studies using other large-scale cardiovascular disease databases have concluded that machine learning approaches offered no clear advantage in predicting short-term mortality [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Based on these findings, this study primarily employed logistic regression models incorporating four approaches: without regularization, L1 regularization, L2 regularization, and Elastic Net.\u003c/p\u003e\u003cdiv id=\"Sec6\" class=\"Section3\"\u003e\u003ch2\u003e2.3.1. L1 regularization method\u003c/h2\u003e\u003cp\u003eThe L1 regularization method (L1), also known as the least absolute shrinkage and selection operator (LASSO), is commonly used for variable selection. By adding the sum of the absolute values of the regression coefficients to the loss function of logistic regression, L1 induces sparsity, meaning that some regression coefficients shrink to exactly zero. Consequently, it allows for both feature selection and coefficient shrinkage simultaneously.\u003c/p\u003e\u003cp\u003eThe L1 estimator \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\beta\\:}}_{L1}\\)\u003c/span\u003e\u003c/span\u003e is obtained by minimizing the following objective function [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{\\widehat{\\beta\\:}}_{L1}=\\text{arg}\\underset{\\beta\\:}{\\text{m}\\text{i}\\text{n}}\\left\\{-{\\sum\\:}_{i=1}^{n}\\left[{Y}_{i}\\text{l}\\text{o}\\text{g}\\left({\\:\\pi\\:}_{i}\\right)+\\left(1-{Y}_{i}\\right)\\text{l}\\text{o}\\text{g}\\left(1-{\\pi\\:}_{i}\\right)\\right]+\\lambda\\:{\\sum\\:}_{j=1}^{p}\\left|{\\beta\\:}_{j}\\right|\\right\\},$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Y}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the binary outcome variable for the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e-th case, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{X}_{i}={\\left({X}_{i1},\\:{X}_{i2},\\:\\dots\\:,\\:{X}_{ip}\\right)}^{T}\\)\u003c/span\u003e\u003c/span\u003e represents the predictor variables for the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e-th case. The probability of mortality given \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{X}_{i}\\)\u003c/span\u003e\u003c/span\u003e is modeled as\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:{\\pi\\:}_{i}=\\frac{1}{{1+\\text{e}\\text{x}\\text{p}(-(\\beta\\:}_{0}+\\sum\\:_{j=1}^{p}{\\beta\\:}_{j}{X}_{ij}\\left)\\right)},$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\lambda\\:\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e is the regularization parameter that controls the complexity of the model.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section3\"\u003e\u003ch2\u003e2.3.2. L2 regularization method\u003c/h2\u003e\u003cp\u003eThe L2 regularization method (L2), also known as Ridge regression, incorporates the sum of the squared regression coefficients into the loss function of logistic regression. Unlike L1, L2 does not perform feature selection because it shrinks the regression coefficients toward zero without making them exactly zero. Instead, it distributes the regularization effect across all features, preventing an excessive influence from any single predictor.\u003c/p\u003e\u003cp\u003eThe L2 estimator \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\beta\\:}}_{L2}\\)\u003c/span\u003e\u003c/span\u003e is obtained by minimizing the following objective function [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]:\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:{\\widehat{\\beta\\:}}_{L2}=\\text{arg}\\underset{\\beta\\:}{\\text{min}}\\left\\{-{\\sum\\:}_{i=1}^{n}\\left[{Y}_{i}\\text{l}\\text{o}\\text{g}\\left({\\:\\pi\\:}_{i}\\right)+\\left(1-{Y}_{i}\\right)\\text{l}\\text{o}\\text{g}\\left(1-{\\pi\\:}_{i}\\right)\\right]+\\lambda\\:{\\sum\\:}_{j=1}^{p}{\\beta\\:}_{j}^{2}\\right\\}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section3\"\u003e\u003ch2\u003e2.3.3. Elastic Net regularization method\u003c/h2\u003e\u003cp\u003eElastic Net constructs a loss function that combines both L1 and L2 regularization, introducing a mixing parameter \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\alpha\\:\\)\u003c/span\u003e\u003c/span\u003e that adjusts the balance between the two penalties. This approach simultaneously enables feature selection and coefficient shrinkage, mitigating the issue in which LASSO tends to select only one of a set of highly correlated variables, whereas Ridge retains all features.\u003c/p\u003e\u003cp\u003eThe Elastic Net estimator \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\beta\\:}}_{elastic}\\)\u003c/span\u003e\u003c/span\u003e is obtained by minimizing the following function [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]:\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$$\\:{\\widehat{\\beta\\:}}_{elastic}=\\text{arg}\\underset{\\beta\\:}{\\text{min}}\\left\\{-{\\sum\\:}_{i=1}^{n}\\left[{Y}_{i}\\text{l}\\text{o}\\text{g}\\left({\\:\\pi\\:}_{i}\\right)+\\left(1-{Y}_{i}\\right)\\text{l}\\text{o}\\text{g}\\left(1-{\\pi\\:}_{i}\\right)\\right]+\\lambda\\:{\\sum\\:}_{j=1}^{p}\\left(\\alpha\\:{\\beta\\:}_{j}^{2}+\\left(1-\\alpha\\:\\right)\\left|{\\beta\\:}_{j}\\right|\\right)\\right\\},$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\alpha\\:\\in\\:\\:\\left[0,\\:1\\right]\\)\u003c/span\u003e\u003c/span\u003e determines the relative contribution of L1 and L2 regularization. Setting \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\alpha\\:=1\\)\u003c/span\u003e\u003c/span\u003e corresponds to pure Ridge regression, whereas \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\alpha\\:=0\\)\u003c/span\u003e\u003c/span\u003e corresponds to pure LASSO. Intermediate values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\alpha\\:\\)\u003c/span\u003e\u003c/span\u003e provide a trade-off between feature selection and coefficient stability.\u003c/p\u003e\u003cp\u003eThe regularization parameter \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\lambda\\:\\)\u003c/span\u003e\u003c/span\u003e was selected within the range of 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e to 10\u003csup\u003e3\u003c/sup\u003e using five-fold cross-validation, where the value that achieved the highest area under the receiver operating characteristic curve (AUROC) on the validation dataset was chosen. For Elastic Net, in addition to the regularization parameter \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\lambda\\:\\)\u003c/span\u003e\u003c/span\u003e, the mixing parameter \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\alpha\\:\\)\u003c/span\u003e\u003c/span\u003e was selected from three candidate values: 0.1, 0.5, and 0.9, by identifying the optimal combination. Furthermore, all predictor variables were standardized before being input into the models.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e2.4. Federated learning algorithm\u003c/h2\u003e\u003cp\u003eIn federated learning, the model update process is performed iteratively between the clients, who train the models and update their parameters using local data from their respective regions, and the server, which aggregates the regression coefficients updated by the clients to construct and distribute a global model. The updating process follows the following steps:\u003c/p\u003e\u003cp\u003e\u003col\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eThe server randomly selects a subset of clients and distributes the global model.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eEach client updates the global model using their respective local data and sends the updated model back to the server.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eThe server aggregates the regression coefficients updated by the clients and utilizes them to generate a new global model.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e\u003cp\u003eIn this study, we employed Federated Averaging (FedAvg), a fundamental algorithm in federated learning, to aggregate the regression coefficients. In FedAvg, the regression coefficients are aggregated using a weighted average based on the sample size of each client [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThe global model is updated using the following weighted aggregation formula:\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e\n$$\\:{w}_{t+1}\\leftarrow\\:\\sum\\:_{k\\in\\:{S}_{t}}\\frac{{n}_{k}}{n}{w}_{t+1}^{\\left(k\\right)},\\:\\:\\:\\:\\:n=\\sum\\:_{k\\in\\:{S}_{t}}{n}_{k}$$\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:t\\)\u003c/span\u003e\u003c/span\u003e denotes the round number for updating the regression coefficients, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{S}_{t}\\)\u003c/span\u003e\u003c/span\u003e represents the set of clients selected in round \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:t\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:n\\)\u003c/span\u003e\u003c/span\u003e is the total number of samples across all clients, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{n}_{k}\\)\u003c/span\u003e\u003c/span\u003e corresponds to the number of samples held by the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:k\\)\u003c/span\u003e\u003c/span\u003e-th client, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{t+1}^{\\left(k\\right)}\\)\u003c/span\u003e\u003c/span\u003e denotes the regression coefficients of the model updated by client \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:k\\)\u003c/span\u003e\u003c/span\u003e using its local dataset in round \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:t+1\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{t+1}\\)\u003c/span\u003e\u003c/span\u003e represents the regression coefficients of the global model at round \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:t+1\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eIn this study, the total number of update rounds for the regression coefficients was set to ten. Although federated learning typically selects a random subset of clients in each round for model aggregation, this approach results in an unstable convergence. To address this issue, we incorporated the regression coefficients from all 16 clients (regions) in each round for model aggregation.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e2.5. Model evaluation metrics and procedures\u003c/h2\u003e\u003cp\u003eWe evaluated discriminative performance using the AUROC, and assessed calibration via the calibration slope and intercept (calibration-in-the-large). Although the area under the precision\u0026ndash;recall curve (AUPRC) is sometimes recommended for class-imbalanced outcomes such as mortality, it ignores true negatives, is sensitive to outcome prevalence, and is less straightforward to compare across populations; moreover, because precision equals positive predictive value, it partially reflects threshold-dependent clinical utility rather than pure ranking-based discrimination, thereby limiting its value as a primary evaluation metric for clinical prediction models [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. Accordingly, we report AUROC and do not report AUPRC in this study. First, for within-region validation, we performed stratified five-fold cross-validation to develop and validate local models within each region. The data were stratified by outcome status to ensure a consistent outcome ratio across folds. In addition, the centralized and federated learning models, trained using all available data, were evaluated on the test set of each fold and compared with the local models. To ensure full formal consistency, the centralized and federated models should ideally be trained with exclusion of the one-fifth not used for training by the local models. One-fifth of 16 regions amounts to only about 1.25% of the total data. Indeed, preliminary analyses showed negligible differences in performance when using a simpler approach that trained centralized and federated models on the entire dataset. Therefore, for within-region validation, we report the validation results obtained using centralized and federated models trained on the full dataset. Next, for between-region validation to assess variability across regions, we applied locally developed models to other regions and compared their predictive performances with those of the centralized and federated models. For this evaluation, the global models were developed by excluding the region used for validation\u0026mdash;that is, each model was trained on data from all 15 other regions. For this evaluation, point estimates and 95% confidence intervals were calculated for each target region. The confidence intervals were derived from 1,000 bootstrap resamples.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e2.6. Model interpretability\u003c/h2\u003e\u003cp\u003eFirst, we computed the standardized regression coefficients for each model. Rather than presenting them individually, we performed principal component analysis (PCA)\u0026mdash;a dimensionality-reduction technique\u0026mdash;on the coefficient matrix (models \u0026times; predictors) to because direct inspection of full coefficient vectors is high-dimensional and obscures between-model similarities. We then plotted the first two principal components to visualize the relative similarity among the models.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003e2.7. Analytical software and packages\u003c/h2\u003e\u003cp\u003eAll analyses were conducted using Python (version 3.8.10). Model development and evaluation were performed using scikit-learn, whereas federated learning was implemented using the Flower framework. The statistical code is provided in the Supplemental Methods section of the Supplemental Material.\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\u003ch2\u003e3.1. Baseline characteristics\u003c/h2\u003e\u003cp\u003eIn the GUSTO dataset, 2,851 (7.0%) of 40,830 patients died within 30 days. Region 16 had the fewest cases (1,231 patients), whereas Region 12 had the most cases (4,352 patients). Among all regions, Region 13 had the lowest (5.3%), and Region 6 had the highest mortality rate (8.4%). Although no significant differences were observed in terms of age or sex, certain regions exhibited notable variations in the prevalence of risk factors and medical histories (Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\u003ch2\u003e3.2. AUROCs in development regions\u003c/h2\u003e\u003cp\u003eTables\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and S2 present the mean and standard deviation of the AUROC values for the local models developed within each region, as well as for the centralized and federated learning models, evaluated on the test data using stratified five-fold cross-validation. Except for Region 10, the AUROC of the centralized and federated learning models exceeded those of the local models across all regions. Notably, in Region 16, the AUROC of the centralized and federated learning models was more than 0.04 higher than that of the cross-validated local model. The centralized and federated learning models achieved the highest AUROC of 0.847 in Region 1, whereas the lowest AUROC of 0.779 was observed in Region 16. This trend remained consistent, regardless of the regularization application (L1, L2, or Elastic Net). Moreover, the AUROC values for the validation of the centralized and federated learning models were nearly identical.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003e\u003cb\u003eCross-validated AUROC comparison of local, centralized, and federated L1-regularized logistic regression models\u003c/b\u003e Mean (SD) AUROC across stratified 5-fold cross-validation within each region. Local models were trained and validated within their development region using five folds. Centralized and federated global models were trained on the full dataset and evaluated on the same held-out folds for comparability. L1 denotes the lasso penalty. Higher AUROC indicates better discrimination. Results for unpenalized, L2 (ridge), and Elastic Net models are reported in Table S2.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRegion, n\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eEvent (%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eLocal\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eCentralized global\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eFL global\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRegion 1, n\u0026thinsp;=\u0026thinsp;2188\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e6.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.846 (0.048)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.847 (0.044)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.847 (0.044)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRegion 2, n\u0026thinsp;=\u0026thinsp;2952\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e7.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.813 (0.044)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.817 (0.043)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.817 (0.043)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRegion 3, n\u0026thinsp;=\u0026thinsp;2030\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e8.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.813 (0.038)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.828 (0.041)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.828 (0.041)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRegion 4, n\u0026thinsp;=\u0026thinsp;2876\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e7.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.832 (0.022)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.837 (0.023)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.836 (0.022)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRegion 5, n\u0026thinsp;=\u0026thinsp;1909\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e7.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.821 (0.036)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.823 (0.035)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.824 (0.036)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRegion 6, n\u0026thinsp;=\u0026thinsp;1585\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e8.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.773 (0.047)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.790 (0.032)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.790 (0.032)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRegion 7, n\u0026thinsp;=\u0026thinsp;3150\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e6.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.807 (0.034)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.815 (0.027)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.814 (0.027)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRegion 8, n\u0026thinsp;=\u0026thinsp;2916\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e6.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.826 (0.041)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.834 (0.047)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.834 (0.047)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRegion 9, n\u0026thinsp;=\u0026thinsp;3123\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e7.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.829 (0.019)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.830 (0.022)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.831 (0.022)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRegion 10, n\u0026thinsp;=\u0026thinsp;1717\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e5.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.811 (0.048)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.809 (0.032)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.810 (0.031)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRegion 11, n\u0026thinsp;=\u0026thinsp;2491\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e7.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.830 (0.034)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.833 (0.038)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.832 (0.037)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRegion 12, n\u0026thinsp;=\u0026thinsp;4352\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e6.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.826 (0.034)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.831 (0.032)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.830 (0.031)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRegion 13, n\u0026thinsp;=\u0026thinsp;2297\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e5.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.821 (0.066)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.836 (0.047)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.835 (0.049)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRegion 14, n\u0026thinsp;=\u0026thinsp;3437\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e7.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.808 (0.041)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.817 (0.046)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.817 (0.046)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRegion 15, n\u0026thinsp;=\u0026thinsp;2576\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e6.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.786 (0.036)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.803 (0.036)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.803 (0.037)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRegion 16, n\u0026thinsp;=\u0026thinsp;1231\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e8.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.733 (0.071)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.779 (0.086)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.779 (0.085)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eAUROC: area under the receiver operating characteristic curve; n: number of patients in each region; Local: model trained on its own development region; Centralized global: global model trained on pooled data; FL global: global model developed with federated learning. The data are presented as the mean (standard deviation) of the AUROC on the validation data in a stratified 5-fold cross-validation for each region.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e\u003ch2\u003e3.3. Performance in other regions\u003c/h2\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents the AUROC values for L1 models trained in each region and applied to other regions, as well as for centralized L1 models trained on pooled data and federated L1 models. Overall, both the centralized and federated learning models outperformed the local models in terms of external AUROC, and this trend remained consistent regardless of the application of regularization (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e2\u003c/span\u003e, Figure \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e to 3). However, the performance of the local models varied considerably. Notably, the model developed using Region 10 exhibited a substantial decrease in discrimination when applied to other regions. Figures\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e3\u003c/span\u003e show the calibration slope and intercept for each approach, respectively. In particular, the model developed using Region 16 showed substantial deviations in the slope and intercept (Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e3\u003c/span\u003e, Figures S4 to 9). Compared with the local L1 models, the centralized and federated L1 models exhibited more stable calibration. Results were similar with other modeling strategies (unpenalized, L2, or Elastic Net).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e\u003ch2\u003e3.4. Standardized regression coefficients of each model\u003c/h2\u003e\u003cp\u003eThe centralized models trained on pooled data and the federated learning models exhibited similar standardized regression coefficient distributions according to PCA (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e4\u003c/span\u003e). In contrast, certain regions, such as Regions 10 and 16, displayed quite distinct coefficient distributions, deviating from those observed in other regions.\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThis comparative study confirmed the promise of federated learning approaches for prediction model development and validation. We compared local models with global models, including a centralized model trained on pooled data and a federated learning model, on the following scenarios: (1) application within their respective development regions and (2) application of models developed in one region to other regions. The results showed that the discriminatory performances and calibrations of the centralized and federated learning models were nearly identical, which was further supported by the similarities in their regression coefficients. This result was found for unpenalized and penalized estimation approaches. Additionally, in the local cross-validation, the global models outperformed the local models in most regions. Moreover, when the local models were applied to other regions, substantial variability was observed, with some regional models exhibiting markedly poor discrimination and calibration.\u003c/p\u003e\u003cdiv id=\"Sec19\" class=\"Section2\"\u003e\u003ch2\u003e4.1 Predictive performance for the GUSTO-I dataset\u003c/h2\u003e\u003cp\u003eMultiple algorithms were previously compared to unpenalized logistic regression in the GUSTO dataset, including various nonlinear and flexible models. The unpenalized logistic regression model achieved the highest discrimination performance, with an AUROC of 0.820 [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Therefore, we adopted logistic regression modeling for the analysis in this study. The advanced logistic regression models incorporating L1 and L2 regularization showed minimal differences in discrimination performance compared to the unregularized model, suggesting that conventional maximum likelihood estimation may be sufficient in this setting with relatively large sample sizes by region. Another study compared multiple logistic regression models and confirmed that the model developed using the GUSTO-I dataset achieved an AUROC of approximately 0.82 [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. In the same study, models developed in other cohorts showed slightly lower discriminative performance, with AUROCs ranging from 0.76\u0026ndash;0.78 when applied to the GUSTO-I dataset, with some improvement by re-estimating the regression coefficients. Similarly, in our study, the L1 model developed using Region 16 of the GUSTO dataset achieved a high AUROC of 0.849 (0.812\u0026ndash;0.882) when applied to Region 1. However, it exhibited poor calibration. These findings further underscore the importance of caution when transporting local models to different geographical regions.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec20\" class=\"Section2\"\u003e\u003ch2\u003e4.2 Utility of Federated Learning\u003c/h2\u003e\u003cp\u003eIf the sample size is large, using a model developed in a specific region within that same region is the most rational choice at the practical implementation stage of clinical prediction models given its superior accuracy. This is because the model optimally reflects the characteristics of the data from the development region. However, securing a sufficient sample size is often challenging for a specific region or hospital. In our comparison of local and global models, the local models failed to outperform the global models in terms of the AUROC on the test data. Furthermore, when applying local models outside their development regions, factors such as covariate shift, target shift, and concept drift may lead to a decline in predictive performance, necessitating careful consideration of these risks [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. To address the challenges associated with the limitations of applying local models beyond their development regions, the TRIPOD\u0026thinsp;+\u0026thinsp;AI guidelines recommend reporting the impact of heterogeneity on predictive performance, and emphasize that reports should ideally include information from diverse geographic regions [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eAs demonstrated in this study, constructing prediction models using data from multiple regions may enable stable accuracy across different regions. Privacy constraints may however hamper the continuous collection of clinical data from multiple institutions across national borders. Federated learning, which implies sharing only model parameters instead of raw data, offers a promising approach for mitigating privacy risks. The performance of the federated learning models was comparable to that of the centralized models trained on pooled data, which is consistent with the findings of previous studies [\u003cspan additionalcitationids=\"CR5 CR6 CR7\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Overall, our results for predicting mortality in patients with AMI confirm that federated learning has huge potential for the pipeline of development, validation, and updating of prediction models while preserving data privacy [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e].\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec21\" class=\"Section2\"\u003e\u003ch2\u003e4.3 Limitations\u003c/h2\u003e\u003cp\u003eIn this study, the FedAvg approach was adopted for federated learning, although variants can be considered. In addition, the GUSTO-I data were obtained from a randomized controlled trial with pre-specified data collection and strict definitions. This may have contributed to limited heterogeneity between locally developed models. Federated learning with observational data may show larger heterogeneity, and hence, more potential for local learning methods.\u003c/p\u003e\u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eFederated learning can achieve predictive performance similar to that of a model trained on centralized data. Both federated and centralized global models may exhibit superior predictive performance compared to models developed using data from a single setting. Federated learning allows the development of prediction models while preserving data privacy and eliminating the need for direct data sharing, making it an essential technology for the cross-border use of medical data.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cdiv class=\"DefinitionList\"\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003eAI\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003eartificial intelligence\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003eAMI\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003eacute myocardial infarction\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003eAUPRC\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003earea under the precision\u0026ndash;recall curve\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003eAUROC\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003earea under the receiver operating characteristic curve\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003eCOVID-19\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003ecoronavirus disease 2019\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003eCT\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003ecomputed tomography\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003eFedAvg\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003eFederated Averaging\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003eGUSTO-I\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003eGlobal Utilization of Streptokinase and Tissue Plasminogen Activator for Occluded Coronary Arteries (trial)\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003eL1\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003eL1 regularization (lasso penalty)\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003eL2\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003eL2 regularization (ridge penalty)\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003eLASSO\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003eleast absolute shrinkage and selection operator\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003ePCA\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003eprincipal component analysis\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003eTRIPOD\u0026thinsp;+\u0026thinsp;AI\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003eTransparent Reporting of a multivariable prediction model for Individual Prognosis Or Diagnosis\u0026thinsp;+\u0026thinsp;Artificial Intelligence\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable. This study is a secondary analysis of the publicly available, de-identified GUSTO-I randomized trial dataset (enrollment 1990–1993); no new participant recruitment or intervention assignment was undertaken. The original trial obtained ethics approval at participating centers with informed consent from all participants (see primary trial publications).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eClinical trial number\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable. This manuscript contains no individual person’s data in any form (including images, videos, or identifiable details).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe GUSTO-I dataset is publicly available from the Duke Clinical Research Institute: It can be loaded into R using the following command: load(url(\"http://hbiostat.org/data/repo/gusto.rda\")).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNone.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study was supported by a Grant-in-Aid for Scientific Research (JSPS KAKENHI Grant Number: JP25H01083) from the Japanese Society for the Promotion of Science (JSPS).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCRediT authorship contribution statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eKoutraou\u003c/strong\u003e\u003cstrong\u003eMatsumoto\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e Writing\u0026nbsp;– original draft, Methodology, Software, Formal analysis, Data curation, Conceptualization.\u0026nbsp;\u003cstrong\u003eYuta\u003c/strong\u003e\u003cstrong\u003eNakamura\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e Software, Formal analysis, Data curation.\u0026nbsp;\u003cstrong\u003eMasahiro\u003c/strong\u003e\u003cstrong\u003eKamouchi\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e Writing\u0026nbsp;–\u0026nbsp;review \u0026amp; editing, Funding acquisition,\u0026nbsp;Supervision. \u003cstrong\u003eEwout Steyerberg:\u003c/strong\u003e Writing – review \u0026amp; editing, Methodology, Conceptualization.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe would like to thank the GUSTO investigators for providing access to the GUSTO-I dataset for our analysis.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eCollins GS, Moons KGM, Dhiman P, Riley RD, Beam AL, Van Calster B, et al. TRIPOD+AI statement: Updated guidance for reporting clinical prediction models that use regression or machine learning methods. BMJ. 2024;385:e078378. https://doi.org/10.1136/bmj-2023-078378.\u003c/li\u003e\n\u003cli\u003eBinuya MAE, Engelhardt EG, Schats W, Schmidt MK, Steyerberg EW. Methodological guidance for the evaluation and updating of clinical prediction models: A systematic review. BMC Med Res Methodol. 2022;22:316. https://doi.org/10.1186/s12874-022-01801-8.\u003c/li\u003e\n\u003cli\u003eMcMahan HB, Moore E, Ramage D, Hampson S, Ag\u0026uuml;era y Arcas B. Communication-efficient learning of deep networks from decentralized data. Proceedings of the 20th international conference on artificial intelligence and statistics (AISTATS). 2017;54:1273\u0026ndash;82.\u003c/li\u003e\n\u003cli\u003eDou Q, So TY, Jiang M, Liu Q, Vardhanabhuti V, Kaissis G, et al. Federated deep learning for detecting COVID-19 lung abnormalities in CT: A privacy-preserving multinational validation study. NPJ Digit Med. 2021;4:60. https://doi.org/10.1038/s41746-021-00431-6.\u003c/li\u003e\n\u003cli\u003eDayan I, Roth HR, Zhong A, Harouni A, Gentili A, Abidin AZ, et al. Federated learning for predicting clinical outcomes in patients with COVID-19. Nat Med. 2021;27:1735\u0026ndash;43. https://doi.org/10.1038/s41591-021-01506-3.\u003c/li\u003e\n\u003cli\u003eHaggenm\u0026uuml;ller S, Schmitt M, Krieghoff-Henning E, Hekler A, Maron RC, Wies C, et al. Federated learning for decentralized artificial intelligence in melanoma diagnostics. JAMA Dermatol. 2024;160:303\u0026ndash;11. https://doi.org/10.1001/jamadermatol.2023.5550.\u003c/li\u003e\n\u003cli\u003eFeng B, Shi J, Huang L, Yang Z, Feng ST, Li J, et al. Robustly federated learning model for identifying high-risk patients with postoperative gastric cancer recurrence. Nat Commun. 2024;15:742. https://doi.org/10.1038/s41467-024-44946-4.\u003c/li\u003e\n\u003cli\u003eLee GH, Shin S-Y. Federated learning on clinical benchmark data: Performance assessment. J Med Internet Res. 2020;22:e20891. https://doi.org/10.2196/20891.\u003c/li\u003e\n\u003cli\u003eLi S, Liu P, Nascimento GG, Wang X, Leite FRM, Chakraborty B, et al. Federated and distributed learning applications for electronic health records and structured medical data: A scoping review. J Am Med Inform Assoc. 2023;30:2041\u0026ndash;9. https://doi.org/10.1093/jamia/ocad170.\u003c/li\u003e\n\u003cli\u003eGUSTO investigators. An international randomized trial comparing four thrombolytic strategies for acute myocardial infarction. N Engl J Med. 1993;329:673\u0026ndash;82. https://doi.org/10.1056/NEJM199309023291001.\u003c/li\u003e\n\u003cli\u003eLee KL, Woodlief LH, Topol EJ, Weaver WD, Betriu A, Col J et al. Predictors of 30-day mortality in the era of reperfusion for acute myocardial infarction. Results from an international trial of 41,021 patients. GUSTO-I Investigators. Circulation. 1995;91:1659\u0026ndash;68. https://doi.org/10.1161/01.cir.91.6.1659.\u003c/li\u003e\n\u003cli\u003eEnnis M, Hinton G, Naylor D, Revow M, Tibshirani R. A comparison of statistical learning methods on the GUSTO database. Stat Med. 1998;17:2501\u0026ndash;8. https://doi.org/10.1002/(sici)1097-0258(19981115)17:21\u0026lt;2501::aid-sim938\u0026gt;3.0.co;2-m.\u003c/li\u003e\n\u003cli\u003eSteyerberg EW, Harrell FE, Jr., Borsboom GJ, Eijkemans MJ, Vergouwe Y, Habbema JD. Internal validation of predictive models: Efficiency of some procedures for logistic regression analysis. J Clin Epidemiol. 2001;54:774\u0026ndash;81. https://doi.org/10.1016/s0895-4356(01)00341-9.\u003c/li\u003e\n\u003cli\u003eSteyerberg EW, Borsboom GJJM, van Houwelingen HC, Eijkemans MJC, Habbema JDF. Validation and updating of predictive logistic regression models: A study on sample size and shrinkage. Stat Med. 2004;23:2567\u0026ndash;86. https://doi.org/10.1002/sim.1844.\u003c/li\u003e\n\u003cli\u003eSteyerberg EW, Eijkemans MJC, Boersma E, Habbema JDF. Applicability of clinical prediction models in acute myocardial infarction: A comparison of traditional and empirical Bayes adjustment methods. Am Heart J. 2005;150:920. https://doi.org/10.1016/j.ahj.2005.07.008.\u003c/li\u003e\n\u003cli\u003eSteyerberg EW, Eijkemans MJC, Boersma E, Habbema JDF. Equally valid models gave divergent predictions for mortality in acute myocardial infarction patients in a comparison of logistic regression models. J Clin Epidemiol. 2005;58:383\u0026ndash;90. https://doi.org/10.1016/j.jclinepi.2004.07.008.\u003c/li\u003e\n\u003cli\u003eSteyerberg EW, Vergouwe Y. Towards better clinical prediction models: seven steps for development and an ABCD for validation. Eur Heart J. 2014;35:1925\u0026ndash;31. https://doi.org/10.1093/eurheartj/ehu207.\u003c/li\u003e\n\u003cli\u003eSteyerberg EW. Clinical prediction models: A practical approach to development, validation, and updating. 2nd ed. Switzerland: Springer Nature; 2019. https://doi.org/10.1007/978-3-030-16399-0.\u003c/li\u003e\n\u003cli\u003eIba K, Shinozaki T, Maruo K, Noma H. Re-evaluation of the comparative effectiveness of bootstrap-based optimism correction methods in the development of multivariable clinical prediction models. BMC Med Res Methodol. 2021;21:9. https://doi.org/10.1186/s12874-020-01201-w.\u003c/li\u003e\n\u003cli\u003eNoma H, Shinozaki T, Iba K, Teramukai S, Furukawa TA. Confidence intervals of prediction accuracy measures for multivariable prediction models based on the bootstrap-based optimism correction methods. Stat Med. 2021;40:5691\u0026ndash;701. https://doi.org/10.1002/sim.9148.\u003c/li\u003e\n\u003cli\u003eRiley RD, Collins GS. Stability of clinical prediction models developed using statistical or machine learning methods. Biom J. 2023;65:e2200302. https://doi.org/10.1002/bimj.202200302.\u003c/li\u003e\n\u003cli\u003eRiley RD, Archer L, Snell KIE, Ensor J, Dhiman P, Martin GP, et al. Evaluation of clinical prediction models (part 2): How to undertake an external validation study. BMJ. 2024;384:e074820. https://doi.org/10.1136/bmj-2023-074820.\u003c/li\u003e\n\u003cli\u003eAustin PC, Lee DS, Steyerberg EW, Tu JV. Regression trees for predicting mortality in patients with cardiovascular disease: What improvement is achieved by using ensemble-based methods? Biom J. 2012;54:657\u0026ndash;73. https://doi.org/10.1002/bimj.201100251.\u003c/li\u003e\n\u003cli\u003eTibshirani R. Regression shrinkage and selection via the lasso. J R Stat Soc B. 1996;58:267\u0026ndash;88. https://doi.org/10.1111/j.2517-6161.1996.tb02080.x.\u003c/li\u003e\n\u003cli\u003eHoerl AE, Kennard RW. Ridge regression: Biased estimation for nonorthogonal problems. Technometrics. 1970;12:55\u0026ndash;67. https://doi.org/10.1080/00401706.1970.10488634.\u003c/li\u003e\n\u003cli\u003eSchaefer RL, Roi LD, Wolfe RA. A ridge logistic estimator. Commun Stat Theor Methods. 1984;13:99\u0026ndash;113. https://doi.org/10.1080/03610928408828664.\u003c/li\u003e\n\u003cli\u003eZou H, Hastie T. Regularization and variable selection via the elastic net. J R Stat Soc B. 2005;67:301\u0026ndash;20. https://doi.org/10.1111/j.1467-9868.2005.00503.x.\u003c/li\u003e\n\u003cli\u003eBen Van Calster, Gary S. Collins, Andrew J. Vickers, Laure Wynants, Kathleen F. Kerr, Lasai Barre\u0026ntilde;ada, et al. Performance evaluation of predictive AI models to support medical decisions: overview and guidance. arXiv. 2024;2412.10288 https://doi.org/10.48550/arXiv.2412.10288\u003c/li\u003e\n\u003cli\u003eSahiner B, Chen W, Samala RK, Petrick N. Data drift in medical machine learning: Implications and potential remedies. Br J Radiol. 2023;96:20220878. https://doi.org/10.1259/bjr.20220878\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"federated learning, acute myocardial infarction, clinical prediction model, clinical decision-making, mortality prediction","lastPublishedDoi":"10.21203/rs.3.rs-7454748/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7454748/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground\u003c/h2\u003e\u003cp\u003eFederated learning may reduce privacy risks by allowing each institution to retain its data while performing distributed prediction model training and validation. This study evaluated the performance of federated learning approaches in predicting 30-day mortality in patients with acute myocardial infarction (AMI).\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e\u003cp\u003eWe analyzed data from 40,830 patients with AMI across 16 regions in the GUSTO-I trial. Logistic regression models were developed using three approaches: (1) federated learning\u0026mdash; each institution trained a local model on its own data and transmitted regression coefficients to a central server for aggregation; (2) centralized learning\u0026mdash;individual patient data were centrally available for analysis; and (3) local modeling\u0026mdash;training of 16 local models. Each approach included logistic models without regularization and those with L1, L2, and Elastic Net regularization. Model performances were evaluated using the area under the receiver operating characteristic curve (AUROC) and calibration metrics.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e\u003cp\u003eWhen applied within their respective development regions using stratified five-fold cross-validation, the models achieved AUROC values ranging from 0.733 to 0.846, with local models consistently underperforming compared to the federated learning and centralized models. Applying local models to other regions led to substantial performance degradation, with some exhibiting markedly poor discrimination and calibration. Federated learning and centralized models exhibited stable performance across regions. The AUROC of the federated learning model was very similar to that of the centralized model (0.847 vs. 0.847) and demonstrated stable calibration. These findings were further supported by the similarity in the regression coefficients between the federated learning and centralized models, while coefficients varied by region.\u003c/p\u003e\u003ch2\u003eConclusion\u003c/h2\u003e\u003cp\u003eFederated learning enables privacy-preserving utilization of regional data while maintaining nearly identical predictive performance as centralized models. Further implementation is recommended for multi-institutional settings under data-sharing constraints.\u003c/p\u003e\u003ch2\u003eTrial registration:\u003c/h2\u003e\u003cp\u003eNot applicable; this is a secondary analysis of the GUSTO-I randomized trial (enrollment 1990\u0026ndash;1993) with no new participant enrollment or intervention assignment.\u003c/p\u003e","manuscriptTitle":"Federated learning enabled privacy-preserving data access for predicting 30-day mortality in acute myocardial infarction","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-22 09:25:00","doi":"10.21203/rs.3.rs-7454748/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"86eadb56-5b66-4161-98ff-db92a5812f91","owner":[],"postedDate":"September 22nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-29T16:24:49+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-22 09:25:00","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7454748","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7454748","identity":"rs-7454748","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}