Results

Baseline Characteristics of the Patients

The development cohort comprised four centers, with 5,718, 998, 912, and 543 patients initially enrolled, respectively. After applying exclusion criteria, 4,894, 920, 562, and 487 patients remained for analysis. The external validation center initially enrolled 373 patients, with 353 remaining after exclusions (Figure 1). Before imputation, substantial between‐center differences were observed in the distribution of key demographic, clinical, perioperative, and outcome variables across the five participating centers (Table S1). When pooling the data together, the training set consisted of 5,489 patients, and the internal validation set included 1,374 patients. The incidence of POD was 13.8% (756/5,489) in the training set, 13.8% (189/1,374) in the internal validation set, and 5.7% (20/353) in the external validation set (Table S2). Corresponding incidence rates of AKI were 5.3% (292/5,489), 5.3% (73/1,374), and 6.2% (22/353), respectively (Table S3).

FIGURE 1: Flowchart of dataset development for training, internal validation, and external validation.

POD Local Learning Models Based on Different ML Algorithms

The internal validation results of LLMs for predicting POD were evaluated across four centers using six different ML algorithms. Figure 2A presents the receiver operating characteristic (ROC) curves aggregated across the four centers together with the averaged area under the curve (AUC) values, showing that MLP achieved the highest mean AUC of 0.688 (95% CI: 0.567‐0.910), followed closely by logistic regression (LR) (AUC 0.682, 95% CI: 0.462‐0.858) and eXtreme gradient boosting (XGBoost) (AUC 0.674, 95% CI: 0.386‐0.801). Gradient boosting machine (GBM) showed the lowest mean performance with an AUC of 0.639 (95% CI: 0.365‐0.696). Figure S1 illustrates the AUC values for each ML method stratified by center, highlighting some variability in model performance across different centers. For example, Center 4 showed the highest individual AUC for multi‐layer perceptron (MLP) (0.752), while LR yielded the best performance in Center 1 (0.743). These findings indicate that MLP was among the most effective local models for predicting postoperative delirium across diverse clinical settings.

FIGURE 2: (A) Average ROC curves of POD LLMs based on different machine learning methods across four centers. (B) Internal validation ROC curves of POD FLMs. (C) External validation ROC curves of POD FLMs. (D) ROC curves of POD CLMs.

POD Prediction Models Based on FL

Subsequently, FLMs were developed to predict POD. These models were first validated on the pooled internal validation set, as shown in Figure 2B, where the FLMs demonstrated acceptable discrimination with AUC values ranging from 0.725 to 0.726. Figure 2C shows that performance remained consistent in the external validation cohort, with AUCs between 0.700 and 0.701. Further robustness assessment with 10‐fold cross‐validation (Table S4) confirmed stable performance across folds, with AUC values ranging from 0.634 to 0.710, accompanied by balanced accuracy, sensitivity, and specificity across the iterations. Together, these results highlight the effectiveness and generalizability of the FLMs in predicting POD across diverse datasets.

POD FLMs Compared With LLMs and CLMs

The trained FLMs were further evaluated on the internal validation sets of each center and compared with LLMs. As shown in Table 1, FLMs constructed using different aggregation strategies including FedAvg, FedLSD, and FedProx, generally showed numerically higher AUCs than the local models across the four centers. For example, in Center 1, FLMs achieved AUCs around 0.717‐0.718, compared to 0.703 for LLM. Similar trends were observed in Centers 2, 3, and 4, where FLMs also showed higher AUCs than LLMs. Sensitivity values were also improved in several centers with FLMs, particularly in Center 3 where federated models reached sensitivities of 0.944 compared to 0.556 for the local model. DeLong's test indicated that statistically significant differences in AUC between FLMs and LLMs were observed only in Center 3, with p values of 0.012 for FedAvg, 0.013 for FedLSD, and 0.012 for FedProx, whereas the comparisons in the other centers were not statistically significant. Overall, these results indicate that FLMs showed a consistent trend toward numerically improved discrimination compared with local models across centers.

Center | Model | Acc | Sensitivity | Specificity | AUC | p
1 | Local | 0.579 | 0.671 | 0.563 | 0.703 | 
FedAvg | 0.681 | 0.624 | 0.692 | 0.718 | 0.403
FedLSD | 0.682 | 0.631 | 0.692 | 0.717 | 0.413
FedProx | 0.682 | 0.624 | 0.693 | 0.717 | 0.408
2 | Local | 0.647 | 0.500 | 0.657 | 0.631 | 
FedAvg | 0.538 | 0.667 | 0.529 | 0.635 | 0.971
FedLSD | 0.533 | 0.667 | 0.523 | 0.640 | 0.949
FedProx | 0.538 | 0.667 | 0.529 | 0.634 | 0.978
3 | Local | 0.788 | 0.556 | 0.832 | 0.665 | 
FedAvg | 0.637 | 0.944 | 0.579 | 0.825 | 0.012
FedLSD | 0.646 | 0.944 | 0.589 | 0.820 | 0.013
FedProx | 0.637 | 0.944 | 0.579 | 0.825 | 0.012
4 | Local | 0.704 | 0.600 | 0.716 | 0.752 | 
FedAvg | 0.643 | 0.600 | 0.648 | 0.765 | 0.883
FedLSD | 0.612 | 0.600 | 0.614 | 0.772 | 0.786
FedProx | 0.643 | 0.600 | 0.648 | 0.766 | 0.883

Finally, using the centralized data from the four centers, we constructed POD CLMs based on the MLP algorithm. Figure 2D displays the ROC curves of the CLMs, demonstrating good predictive performance with an AUC of 0.732 (95% CI: 0.693‐0.769) on the internal validation set and 0.706 (95% CI: 0.599‐0.817) on the external validation set. Subsequently, we compared the CLMs with FLMs across the same internal and external validation cohorts (Table 2). The FLMs showed comparable AUCs to the CLMs in both datasets. DeLong's test indicated no statistically significant differences between the CLMs and any FLM, with all _p‐_values greater than 0.05.

Dataset | Model | Acc | Sensitivity | Specificity | AUC | AUC 95%CI | p
Internal Validation | Centralized | 0.726 | 0.608 | 0.745 | 0.732 | 0.693–0.769 | 
FedAvg | 0.684 | 0.640 | 0.691 | 0.725 | 0.684–0.760 | 0.542
FedLSD | 0.687 | 0.646 | 0.694 | 0.726 | 0.686–0.761 | 0.612
FedProx | 0.685 | 0.640 | 0.692 | 0.725 | 0.684–0.760 | 0.544
External Validation | Centralized | 0.629 | 0.650 | 0.628 | 0.706 | 0.599–0.817 | 
FedAvg | 0.632 | 0.750 | 0.625 | 0.701 | 0.580–0.813 | 0.908
FedLSD | 0.629 | 0.750 | 0.622 | 0.700 | 0.578–0.813 | 0.902
FedProx | 0.632 | 0.750 | 0.625 | 0.700 | 0.580–0.813 | 0.897

Moreover, DCA curves (Figure S2) showed that both CLMs and FLMs provided similar net clinical benefits across a range of threshold probabilities in internal (Figure S2A) and external validation sets (Figure S2B), suggesting comparable clinical utility. Calibration curves and quantitative calibration metrics showed broadly similar calibration patterns across the centralized and federated models (Figure S3 and Table S5). In internal validation, the calibration intercepts were close to 0 and the slopes were close to 1. In the external validation cohort, however, the model‐specific curves were generally below the ideal calibration line, and the negative calibration intercepts indicated systematic overestimation of POD risk. Overall, the FLMs showed discrimination and clinical utility comparable to the centralized model, while exhibiting similar but imperfect external calibration.

Additional post hoc reduced‐variable benchmark analyses for POD prediction showed that the full‐variable centralized benchmark model achieved higher AUCs than both the Age + American Society of Anesthesiologists (ASA) minimal model and the preoperative‐only model in the internal validation cohort (0.732 vs. 0.612 and 0.683, respectively) and in the external validation cohort (0.706 vs. 0.568 and 0.584, respectively) (Table S6).

POD SHAP Analysis Results

To further explore model interpretability and inter‐center heterogeneity, we compared SHAP summary plots across the three federated strategies within each development center and additionally included the SHAP summary plot of the centralized learning model (Figure S4). Across the four centers, surgery duration was consistently among the most influential predictors of POD, and age also ranked highly in most models. The core predictors were broadly stable across the three federated aggregation strategies within each center. By contrast, inter‐center heterogeneity was mainly reflected in the relative importance of secondary features, including intraoperative medications, surgical characteristics, functional indicators, and laboratory or physiologic variables. The centralized model showed a similar overall pattern, with age and surgery duration remaining dominant predictors.

AKI LLMs Based on Different ML Algorithms

Similar to the findings in POD prediction, MLP also demonstrated strong predictive performance with an average AUC of 0.763 (Figure 3A). Model performance varied across centers, with LR achieving the highest AUC in Center 3 (0.849) and XGBoost performing well in Center 1 (0.755) (Figure S5). Overall, these results indicate that MLP is among the most effective local models for AKI prediction in diverse clinical settings.

FIGURE 3: (A) Average ROC curves of AKI LLMs based on different machine learning methods across four centers. (B) Internal validation ROC curves of AKI FLMs. (C) External validation ROC curves of AKI FLMs. (D) ROC curves of AKI CLMs.

AKI Prediction Models Based on FL

Subsequently, FLMs were developed to predict AKI. The models achieved AUC values of 0.780 on the pooled internal validation set and demonstrated stable performance with AUCs between 0.740 and 0.741 on the external validation set (Figure 3B,C). Further robustness assessment via 10‐fold cross‐validation (Table S7) confirmed stable performance across folds, with AUC values ranging from 0.701 to 0.817. These findings indicate stable predictive performance of the FLMs for AKI prediction across diverse datasets.

AKI FLMs Compared With LLMs and CLMs

The trained FLMs were evaluated on each center's internal validation set and compared with LLMs (Table 3). FLMs constructed using different aggregation strategies, including FedAvg, FedLSD, and FedProx, showed numerically higher or similar AUCs compared with local models across the four centers. However, DeLong's test indicated that these differences were not statistically significant in any center.

Center | Model | Acc | Sensitivity | Specificity | AUC | p
1 | Local | 0.598 | 0.821 | 0.584 | 0.760 | 
FedAvg | 0.696 | 0.750 | 0.692 | 0.786 | 0.113
FedLSD | 0.696 | 0.768 | 0.691 | 0.787 | 0.101
FedProx | 0.695 | 0.750 | 0.691 | 0.786 | 0.113
2 | Local | 0.614 | 0.778 | 0.606 | 0.683 | 
FedAvg | 0.587 | 0.889 | 0.571 | 0.728 | 0.667
FedLSD | 0.587 | 0.778 | 0.577 | 0.724 | 0.694
FedProx | 0.587 | 0.889 | 0.571 | 0.728 | 0.670
3 | Local | 0.708 | 0.750 | 0.706 | 0.787 | 
FedAvg | 0.699 | 0.750 | 0.697 | 0.796 | 0.912
FedLSD | 0.690 | 0.750 | 0.688 | 0.796 | 0.883
FedProx | 0.690 | 0.750 | 0.688 | 0.794 | 0.912
4 | Local | 0.735 | 0.750 | 0.734 | 0.822 | 
FedAvg | 0.776 | 0.750 | 0.777 | 0.827 | 0.906
FedLSD | 0.776 | 0.750 | 0.777 | 0.827 | 0.906
FedProx | 0.776 | 0.750 | 0.777 | 0.827 | 0.906

Based on centralized data from four centers, AKI CLMs were constructed using the MLP algorithm, achieving AUCs of 0.786 (95% CI: 0.727‐0.837) internally and 0.733 (95% CI: 0.646‐0.815) externally (Figure 3D). Compared with FLMs, no significant differences in AUC were observed (all p > 0.05) (Table 4). DCA showed similar net clinical benefits between the centralized and federated models (Figure S6). The calibration curves and quantitative metrics also showed broadly similar patterns across models, although the calibration slopes indicated deviation from ideal calibration (Figure S7 and Table S8). The calibration intercepts were close to 0, whereas the calibration slopes were below 1, with broadly similar Brier scores across the centralized and federated models.

Dataset | Model | Acc | Sensitivity | Specificity | AUC | AUC 95%CI | p
Internal Validation | Centralized | 0.641 | 0.849 | 0.630 | 0.786 | 0.727–0.837 | 
FedAvg | 0.687 | 0.781 | 0.682 | 0.780 | 0.724–0.832 | 0.736
FedLSD | 0.686 | 0.767 | 0.682 | 0.780 | 0.725–0.832 | 0.729
FedProx | 0.686 | 0.767 | 0.681 | 0.780 | 0.724–0.831 | 0.735
External Validation | Centralized | 0.609 | 0.773 | 0.598 | 0.733 | 0.646–0.815 | 
FedAvg | 0.700 | 0.682 | 0.701 | 0.741 | 0.636–0.835 | 0.792
FedLSD | 0.703 | 0.682 | 0.704 | 0.740 | 0.637–0.834 | 0.820
FedProx | 0.700 | 0.682 | 0.701 | 0.741 | 0.637–0.835 | 0.791

Additional post hoc reduced‐variable benchmark analyses for AKI prediction showed that the full‐variable centralized benchmark model achieved higher AUCs than both the Age + ASA minimal model and the preoperative‐only model in the internal validation cohort (0.786 vs. 0.667 and 0.721, respectively) and in the external validation cohort (0.733 vs. 0.560 and 0.586, respectively) (Table S9).

AKI SHAP Analysis Results

Compared with POD, the SHAP patterns for AKI suggest a different feature structure. Across the four development centers, surgery duration, surgical department, ASA classification, age, and type of surgery were repeatedly identified as important predictors. The main SHAP patterns were broadly similar across the three federated aggregation strategies within each center, whereas inter‐center variation was more apparent in the ranking of secondary features, including hypertension, postoperative analgesia, surgical site, MET score, serum albumin, malignant tumor, and medication‐related variables (Figure S8). The centralized model showed a similar overall pattern, with surgery duration, ASA classification, age, type of surgery, and surgical department ranking highest.