Prediction of delayed graft function after deceased donor kidney transplantation: development and temporal validation in a single-center cohort

Abstract

Background

Delayed graft function (DGF) is a common complication of kidney transplantation and is associated with poor graft outcome. Accurate prediction of DGF is crucial for timely intervention and optimization of post-transplant management. Although predictive models for DGF have been reported, whether more complex supervised learning approaches provide meaningful incremental value over simpler and more interpretable models remains uncertain.

Methods

In this single-center study, we conducted a secondary analysis of an ongoing prospective cohort of consecutive kidney transplant recipients at our center, using data from patients enrolled between June 2023 and April 2025 as the development cohort. The models were validated in an independent retrospective cohort of consecutive recipients transplanted between January 2019 and May 2023. Nine individual supervised machine learning algorithms and 84 stacked ensemble models were constructed and compared. Predictors were selected in the development cohort using univariate analysis followed by bidirectional stepwise logistic regression (LR) based on the Akaike information criterion. Model performance in the validation cohort was assessed in terms of discrimination, calibration, and clinical utility. Model interpretation was supplemented using Shapley additive explanations.

Results

The development cohort and validation cohort included 140 and 314 kidney transplant recipients, respectively. Four donor-derived variables were retained in the final predictor set: donor body mass index, donation after circulatory death status, cold ischemia time, and donor terminal serum creatinine. Among the nine individual models, the LR model showed the best overall performance in the validation cohort, with an area under the receiver operating characteristic curve of 0.839. The best stacked ensemble model showed similar performance and did not provide meaningful incremental benefit over the LR model.

Conclusions

In conclusion, in this single-center cohort with independent temporally distinct validation, a parsimonious LR model based on four routinely available donor variables performed comparably to more complex supervised learning algorithms and stacked ensemble approaches for DGF prediction. These findings support the practical value of a simple and interpretable model for pre-transplant DGF risk stratification, although further external validation is needed before broader clinical application.

Supplementary information

The online version contains supplementary material available at 10.1186/s12882-026-04992-0.

Introduction

Kidney transplantation remains the preferred treatment for end-stage renal disease, offering better patient survival and quality of life than dialysis [1, 2]. Nevertheless, recipients frequently experience serious complications, including delayed graft function (DGF), allograft rejection, infections, post-transplant diabetes, metabolic bone disease, and malignancy [3].

DGF is the most common early complication following kidney transplantation, occurring in 20% to 50% of deceased-donor recipients [4]. It is clinically defined as the requirement for dialysis within the first week after transplantation [5, 6]. In addition to prolonging hospitalization and increasing dialysis dependence, DGF significantly increases the risk of acute rejection [7]. Furthermore, DGF is strongly associated with reduced long-term graft survival. Therefore, early identification of recipients at high risk of DGF may support perioperative risk stratification, clinical planning, and closer postoperative monitoring [8, 9].

Several prediction models for DGF have been developed over the past two decades. Irish et al. first proposed a DGF prediction model in 2003 and refined it in 2010 using 18 variables available at the time of transplantation [10, 11]. Subsequent models adopted simpler designs. For example, Chapal et al. used six variables, and Jeldres et al. developed a score based on five variables [12, 13]. More recently, more complex machine learning (ML) algorithms beyond classical logistic regression (LR), have been applied to DGF prediction [14]. Kawakita et al. used extreme gradient boosting (XGB) with 26 predictors and reported an area under the receiver operating characteristic curve (ROC-AUC) of 0.735 [15]. Jen et al. compared seven ML algorithms based on ten donor variables, with a neural network (NNet) model showing the best performance (ROC-AUC of 0.7595) [16].

In supervised ML algorithms, models are trained on labeled clinical data to learn the relationship between predictors and a known outcome, and then estimate the probability of that outcome in new patients. Different algorithms vary in complexity and interpretability. Some methods, such as LR, are relatively transparent and allow direct interpretation of predictor effects, whereas others, such as NNet and XGB, may capture more complex patterns but are often less intuitive for clinicians. In clinical prediction, limited interpretability may reduce ease of communication, clinician confidence, and practical implementation, particularly when simpler models achieve similar predictive performance. Therefore, although ML approaches have attracted increasing interest in clinical prediction, it remains uncertain whether more complex algorithms provide clinically meaningful advantages over simpler and more interpretable models in routine practice. In addition, the incremental value of stacked ensemble methods for DGF prediction has not been well characterized.

Therefore, we aimed to compare multiple supervised learning approaches for predicting DGF after deceased-donor kidney transplantation in a single-center cohort. Specifically, we evaluated whether increased algorithmic complexity, including more complex individual algorithms and stacked ensemble strategies, provided meaningful performance gains over a parsimonious LR model.

Methods

Study population

Model development used data from an ongoing single-center prospective cohort study at our transplant center (Chinese Clinical Trial Registry No. ChiCTR2300073100, registered on June 30, 2023; Ethics Approval No. 2023-KY-083-02) as a secondary analysis, including all patients who received kidney transplantation from deceased donors between June, 2023, and April, 2025 (development cohort). This ongoing prospective cohort, initiated on June, 2023, investigates the association between donor kidney quality and long-term transplant outcomes, and enrolls recipients before transplantation. Model validation used an independent retrospective cohort, including all patients who underwent deceased-donor kidney transplantation at our center between January 2019 and May 2023 (validation cohort). The exclusion criteria were: (1) donor age < 18 years; (2) patient death or graft loss within the first post-transplant week; (3) primary nonfunction and (4) dual kidney transplantation.

All grafts used in transplantation were obtained from deceased donors. No organs or tissues were obtained from prisoners. All donor grafts were donated to the Red Cross Society of Guangdong Province and allocated by the China Organ Transplant Response System.

The study protocol adhered to the Declaration of Helsinki. The present secondary analysis together with the retrospective validation cohort was approved by the Ethics Committee of Zhujiang Hospital of Southern Medical University (Ethics Approval No. 2025-KY-263-01).

Data collection and variable definition

The candidate clinical variables included recipient factors (sex, age at transplantation, body mass index [BMI], pre-transplant dialysis modality, history of diabetes mellitus, induction therapy, implantation surgery duration, number of human leukocyte antigen [HLA] mismatches at the A, B, and DR loci, prior history of transplantation, and panel reactive antibody [PRA] level) and donor factors (sex, age at donation, BMI, donor-to-recipient body weight ratio, cause of death, donor type, cold ischemia time [CIT], and pre-donation serum creatinine level).

Deceased donor type was classified as donation after circulatory death (DCD) or donation after brain death (DBD) [17]. DGF was defined as the need for dialysis during the first post-transplant week [5, 6]. Patient death was defined as all-cause mortality, and graft loss was defined as return to permanent dialysis or the need for retransplant [18].

Model development

Exploratory univariate analyses were performed in the development cohort, and variables with p < 0.05 were entered into a bidirectional stepwise LR procedure using the Akaike information criterion (AIC) to derive the final predictor set. Nine supervised ML algorithms were employed to predict DGF, including decision tree (DT) [19], LR, naive bayes (NB) [20], random forest (RF) [21], k-nearest neighbor (KNN) [22], support vector machine (SVM) [23], elastic net regression (ENet) [24], NNet [25], and XGB [26]. The LR model was fitted without regularization and followed the same preprocessing and evaluation procedures as the other models. For the remaining eight models, hyperparameters were tuned in the development cohort using a grid search with 5-fold cross-validation [27].

To further explore whether increased model complexity improved predictive performance, we also evaluated stacked ensemble models [28, 29]. In this framework, predicted probabilities from multiple base learners were used as inputs for a LR meta-learner. We enumerated 84 unique combinations of three base learners from the nine candidate algorithms and trained the corresponding meta-learners using the development cohort only. The ensemble analysis was exploratory and intended to assess the incremental value of stacking relative to simpler single-model approaches.

Performance comparison

Model performance was evaluated in the validation cohort. Discrimination was assessed by the ROC-AUC. For each individual model, the ROC-AUC and its 95% confidence interval (CI) were calculated from the predicted probabilities in the validation cohort using the DeLong method. We also calculated the area under the precision-recall curve (PR-AUC) to account for class imbalance. Additional metrics included accuracy, balanced accuracy, sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), and F1-score. The optimal probability cutoff for classification was determined by maximizing the Youden index. Calibration was evaluated using calibration plots and quantified by the Brier score, calibration intercept, and calibration slope. We also performed decision curve analysis (DCA) to assess clinical utility by estimating the net benefit across a range of threshold probabilities for intervention.

Model explanation

To improve interpretability and facilitate visualization of model predictions, we applied Shapley additive explanations (SHAP) to the final model in the validation cohort [30]. SHAP values quantify the extent to which each predictor shifts the model output from a baseline (expected prediction) to the individual’s predicted risk, providing a consistent and locally accurate measure of feature importance. In the present study, SHAP was used as a supplementary explanatory tool to visualize both global feature importance and patient-level prediction decomposition.

Statistical analysis

All analyses were performed using R version 4.5.1. Continuous variables were assessed for normality using the Shapiro-Wilk test. Normally distributed variables were presented as mean ± standard deviation (SD) and compared using the Student’s t-test. Non-normally distributed variables were expressed as medians (interquartile range, IQR) and analyzed using the Mann-Whitney U test. Categorical variables were reported as numbers (percentages) and compared using Pearson’s chi-square or Fisher’s exact tests, as appropriate. All statistical tests were two-sided, and statistical significance was set at p-values < 0.05.

Results

Patient population

The study design is illustrated in Fig. 1. The development cohort included 140 recipients, 67 (47.9%) of whom developed DGF. The validation cohort included 314 recipients, 159 (50.6%) of whom developed DGF.

Fig. 1.

Schematic overview of model development and temporal validation for DGF prediction after deceased-donor kidney transplantation. The workflow includes cohort assembly, candidate predictor evaluation in the development cohort, development and comparison of multiple supervised learning models, temporal validation, and supplementary model-interpretation analysis. Abbreviations: DGF, delayed graft function; ML, machine learning; KT, kidney transplantation; CIT, cold ischemia time; DCD, donation after circulatory death; BMI, body mass index; LR, logistic regression; ROC-AUC, area under the receiver operating characteristic curve; PR-AUC, area under the precision recall curve; NPV, negative predictive value; PPV, positive predictive value

The baseline demographic and clinical characteristics of the development cohort are presented in Table 1. Univariate analysis revealed significant associations between DGF and the following factors: DCD donors (25.4% [17/67] vs. 11.0% [8/73]; p = 0.026), prolonged CIT (median, 13.4 h [IQR, 11.4 - 20.5] vs. 10.6 h [IQR, 7.9 - 13.7]; p < 0.001), elevated donor BMI (median, 24.1 kg/m² [IQR, 22.4 - 25.6] vs. 21.4 kg/m² [IQR, 20.8 - 23.9]; p < 0.001), and increased pre-donation serum creatinine levels (median, 191 μmol/L [IQR, 123 - 309.3] vs. 114 μmol/L [IQR, 83 - 152]; p < 0.001). These four variables were subsequently entered into a bidirectional stepwise LR procedure based on AIC in the development cohort. The model retaining all four predictors had the lowest AIC (144.58) among the candidate models and was therefore used for subsequent model development.

Table 1.

Demographics and clinical characteristics of recipients and donors in the training set

Variable	Non-DGF (n = 73)	DGF (n = 67)	P
Recipients
Prior transplantation, n (%)	9 (12.3)	8 (11.9)	0.944
Pretransplant PRA ≥ 10%, n (%)	11 (15.1)	7 (10.4)	0.415
History of diabetes mellitus, n (%)	12 (16.4)	10 (14.9)	0.806
Sex, n (%)			0.189
Female	33 (45.2)	23 (34.3)
Male	40 (54.8)	44 (65.7)
Induction therapy, n (%)			1.000
Basiliximab	13 (17.8)	11 (16.4)
Lymphocyte depleting	50 (68.5)	47 (70.1)
Basiliximab + Lymphocyte depleting	7 (9.6)	7 (10.4)
No biological agents	3 (4.1)	2 (3.0)
Pretransplant dialysis, n (%)			0.163
Hemodialysis	61 (83.6)	51 (76.1)
Peritoneal dialysis	10 (13.7)	15 (22.4)
Peritoneal dialysis + Hemodialysis	2 (2.7)	0 (0)
Preemptive transplant	0 (0)	1 (1.5)
BMI, kg/m2	22.5 (20, 25.1)	23.1 (20.9, 25.5)	0.303
Age at transplant, year	45.7 ± 11.3	48.4 ± 10.3	0.135
Donor/recipient body weight ratio	1 (0.9, 1.2)	1.1 (0.9, 1.3)	0.239
HLA mismatch number	4 (3, 4)	3 (3, 4)	0.256
Surgery duration, min	170 (150, 192)	180 (145, 200)	0.360
Donors
Sex, n (%)			0.370
Female	20 (27.4)	14 (20.9)
Male	53 (72.6)	53 (79.1)
Donor type, n (%)			0.026
DBD	65 (89.0)	50 (74.6)
DCD	8 (11.0)	17 (25.4)
Cause of death, n (%)			0.638
Anoxia	2 (2.7)	5 (7.5)
Head trauma	31 (42.5)	22 (32.8)
Cerebral infarction	5 (6.8)	5 (7.5)
Cerebral hemorrhage	32 (43.8)	32 (47.8)
Others	3 (4.1)	3 (4.5)
CIT, hour	10.6 (7.9, 13.7)	13.4 (11.4, 20.5)	<0.001
BMI, kg/m2	21.4 (20.8, 23.9)	24.1 (22.4, 25.6)	<0.001
Age at donation, year	43.7 ± 12.6	44 ± 11.7	0.874
Pre-donation creatinine level, μmol/L	114.0 (83.0, 152.0)	191.0 (123.0, 309.3)	<0.001

Data were presented as mean ± SD, median (Q1, Q3), or n (%)

Bold values indicate statistical significance

DGF, delayed graft function; PRA, panel-reactive antibody; BMI, body mass index; HLA, human leukocyte antigen; DBD, donation after brain death; DCD, donation after circulatory death; CIT, cold ischemia time

The corresponding characteristics of the validation cohort are shown in Supplementary Table S1. Similar to the development cohort, recipients who experienced DGF more frequently received kidneys from DCD donors (35.8% vs. 9.7%; p < 0.001) and, had a longer CIT (median, 13.2 h [IQR, 8.3 - 20.1] vs. 8.9 h [IQR, 7 - 12]; p < 0.001). Donor BMI was higher in DGF patients (median, 23.5 kg/m² [IQR, 21.7 - 25.8] vs. 22.5 kg/m² [IQR, 21.3 - 24.2]; p = 0.006), and higher pre-donation serum creatinine levels (median, 203 μmol/L [IQR, 128 - 362.5] vs. 93 μmol/L [IQR, 63 - 144.3]; p < 0.001).

Model development: performance of individual ML models

The performance metrics of the nine supervised learning models in the independent validation cohort are shown in Fig. 2A. Overall, the LR, NB, NNet, and ENet models demonstrated the best discrimination, whereas DT and XGB showed comparatively lower performance.

Fig. 2.

Performance of nine ML models (DT, LR, NB, RF, KNN, SVM, ENet, NNet, and XGB) in the validation cohort. Metrics include ROC-AUC, PR-AUC, accuracy, balanced accuracy, Brier score, F1 score, NPV, PPV, sensitivity, and specificity. (A) Heatmap of model performance, with color gradients representing the relative strengths and weaknesses across metrics. (B) ROC curves for all nine models in the validation cohort, indicating discriminatory performance by ROC-AUC values. Abbreviations: ML, machine learning; DT, decision tree; LR, logistic regression; NB, naive bayes; RF, random forest; KNN, k-nearest neighbor; SVM, support vector machine; ENet, elastic net regression; NNet, neural network; XGB, extreme gradient boosting; ROC-AUC, area under the receiver operating characteristic curve; PR-AUC, area under the precision recall curve; NPV, negative predictive value; PPV, positive predictive value

Among all models, the LR model achieved the highest ROC-AUC (0.839, 95% CI: 0.795 to 0.883) and PR-AUC (0.859), with an accuracy of 0.787, balanced accuracy of 0.787, Brier score of 0.163, F1-score of 0.774, NPV of 0.750, PPV of 0.833, sensitivity of 0.723, and specificity of 0.852. The NNet model yielded a comparable ROC-AUC of 0.832 (95% CI: 0.786 to 0.878) and PR-AUC of 0.852, with an accuracy of 0.790, balanced accuracy of 0.790, Brier score of 0.162, and PPV of 0.821. The NB model also performed similarly, with a ROC-AUC of 0.829 (95% CI: 0.783 to 0.875), PR-AUC of 0.847, accuracy of 0.783, balanced accuracy of 0.784, Brier score of 0.174, and PPV of 0.797. Although the ENet model achieved a high ROC-AUC (0.837, 95% CI: 0.793 to 0.882) and PR-AUC (0.859), its Brier score was higher (0.245), suggesting less favorable calibration. Intermediate performance was observed for RF (ROC-AUC, 0.801, 95% CI: 0.752 to 0.850), KNN (ROC-AUC, 0.806, 95% CI: 0.757 to 0.854), and SVM (ROC-AUC, 0.803, 95% CI: 0.752 to 0.854), whereas DT (ROC-AUC, 0.750, 95% CI: 0.697 to 0.802) and XGB (ROC-AUC, 0.770, 95% CI: 0.718 to 0.823) showed lower discrimination. Figure 2B presents the ROC curves of the nine individual models.

To further assess discrimination differences, we performed 1,000 stratified nonparametric bootstrap replicates in the validation cohort and compared ROC-AUC values between the LR model and the competing algorithms. The mean ROC-AUC difference between LR and DT, RF, XGB, KNN, and SVM ranged from 0.033 to 0.089 (p < 0.05), indicating significantly better discrimination by LR. By contrast, the LR model showed discrimination comparable to that of NB, ENet, and NNet. The mean ROC-AUC difference was 0.010 for NB (95% CI, −0.006 to 0.024; p = 0.220), 0.002 for ENet (95% CI, −0.004 to 0.007; p = 0.536), and 0.007 for NNet (95% CI, −0.006 to 0.019; p = 0.256) (Table 2). These findings indicate that the classic LR model performed at least comparably to, and in some cases better than, the more complex algorithms evaluated in this study.

Table 2.

Bootstrap comparison of ROC-AUC between the LR model and other algorithms on the validation cohort

Compare	mean difference	95%CI	p
DT	0.089	0.052 - 0.125	<0.001
NB	0.010	−0.006 - 0.024	0.220
RF	0.038	0.012 - 0.064	<0.001
KNN	0.033	0.009 - 0.057	0.008
SVM	0.036	0.013 - 0.061	<0.001
ENet	0.002	−0.004 - 0.007	0.536
NNet	0.007	−0.006 - 0.019	0.256
XGB	0.068	0.037 - 0.101	<0.001

CI, confidence interval; DT, decision tree; NB, naive Bayes; RF, random forest; KNN, k-nearest neighbor; SVM, support vector machine; ENet, elastic net regression; NNet, neural network; XGB, extreme gradient boosting

Stacked ensemble models

We next explored whether combining models through stacking could provide incremental predictive value. A total of 84 stacked ensemble models, each comprising three base learners and a logistic regression meta-learner, were evaluated. Figure 3B shows the ROC-AUC values of all 84 stacked ensembles ranked in descending order.

Fig. 3.

Performance of 84 stacked ensemble models in the validation cohort. (B) Ranking of all 84 three-model stacking combinations by ROC-AUC, with the combination based on LR, SVM, and ENet as base learners achieving the highest ROC-AUC of 0.839. (A, C-E) Comparison of other commonly used binary classification metrics, including PR-AUC (A), accuracy (C), F1 score (D), and NPV (E), among the top models, confirming the superior performance of the stacked ensemble model with LR, SVM, and ENet as base learners. Detailed numeric results for all 84 combinations are provided in Supplementary Table S2. Abbreviations: DT, decision tree; LR, logistic regression; NB, naive bayes; RF, random forest; KNN, k-nearest neighbor; SVM, support vector machine; ENet, elastic net regression; NNet, neural network; XGB, extreme gradient boosting; ROC-AUC, area under the receiver operating characteristic curve; PR-AUC, area under the precision recall curve; NPV, negative predictive value

The best-performing ensemble, composed of LR, SVM, and ENet as base learners, achieved a ROC-AUC of 0.839, which was identical to that of the single best LR model. This ensemble also performed favorably on several other binary classification metrics, including PR-AUC, accuracy, F1-score, and NPV (Fig. 3A, and C-E). However, the magnitude of these differences was small and did not translate into a clear overall advantage over the simpler LR model. Detailed performance metrics of all 84 ensemble models are provided in Supplementary Table S2.

Additionally, DCA showed that the net benefit of the best-performing ensemble largely overlapped with those of the LR, NB, and NNet models across clinically relevant threshold probabilities (Fig. 4A). Similarly, the calibration profile of the best ensemble was visually very similar to that of the leading single models (Fig. 4B). We further quantified calibration in the validation cohort using the calibration intercept and calibration slope. The LR model showed a calibration intercept of 0.211 and a calibration slope of 0.886, while the corresponding values were 0.563 and 0.654 for NB, 0.207 and 0.836 for NNet, and 0.247 and 1.056 for the stacked ensemble model. These quantitative calibration measures suggested comparatively poorer calibration for NB, whereas LR, NNet, and the stacked ensemble showed broadly acceptable calibration. Overall, these results suggest that, in the present dataset, stacked ensemble strategies did not provide meaningful incremental benefit over the best single-model approach.

Fig. 4.

Decision curve analysis and calibration plots for the optimal stacked ensemble model and superior single model in the validation cohort. (A) Decision curve analysis illustrating the net benefit of using the model for clinical decision-making at different threshold probabilities. (B) Calibration plots reflecting agreement between predicted and observed probabilities. The 45° dashed line denotes perfect calibration in which the predicted probabilities are identical to the actual probabilities. Deviations above and below this line indicate over and under prediction, respectively. Abbreviations: LR, logistic regression; NB, naive bayes; NNet, neural network; SVM, support vector machine; ENet, elastic net regression

Model explanation

The coefficients, odds ratios, 95% CI, and P values of the final LR model fitted in the development cohort are presented in Table 3. In the multivariable model, longer CIT, higher donor BMI, and higher donor terminal serum creatinine were significantly associated with increased risk of DGF, whereas DCD status showed a positive but not statistically significant association, which may reflect limited precision related to the modest sample size. Overall, the directions of association were consistent with established clinical knowledge.

Table 3.

Coefficients and odds ratios of the final logistic regression model for delayed graft function in the development cohort

Predictor	β coefficient	OR (95% CI)	p
CIT, hour	0.110	1.116 (1.038 - 1.214)	0.006
DCD donor	0.903	2.467 (0.839 - 7.661)	0.106
Donor BMI, kg/m2	0.275	1.316 (1.123 - 1.570)	0.001
Terminal serum creatinine, μmol/L	0.010	1.010 (1.005 - 1.016)	<0.001

OR, odds ratio; CI, confidence interval; CIT, cold ischemia time; DCD, donation after circulatory death; BMI, body mass index

As a supplementary visualization approach, we applied SHAP to the final LR model in the validation cohort to illustrate feature contributions to DGF risk. The SHAP summary plots (Fig. 5A, and C) identified donor terminal serum creatinine as the most influential predictor, followed by donor BMI, CIT, and DCD status. In general, higher values of these features shifted the model toward predicting DGF (as indicated by positive SHAP values), consistent with their known associations with worse outcomes. For instance, kidneys from DCD donors, longer cold ischemia times, higher donor BMI, and elevated donor creatinine were all linked to increased DGF risk.

Fig. 5.

SHAP analysis of the final LR model in the validation cohort. (A) Bar plot of mean absolute SHAP values, indicating the overall magnitude of contribution of each feature to the model output. (B) SHAP waterfall plot for a representative patient with low predicted DGF risk. (C) SHAP beeswarm summary plot showing feature contributions across all individuals. Each point represents the SHAP value of one feature for one individual. Point color represents the original feature value, ranging from purple for low values to yellow for high values. (D) SHAP waterfall plot for a representative patient with intermediate predicted DGF risk. (E) SHAP waterfall plot for a representative patient with high predicted DGF risk. In the waterfall plots, each feature contribution shifts the prediction from the baseline expected value toward the final patient-specific predicted probability of DGF; bars to the right indicate increased predicted risk, whereas bars to the left indicate decreased predicted risk. Abbreviations: LR, logistic regression; SHAP, Shapley additive explanations; DGF, delayed graft function

To illustrate individual-level interpretability, we present SHAP waterfall plots for three patients representing low-, intermediate-, and high-risk predictions, respectively (Fig. 5B, D, and E). The predicted DGF probabilities of 0.064, 0.167, and 0.518 shown in these panels were generated by the final LR model for the three representative patients. In each waterfall plot, the model output begins at the baseline expected prediction and is subsequently adjusted by the SHAP value of each feature, which reflects the extent to which that feature increases or decreases the prediction for the individual patient. The sum of these feature-level contributions results in the final predicted probability of DGF. Accordingly, the values of 0.064, 0.167, and 0.518 correspond to the final patient-specific predicted risks rather than to individual SHAP values. These visualizations were used as a supplementary explanation of individual predictions generated by the final logistic regression model.

Discussion

Owing to the shortage of organ donors, the use of expanded criteria donor kidneys [31] and DCD kidneys [32] has increased, accompanied by a rising incidence of DGF. In the early postoperative period, patients with DGF often require additional dialysis and prolonged hospitalization. Over the long term, DGF has been associated with an increased risk of acute rejection and decreased graft survival [8, 9, 33]. Therefore, reliable pre-transplant identification of recipients at high risk of DGF remains clinically important.

Several prediction models for DGF have been reported over the past two decades, ranging from traditional risk scores to more recent supervised learning approaches [10–13, 15, 16]. However, an unresolved practical question is whether increasing algorithmic complexity meaningfully improves prediction beyond what can already be achieved by simpler and more transparent models using routinely available pre-transplant variables. In the present study, we compared multiple supervised learning algorithms in a single-center cohort and found that the classic LR model performed comparably to, or better than, several more complex algorithms. In addition, stacked ensemble strategies did not provide clinically meaningful incremental benefit in discrimination, calibration, or decision-curve performance. Taken together, these findings suggest that, in this setting, added model complexity did not translate into improved clinical prediction.

An important strength of the final model is its parsimony. The model relied on only four donor-derived pre-transplant variables - donor BMI, terminal serum creatinine, CIT, and DCD status - all of which are routinely available in clinical practice. These variables are consistent with known risk factors for DGF. Elevated donor BMI and terminal serum creatinine levels have been associated with higher risk of DGF after transplantation [34, 35]. Similarly, DCD status and prolonged CIT are well-established independent risk factors for DGF [36, 37]. Data from the United States Renal Data System indicate that for every 6-hour increase in CIT, the DGF risk increases by 23% [38]. DCD kidneys are typically exposed to longer warm ischemia times than DBD kidneys, making them more susceptible to ischemic injury, thereby increasing the risk of DGF. Thus, although these variables are not novel predictors, their consistent performance across both cohorts supports their continued relevance for pragmatic risk stratification.

We also systematically explored stacked ensemble strategies by evaluating 84 combinations of three base learners with a logistic meta-learner. Although stacking is often proposed as a means to improve predictive performance by combining complementary model structures, this was not observed in our study. The best-performing ensemble achieved discrimination similar to that of the best single LR model, and its calibration and decision-curve profiles were likewise comparable. This finding suggests that the information captured by our predictor set was already effectively extracted by a single strong model and that additional model complexity did not translate into better performance. From a practical perspective, this is encouraging, as it implies that a parsimonious LR model based on four routinely available donor variables may be sufficient for DGF risk prediction in this setting, thereby facilitating clinical implementation.

An important question raised by our findings is why a relatively simple final model emerged from a broader comparison of more complex learning approaches. Importantly, LR is itself a classical and transparent supervised learning method. One likely explanation is that the present predictor set consisted of a small number of strongly informative and clinically grounded donor-related variables. When a limited set of predictors already captures much of the relevant signal, additional model flexibility may offer little incremental value. Under such circumstances, more complex algorithms may not yield a more nuanced or better-performing model if the underlying information available to all models is largely the same. In addition, the relatively modest development sample size may have limited the extent to which more flexible algorithms could reliably exploit higher-order nonlinearities or interactions without increased risk of instability or optimism. This is conceptually similar to traditional multivariable modeling, in which the number of covariates that can be stably supported is constrained by the available sample size and event count. Therefore, the present findings should not be interpreted as suggesting that more complex methods are generally unnecessary, but rather that in this particular setting, increased algorithmic complexity did not provide meaningful benefit over a parsimonious LR model. More complex supervised learning approaches may be most advantageous when the predictor space is high-dimensional, nonlinear, or interaction-rich. By contrast, when a limited number of strongly informative and clinically grounded predictors already captures most of the relevant signal, a simpler method such as LR may be sufficient. Similarly, stacked ensemble models may offer greater benefit when the base learners capture complementary rather than largely overlapping information. In the present study, the limited predictor set and the similar performance of the leading models may have reduced the potential for stacking to provide meaningful incremental value.

Another aspect of this study was the effort to improve the communication and interpretability of model predictions. The primary interpretability of the final model derives from its logistic regression structure and the corresponding regression coefficients, which allow direct assessment of the direction and magnitude of association for each predictor. We also used SHAP analysis as a supplementary visualization tool to display overall feature contribution rankings and to illustrate how individual predictor values influenced patient-level predicted risk. In the context of clinical prediction, such transparency may be particularly valuable when more complex models do not provide meaningful improvement over a simpler and more interpretable alternative, because model outputs may then be easier to understand, communicate, and implement in practice.

Several limitations should be acknowledged. First, the development cohort was relatively modest in size, which may have reduced the ability of more complex algorithms to stably detect nonlinearities or interactions, increased the risk of model optimism, and limited the extent to which additional predictors or algorithmic complexity could provide reliable incremental benefit. Second, the use of significance-based preselection and stepwise regression is not the most robust modern approach for predictor selection and may risk excluding clinically relevant variables, particularly in relatively small datasets. Future studies should consider clinically prespecified predictors or penalized regression methods. Third, the model’s generalizability may be constrained by the single-center sample, and external validation in larger, multicenter cohorts is needed to confirm and refine its performance. Fourth, although cross-validation was used for model tuning and bootstrap procedures were used to compare ROC-AUC values in the validation cohort, formal optimism correction for the entire model-development pipeline was not performed. Fifth, although recipient-related variables such as recipient age, BMI, and diabetes mellitus were included as candidate predictors, they were not retained in the final model under the present development strategy. Accordingly, the current model should be interpreted as a parsimonious donor - dominant prediction model rather than a comprehensive donor - recipient risk model. This may limit its external validity, particularly in populations with a higher burden of metabolic disease. Future studies integrating multidimensional data across the pre- and post-transplant periods may support the development of more accurate dynamic prediction systems. Finally, we did not perform formal benchmarking against established DGF prediction tools. Therefore, although the present model performed well in our cohort, its relative performance and potential incremental value compared with existing published models remain uncertain.

Despite these limitations, the present study offers a practical contribution. In a real-world single-center cohort of deceased-donor kidney transplantation, a parsimonious LR model based on four routinely available donor variables achieved stable predictive performance in an independent temporal cohort, whereas more complex supervised learning and stacked ensemble approaches did not confer meaningful additional benefit. This may help inform future efforts toward more transparent and implementable DGF prediction models.

Conclusions

In conclusion, this study compared multiple supervised learning approaches for DGF prediction after deceased-donor kidney transplantation in a single-center cohort with independent temporally distinct validation. A parsimonious LR model based on four routinely available donor variables performed comparably to more complex supervised learning algorithms and stacked-ensemble approaches. In this setting, additional algorithmic complexity did not translate into meaningful improvement in predictive performance. These findings support the potential practical value of a simple and interpretable model for pre-transplant risk stratification. However, given the single-center design and limited sample size, further external validation and more rigorous model-development studies are needed before broader clinical application.

Electronic supplementary material

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Abbreviations

AIC

Akaike information criterion

BMI

Body mass index

CIT

Cold ischemia time

DBD

Donation after brain death

DCA

Decision curve analysis

DCD

Donation after circulatory death

DGF

Delayed graft function

DT

Decision tree

ENet

Elastic net regression

HLA

Human leukocyte antigen

IQR

Interquartile range

KNN

k-Nearest neighbor

LR

Logistic regression

ML

Machine learning

NB

Naive bayes

NNet

Neural network

NPV

Negative predictive value

PPV

Positive predictive value

PRA

Panel reactive antibody

PR-AUC

Area under the precision-recall curve

RF

Random forest

ROC-AUC

Area under the receiver operating characteristic curve

SD

Standard deviation

SHAP

Shapley additive explanations

SVM

Support vector machine

XGB

Extreme gradient boosting

Author contributions

Yongguang Liu and Yuena Huang conceived and designed the study. Wanrong Zhou, Ziyun Kou, and Yuxiao Li were responsible for data collection. Runtao Feng and Guorong Liao performed the data analysis. Jianmin Hu prepared the ethics applications and assisted with project administration. Runtao Feng and Bingzhou Zhong drafted the manuscript and revised it critically for important intellectual content. All authors read and approved the final manuscript.

Funding

This work was supported by the National Natural Science Foundation of China (82170764).

Data availability

The datasets generated and/or analysed during the current study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

The prospective cohort study was approved by the Ethics Committee of Zhujiang Hospital of Southern Medical University (Approval No. 2023-KY-083-02). Written informed consent to participate was obtained from all participants prior to enrollment in the prospective cohort. The present secondary analysis, together with the retrospective validation cohort, was approved by the Ethics Committee of Zhujiang Hospital of Southern Medical University (Approval No. 2025-KY-263-01). For the retrospective validation cohort, the requirement for informed consent was waived by the Ethics Committee because the study design was retrospective and noninterventional.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.