This study was based on multiple high-quality heart transplantation databases to ensure both the representativeness of model development and the broad applicability of evaluation results. The primary development dataset was derived from the United Network for Organ Sharing (UNOS) registry, which included 144,979 adult patients who underwent orthotopic heart transplantation (OHT) in the United States between 1994 and 2024. Covering transplant centers nationwide, the UNOS database contains comprehensive information on recipients, donors, perioperative variables, and long-term follow-up, making it the largest and most detailed transplant registry globally.

Three additional external validation cohorts were included to assess the model's cross-regional generalizability. The Eurotransplant registry dataset (n = 3,061) was obtained from the Eurotransplant organ allocation system, a multinational transplant network coordinating organ sharing across several European countries, and reflects typical clinical practices in Central and Western Europe.

The Scandiatransplant registry dataset (n = 1,546) was derived from the Scandiatransplant collaboration, a Nordic transplant organization covering countries such as Finland, Sweden, and Norway, and provides long-term follow-up data for heart transplant recipients.

The External-CN dataset (n = 14), although limited in sample size, was collected from a real-world clinical setting at the Department of Cardiac Surgery, Jiangxi Provincial People's Hospital, and is characterized by high heterogeneity and a non-Western healthcare background.

These four data sources exhibit substantial differences in demographic structure, clinical pathways, and healthcare resource distribution, thereby forming a multi-center, multi-context, and multi-scale validation platform. Together, they provide a robust foundation for the comprehensive evaluation of the GINN model's performance, robustness, and potential for generalization.

Prior to model construction, we implemented a systematic preprocessing pipeline across all original datasets to standardize input formats, reduce bias, and enhance model stability and generalizability. Prior to imputation, missingness patterns were systematically examined for all candidate variables. Overall, missing data were limited across the features included in the final model, with most variables exhibiting only a small proportion of missing values and no variable showing extensive missingness. Under these conditions, median imputation for continuous variables and mode imputation for categorical variables were considered appropriate and unlikely to materially distort the underlying data distributions (11). To alleviate scale discrepancies that may hinder convergence, all numerical features were standardized using zero-mean, unit-variance (Z-score) normalization (12).

To mitigate domain shift arising from heterogeneous data distributions across centers, we harmonized variable-encoding schemes and remapped or excluded site-specific variables (13). Given the pronounced class imbalance—post-transplant mortality is relatively rare—we applied the Synthetic Minority Over-sampling Technique (SMOTE) to augment minority-class samples in the training set (14). This approach balanced class ratios and reduced the impact of imbalance on parameter learning.

Training–validation splits followed a stratified design that accounted for both calendar time and transplant center to ensure fair evaluation across temporal periods, geographic regions, and risk strata (15). All training was conducted without data leakage, preserving label distribution and feature integrity throughout the pipeline.

The nine input variables were defined a priori based on established clinical relevance and prior evidence from validated heart transplantation risk models. Specifically, these variables correspond to donor, recipient, and perioperative factors incorporated in widely used predictive frameworks such as the IMPACT score and the International Heart Transplant Survival Algorithm (IHTSA), both of which were developed to predict early post-transplant mortality using clinically grounded variables (16). Accordingly, the input feature set was specified prior to model training. The Lasso-style sparse regularizer embedded in the GINN architecture was applied during model optimization to promote parsimony and interpretability by shrinking the contributions of less informative features, rather than serving as a preliminary feature screening procedure.

As illustrated in Figure 1, the Generalizable Interpretable Neural Network (GINN) is an end-to-end hybrid framework that combines the expressive power of deep learning with the transparency of additive models. Its core component is a Risk Response Network (RRN), in which every input feature is processed by an independent univariate sub-network. The feature-specific outputs are then summed to obtain the overall risk logit, followed by a sigmoid activation to yield a calibrated survival probability.

Additive risk decomposition. Let x=(x1,…,xd)∈Rd denote the structured clinical features. GINN decomposes the prediction into additive feature responses:y^=σ(b+∑i=1d⁡fi(xi)),(1)where b is a learnable bias term, fi(⋅) is the response function for the i-th feature, and σ(⋅) is the sigmoid function that outputs the one-year mortality probability.

Risk Response Network. Each fi(⋅) is implemented as a lightweight multilayer perceptron (MLP) with residual connection and layer normalisation, as defined in Equation 2.hi(ℓ+1)=ϕ(Wi(ℓ)hi(ℓ)+βi(ℓ))+γhi(ℓ),fi(xi)=wi⊤hi(L),(2)where hi(0)=xi (after standardisation), ϕ(⋅) denotes a non-linear activation (GELU in our implementation), L is the depth of the sub-network, and γ is a learnable residual scaling coefficient that preserves linear interpretability.

Sparsity and feature selection. A Lasso-style sparse regulariser is applied to the output weights {wi} to automatically filter irrelevant features and enhance interpretability:Rlasso=α∑i=1d∥wi∥1,(3)where α>0 controls the degree of sparsity.

Training objective. GINN is trained end-to-end by minimising a composite loss function, as shown in Equation 4, which combines binary cross-entropy, calibration error, and the Lasso penalty.L=−[ylogy^+(1−y)log(1−y^)]⏟LBCE+λLECE(y^,y)+Rlasso,(4)where LECE denotes the expected calibration error and λ balances calibration against discrimination.

Because each feature channel is modelled independently and aggregated additively (Equation 1), GINN yields explicit partial response curves for every variable. These curves enable both global interpretation of marginal effects and local attribution for individual predictions, while the sparsity constraint in Equation 3 keeps the model compact and clinically tractable. The entire modeling pipeline, including data preprocessing, model training, and evaluation, was implemented in Python using PyTorch. Experiments were conducted under a fixed random seed to ensure reproducibility.

Continuous variables are summarized as medians with interquartile ranges (IQR) and means with standard deviations (SD), while categorical variables are reported as counts and percentages. For comparisons across different time periods or cohorts, continuous variables were assessed using analysis of variance (ANOVA) or the Kruskal–Wallis test, and categorical variables were evaluated using chi-squared (χ2) tests.

Model discrimination was primarily assessed using the area under the receiver operating characteristic curve (AUROC), along with 95% confidence intervals (CI). Model calibration was evaluated through the Hosmer–Lemeshow goodness-of-fit test and visually analyzed via calibration plots following the TRIPOD reporting guidelines. A p-value greater than 0.05 in the HL test was considered indicative of good agreement between predicted probabilities and observed outcomes.

In addition, we conducted robustness analysis via ablation studies to examine the impact of key architectural components—such as the Lasso interpretability layer, donor-related variables, and SMOTE oversampling—on model performance.

All statistical analyses were performed using Python (version 3.8.0). Two-sided p-values less than 0.05 were considered statistically significant.

We trained and evaluated the model using four distinct datasets: UNOS, Eurotransplant registry, Scandiatransplant registry, and External-CN.

The UNOS registry (n=144,979) (17) served as the primary source for model development. This registry includes patients who underwent heart transplantation in the United States between 1994 and 2024. After excluding recipients aged <18 years, donors aged <15 years (63,136 cases), and records with less than 1 year of follow-up (512 cases), 81,327 eligible cases remained (Figure 2).

These cases were then divided into three cohorts: a derivation cohort (1994–2013, n=45,927) used for model training, a temporal test cohort (2014–2018, n=20,200) for evaluation, and a validation cohort (2019–2024, n=15,200) for out-of-time generalisation. Demographic and clinical characteristics of each cohort are detailed in Tables 1, 2.

Additionally, we evaluated the model on three external datasets: Eurotransplant registry (n=3,061) (2), Scandiatransplant registry (n=1,546) (18), and External-CN (n=14). These external datasets were used to assess the model's performance across different patient populations. The External-CN dataset, collected from the Department of Cardiac Surgery, Jiangxi Provincial People's Hospital, is characterized by an extremely small sample size, providing a real-world clinical evaluation of the model. Together, these heterogeneous datasets provide a comprehensive platform for evaluating the robustness and external validity of the GINN model.

In terms of discrimination, the GINN model achieved an AUROC of 0.827 (95% CI: 0.821–0.833) on the UNOS internal validation cohort, substantially outperforming the classical IMPACT score (AUROC = 0.643, 95% CI: 0.634–0.652) (19), the standard deep neural-network model IHTSA (AUROC = 0.773, 95% CI: 0.765–0.780) (16), and its recalibrated version (AUROC = 0.755) (20). These results underscore GINN's superior risk-discrimination capability in high-dimensional structured clinical data (Figures 3–5).

From a calibration perspective, GINN also performed strongly. The calibration slope was 1.082, the calibration-in-the-large (CITL) was −0.020, and the expected-to-observed ratio (E:O) was 0.955, all close to ideal values. The calibration curve in Figure 5a shows the blue curve closely following the diagonal, with evenly distributed 95% CIs, indicating reliable probability estimates (21).

External validation further confirmed cross-centre robustness. Figure 6a presents the ROC curves across these cohorts. GINN attained AUROCs of 0.789 (95% CI: 0.771–0.807) in Eurotransplant registry, 0.776 (95% CI: 0.755–0.797) in Scandiatransplant registry, and 0.821 (95% CI: 0.762–0.880) in the highly heterogeneous, small External-CN cohort, demonstrating good performance even under limited-sample conditions.

In addition, Figure 6b summarizes the classification performance in terms of accuracy, precision, recall, and F1-score across all four datasets. GINN achieved stable and competitive results, with accuracy values of 0.80 (UNOS), 0.77 (Eurotransplant registry), 0.75 (Scandiatransplant registry), and 0.80 (External-CN). Corresponding precision scores were 0.82, 0.79, 0.77, and 0.82; recall scores were 0.80, 0.76, 0.74, and 0.80; and F1-scores were 0.81, 0.77, 0.75, and 0.81, respectively.

To further ensure that the observed performance was not driven predominantly by correct classification of the majority (survival) class, confusion matrices were constructed for the internal test cohort and all external validation datasets (Figure 7). These matrices demonstrate balanced sensitivity and specificity for both survival and death outcomes across cohorts, indicating that the model does not collapse into trivial majority-class prediction and retains meaningful discriminatory capacity for the minority (death) class.

In addition, calibration performance was quantitatively assessed across internal and external cohorts using multiple complementary metrics (Table 4), including calibration slope, calibration-in-the-large (CITL), Brier score, and expected-to-observed (E/O) ratio. Calibration slopes remained close to unity and CITL values were near zero in the UNOS, Eurotransplant registry, and Scandiatransplant registry cohorts, indicating good agreement between predicted probabilities and observed event rates. Calibration estimates for the External-CN cohort showed wider uncertainty, which is expected given the extremely limited sample size (n = 14) and is therefore interpreted with caution.

Overall, GINN demonstrates excellent discrimination and calibration across both internal and external cohorts, consistently outperforming traditional risk scores and black-box deep learning models in predicting one-year post-transplant mortality.

This section provides a global-level interpretation of the GINN model by illustrating the marginal risk contributions of each input variable across the study population. The partial response curves in Figure 4a–i elucidate the nonlinear marginal effects of the nine most predictive variables.

Recipient age exhibits a bimodal U-shaped risk pattern: both the youngest and the oldest patients experience markedly higher one-year mortality (Figure 4a) (3). Median recipient age was lower in the UNOS cohort (52 years; IQR 44–59) than in Eurotransplant registry (55 years) and Scandiatransplant registry (54 years), whereas External-CN displayed the widest variability, indicating substantial inter-regional heterogeneity in age composition.

Donor age is positively associated with mortality in a monotonic manner (Figure 4b). Donors were oldest in Eurotransplant registry (median 42 years) and youngest in External-CN (median 29 years), emphasising international differences in donor pools (2).

Elevated donor serum creatinine correlates strongly with increased post-transplant risk (Figure 4c), consistent with prior registry findings (22).

Ischaemic time shows a clear threshold effect: mortality rises steeply beyond 210 min (Figure 4d). UNOS recorded the shortest median ischaemic time (164 min), whereas Eurotransplant registry and Scandiatransplant registry reported longer durations, suggesting centre-specific variation in transport logistics (23).

Pre-operative support measures—including ECMO, mechanical ventilation and inotropic therapy—each substantially elevate risk (Figures 4e–g). Their prevalence was highest in Eurotransplant registry and External-CN, implying that recipients in these cohorts were generally more critically ill at transplantation.

A diagnosis of non-ischaemic cardiomyopathy (NICM) contributes meaningfully to risk estimation (Figure 4h), reflecting its influence on recipient adaptation to the graft and long-term prognosis.

A history of donor hypertension is a stable positive predictor (Figure 4i), most common in Eurotransplant registry but absent in External-CN, underscoring regional differences in donor clinical profiles.

These response curves quantify regional variability in risk drivers. After standardised preprocessing, GINN generalised reliably across heterogeneous, multicentre datasets; its excellent calibration in the UNOS development domain (Figure 5) confirms close alignment between predicted and observed outcomes.

As shown in Figure 8, recipient and donor age curves display pronounced non-linearity (Figure 8a), whereas donor creatinine and ischaemic time show strong positive correlations with mortality (Figure 8b). Among the binary variables, ECMO support has the highest odds ratio (OR = 7.20), identifying it as the strongest single mortality signal (Figure 8c).

To further assess the robustness of the GINN model under various modeling strategies, we conducted a series of ablation studies. Key results are summarized in Table 3.

First, we removed the Lasso-based interpretability layer, retaining only the base neural network structure. In this configuration, the AUROC decreased slightly from 0.827 to 0.824. This marginal performance loss indicates that while the interpretability module may not substantially enhance predictive accuracy, it provides essential transparency and clinical explainability that support model interpretability in practice.

Second, we excluded donor-related variables—specifically donor age, creatinine level, ischemic time, and history of hypertension. The AUROC dropped significantly to 0.793, highlighting the critical importance of donor characteristics in post-transplant survival prediction. This result underscores the necessity of bidirectional modeling, which considers both donor and recipient variables.

Lastly, we evaluated the impact of class imbalance handling on model performance. When SMOTE (Synthetic Minority Over-sampling Technique) was removed, the model's precision on the majority class (survival) remained relatively stable. However, recall for the minority class (death) declined markedly, with an average drop of 12.4%. This confirms the pivotal role of SMOTE in enhancing the model's sensitivity to high-risk patients, who typically represent a small proportion of the dataset.

Together, these findings validate the design choices made in the GINN architecture and demonstrate its robustness under varying configurations. The ablation experiments confirm that both interpretability modules and comprehensive donor-recipient modeling are indispensable for achieving reliable, generalizable, and clinically meaningful predictions.

To complement the global interpretation, we further provide individual-level explanations by decomposing each patient's predicted risk into additive feature-wise contributions based on the learned response functions. These feature-level contribution scores serve as quantitative supporting data for individual predictions and are visualized in Figure 9.

Eurotransplant registry case. A 58-year-old male recipient requiring preoperative ECMO and mechanical ventilation and diagnosed with NICM received a donor heart with an ischemic time of nearly four hours. GINN predicted a one-year mortality risk of 26.7%, which was consistent with the observed outcome. As shown in Figure 9 (Case A), the elevated predicted risk was primarily driven by preoperative ECMO support and mechanical ventilation, which contributed the largest positive risk scores, followed by prolonged ischemic time and advanced recipient age. Other variables exhibited relatively minor effects, illustrating a concentrated accumulation of high-risk factors at the individual level. In contrast, the IMPACT score estimated a substantially lower risk (13.2%), reflecting limited sensitivity to compounded high-risk conditions.

Scandiatransplant registry case. A 62-year-old female recipient without mechanical circulatory support received a heart from a young donor without major comorbidities. GINN predicted a low one-year mortality risk of 6.2%, which aligned with the favorable observed outcome. The individual risk decomposition in Figure 9 (Case B) shows that the absence of preoperative support measures resulted in negligible positive contributions, while younger donor age and shorter ischemic time exerted protective (negative) effects on the overall risk score. By contrast, IHTSA overestimated the risk at 14.5%, suggesting risk inflation in clinically low-risk profiles.

External-CN case. A younger recipient requiring ECMO, inotropic support, and mechanical ventilation before transplantation was assigned a predicted mortality risk of 32.4% by GINN. As illustrated in Figure 9 (Case C), the high-risk prediction was mainly attributable to strong positive contributions from multiple preoperative support measures, with ECMO exerting the dominant effect, accompanied by inotropic support and ventilation. The patient died within six months after transplantation, demonstrating accurate identification of high-risk individuals even in a small-sample, heterogeneous clinical setting.

Together, these case studies demonstrate how GINN enables a coherent progression from global population-level patterns to local, individual patient-level risk attribution within a unified and interpretable modeling framework.