Data reveal that approximately 463 million adults worldwide were living with diabetes mellitus in 2019, and it will surge by 51% to reach 700 million by 2045 [11]. Despite its growing prevalence, many cases of T2DM could be prevented with lifestyle changes, including weight control, maintaining healthy diet, staying physically active, and so on [12]. Therefore, accurate classifications and clinical management of diabetes are crucial to prevent disease progression and severe complications in the future.

In addition, the pathogenesis of T2DM is highly complex, it involves interaction of multiple biological and environmental factors, which influence one another through complicated pathways rather than simple linear relationships [13]. As a result, diabetes prediction requires advanced methods that are capable of capturing complex nonlinear relationships. Choi et al. [14] demonstrate that machine learning models consistently outperform traditional statistical methods in identifying undiagnosed diabetes, particularly when data is complex and non-linear. This highlights the necessity of training machine learning methods in modern diabetes prediction research to boost prediction performance.

Ijaz et al. [15] addressed imbalance and noisy dataset by using DBSCAN for outlier detection and SMOTE for class balance, improving the performance of RF classifiers.

Hasan et al. [16] provide a framework for ensemble machine learning methods: they used an ensemble of classifiers, including AdaBoost and XGBoost, weighing different models by AUC. Similarly, Ganie et al. [17] used boosting ensembles such as CatBoost and XGBoost with cross-validation and splitting data into multiple folds. These two studies show the effectiveness of ensemble models in early diabetes classifications.

Bala Manoj Kumaret al. [18] used Deep Neural Networks to achieve 98.16% classification accuracy on the Pima Indians Diabetes Dataset. However, their extremely high accuracy often causes concerns regarding overfitting and low generalizability, proving the important balance between prediction accuracy and clinical applicability.

In contrast, Edlitz and Segal [19] used a complex GBDT (Gradient Boosting Decision Tree) model but still holds high interpretability. Vakil et al. [20] combine multiple machine learning models with explainable AI methods and SHAP (Shapley Additive Explanations) for enhancing the interpretability of early detection of diabetes. These studies highlight the importance of balancing prediction performance and clinical interpretability.

Although machine learning methods have made progress in diabetes classifications, a critical challenge still remains in clinical datasets: class imbalance. In most screening populations, non-diabetic individuals constitute the majority of cases. For example, the global diabetes prevalence in 2019 is estimated to be 9.3% (463 million people) [11]. Talebi Moghaddam et al. [21] demonstrated that this class imbalance can significantly affect model performance and often leads to reduced sensitivity. In particular, classifiers tend to favor the majority class and incorrectly classify diabetic individuals as non-diabetic, resulting in a high false negative rate. In clinical screening, these missed diagnoses are especially problematic because patients may lose the opportunity for timely intervention and treatment, increasing the risk of disease progression and long-term complications [22].

Furthermore, different prediction models exhibit distinct strengths and limitations. Seto et al. [23] showed that Gradient Boosting Decision Trees is better in capturing complex non-linear relationships and achieving higher predictive accuracy; Logistic Regression remains valuable because of its simplicity, interpretability, and well-calibrated probability estimates. Similarly, Abousaber et al. [10] evaluated multiple machine learning algorithms for diabetes classification, including Random Forest (RF), Gradient Boosting Machines (GBM), Support Vector Machines (SVM), Artificial Neural Networks (ANN). Their results showed that no single algorithm consistently outperformed all others across different datasets and preprocessing strategies, suggesting that different models possess complementary strengths.

Beyond model selection, the choice of interpretability method is equally important. Lundberg et al. [24] showed that the SHAP method can improve the interpretability of tree-based models, including measuring local feature interaction effects and combining many local explanations of each prediction.

The Pima Indians Diabetes Dataset is originally from the National Institute of Diabetes and Digestive and Kidney Diseases [25]. Original purpose of the dataset is to diagnostically predict the presence of diabetes based on certain measurements. Notably, the dataset has some constraints: all instances in the dataset are females at least 21 years old of Pima Indian heritage.

The dataset captures 768 samples of patients to analyze the biochemical and physical factors [7]. It consists of eight explanatory variables: Pregnancies, Glucose, Blood Pressure, Skin Thickness, Insulin, BMI, Diabetes Pedigree Function, and Age. The target variable, Outcome, is binary-coded, where 1 represents the presence of diabetes and 0 indicates its absence.

On the second row of Table 1, one important finding is that there are zero values in a number of categories including blood pressure, skin thickness, insulin, BMI, and glucose. These zeros are medically impossible: Glucose and Insulin are primary biochemical indicators of glycemic control and pancreatic function, while BMI, Blood Pressure, and Skin Thickness serve as physical markers for obesity and vascular health associated with insulin resistance. Collectively, these five variables define the metabolic profile necessary for accurately assessing diabetic risk and identifying latent physiological abnormalities. Features like Skin Thickness (227 zeros) and Insulin (374 zeros) have a significant amount of missingness, as the table illustrates, indicating that these data points were either randomly absent or not recorded. These zeros are regarded as missing observations and will be handled using sophisticated imputation techniques to preserve the integrity of the ensuing predictive modeling.

Table 1.Descriptive statistics for explanatory variables in the Pima Indians Diabetes Dataset.

To further evaluate the sequential two-stage framework, the Frankfurt Diabetes Dataset, collected from a hospital in Frankfurt, Germany, was introduced as the external test set [26]. The 80% training set drawn from the Pima Indians Diabetes Dataset was used to train the model, and the 20% internal validation set was used to validate the model. The Frankfurt Diabetes Dataset comprises 2000 female patients and shares the same eight explanatory variables and the same binary Outcome label. Thus, the trained model can be directly applied to the external test set.

Similarly, the external test set in Table 2 contains physiologically implausible zero values in Glucose, Blood Pressure, Skin Thickness, Insulin, and BMI. These zero values were regarded as missing values. Therefore, missing data issue exists in both two datasets and, hence, a method is proposed to address this problem in 3.3.

Table 2.Descriptive statistics for explanatory variables in the Frankfurt Diabetes Dataset.

To address the missing values in features in 3.2, a Random Forest (RF) imputation method, specifically the MissForest algorithm, was employed. Unlike simple mean or median imputation, which can distort the data distribution and ignore inter-variable correlations, RF imputation is a non-parametric approach that predicts missing values by leveraging the complex, non-linear relationships between all observed features.

The imputation process treats each variable with missing data as a target (Y) and the remaining variables as predictors (X) [27]. For a missing value in variable j, an ensemble of decision trees learns a functional mapping. The imputation accuracy is evaluated using NRMSE (Normalized Root Mean Square Error):

By leveraging the covariance structure of complete variables like Age and BMI, the model effectively reconstructs high-missingness features such as Skin Thickness and Insulin. This method provides a solid basis for the prediction model by reconstructing high-missing features like skin thickness and insulin from the covariance structure of complete variables like age and BMI using an Iterative Imputer framework.

In Figure 2, the Outcome distribution in two datasets both indicates data imbalance: in the Pima Indians Diabetes Dataset, 500 instances (65.1%) labeled as 0 and 268 instances (34.9%) labeled as 1; in the Frankfurt Diabetes Dataset, 1316 instances (65.8%) labeled as 0 and 684 instances (34.2%) labeled as 1. This data inequality, characterized by a larger proportion of non-diabetic cases, may bias model performance toward the majority class.

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Figure 2.Distribution of the outcome (0 = no diabetes, 1 = diabetes) in the Pima Indians Diabetes Dataset and the Frankfurt Diabetes Dataset. (a) Pima Indians Diabetes Dataset; (b) Frankfurt Diabetes Dataset.

Hence, to address this issue, the Synthetic Minority Oversampling Technique (SMOTE) was employed to generate synthetic samples of the minority class (Outcome = 1) [28]. However, experimental findings showed that SMOTE did not improve the performance of the best model in this investigation. The top-performing single-stage classifier, the Gradient Boosting Machine (GBM), maintained the same accuracy on the original and SMOTE-balanced datasets. The original imbalanced dataset was thus kept for all ensuing modeling and interpretability analyses in order to preserve the real-world data.

The Pima Indians Diabetes Dataset was stratified into an 80% training set and a 20% internal validation set to ensure consistent class distribution across splits. Four widely used classification algorithms were implemented as baseline comparators: Random Forest (RF) [29], Support Vector Machine (SVM) [30], Artificial Neural Network (ANN) [31], and Gradient Boosting Machine (GBM) [32]. Model performance was assessed using confusion matrix-derived metrics, including accuracy, false positive rate (actual non-diabetic cases incorrectly classified as diabetic), and false negative rate (actual diabetic cases incorrectly classified as non-diabetic).

Figure 3 shows Gradient Boosting Machine (GBM) had the highest accuracy of 76.62%. Therefore, GBM was chosen as the secondary model for the later two-stage model.

Figure 3.Comparison of four classification model accuracy on the internal validation set using the original imbalanced dataset.

In the standalone GBM evaluation, Gradient Boosting Machine (GBM) achieved an accuracy of 76.62%. However, it still has a high false negative rate (presence of diabetes is overlooked) of 40.74%, which is unsuitable for clinical screening. A missed diagnosis can cause severe consequences. Therefore, to ensure patients receive necessary early care and reduce the false negative rate, a two-stage model is proposed.

In the first stage, Logistic Regression serves as a high-confidence positive identification stage that identifies positive cases (Outcome = 1); the remaining cases are then passed to GBM, which provides an additional opportunity to identify positive cases that were not classified as positive in the first stage.

To evaluate the robustness and transferability of the two-stage model, two evaluation procedures were conducted: first, the Pima Indians Diabetes Dataset was split into an 80% training set and a 20% internal validation set, where the internal validation set is used for testing the model’s robustness; second, the Frankfurt Diabetes Dataset was used as the external test set to assess transferability using the established model.

Stage 1: Logistic Regression

A logistic regression model is first trained on the 80% training set drawn from the Pima Indians Diabetes Dataset. Logistic Regression (LR) is a foundational statistical model used for binary classification. It utilizes the logistic function to map input variables into a probability space between 0 and 1. As shown in the following formula [33]:

It employs the sigmoid function to estimate the probability p of diabetes (Outcome = 1). In Stage 1, observations with logistic-regression probabilities greater than 0.9 were classified as positive. All remaining observations were passed to the GBM classifier for the final prediction.

Stage 2: Secondary Classifier (Gradient Boosting Model)

Gradient Boosting Machine is an advanced ensemble technique that builds models sequentially, with each new model attempting to correct the residual errors of the previous ones. Following the iterative optimization framework proposed by Friedman, the algorithm minimizes a loss function L ( y , F ( x ) ) by adding weak learners (typically decision trees) using a gradient descent-like procedure. The model F(x) is updated at each step m according to the formula:

where h m ( x ) is the weak learner trained to predict the negative gradient (residuals) of the loss function, and γ m is the step size or learning rate [32]. GBM was selected in this study because of its exceptional prediction capability, as well as its capacity to manage complicated feature relationships and missing data. In addition to Random Forest’s stability and ANN’s structural depth, GBM offers a highly accurate boundary for diabetic risk assessment by concentrating on the “hard-to-classify” cases in the training set.

In the two-stage model, GBM acts as the second-stage classifier: Samples predicted as Outcome = 0 (absence of diabetes) in logistic regression are then passed to a secondary GBM classifier. If the secondary model predicts 1, the final output is Outcome = 1; otherwise, Outcome = 0.

The final diagnosis of diabetes is the union of positive predictions from both stages (A + B in Figure 4), thereby reducing the false negative rate (the rate of missed diagnoses). Instead of aiming only to achieve higher accuracy, this two-stage model combines a high-confidence positive identification stage with GBM classification for the remaining cases.

Figure 4.Procedure of the two-stage combined model.

Detailed preprocessing and model specifications are summarized in Table 3.

Table 3.Model specifications.

The training-only Stage 1 threshold comparison is presented in Table 4.

Table 4.Training-only stage 1 threshold comparison.

0.90 was selected as the threshold as a conservative high-confidence rule-in cutoff, allowing only the most confident positive cases to be classified directly in Stage 1 while passing all remaining cases to the GBM.

Having established the two-stage model to reduce the false negative rate, model interpretability is also equally important in order to identify which variables most strongly drive the model’s risk predictions. SHAP (SHapley Additive exPlanations) is a game-theoretic approach used to explain the outputs of any machine learning model by decomposing each prediction into additive contributions from individual features [34]. Specifically, SHAP treats each feature as a player in a cooperative game. The core idea of SHAP is to decompose a model’s prediction into the sum of contributions from individual features. For a given prediction, SHAP calculates each feature’s contribution by considering all possible combinations of feature values. Unlike conventional importance measures, this method captures both the magnitude and the direction of each feature’s effect.

To efficiently compute SHAP values for tree-based ensembles such as GBM, this study employs TreeExplainer, an algorithm that provides tools for visualizing both global feature importance and the distribution of feature-level effects across individual samples [24]. In this study, SHAP is applied on the GBM model on the training set. Then, TreeExplainer computes the SHAP value of each feature for every sample. The global importance of each feature is calculated using the mean absolute SHAP value across all samples: larger SHAP values indicate greater overall influence on the model predictions.

The model was first trained on the 80% training set drawn from the Pima Indians Diabetes Dataset and evaluated on the remaining 20% internal validation set to ensure model robustness. In addition, to further guarantee the model’s transferability, the Frankfurt Diabetes Dataset, an independent dataset of 2000 female patients collected from a hospital in Frankfurt, Germany, was used as the external test set.

In Table 5, the internal validation set shows that the two-stage model achieved an overall accuracy of 77.27% with a false negative rate of 38.89% (21 out of 54 actual positive cases). In Table 6, the external test set shows that the model achieved an overall accuracy of 89.35% and a lower false negative rate of 20.47% (140 out of 684 actual positive cases). Moreover, the missed positive cases accounted for only 13.64% of the internal validation set (21/154) and 7.00% of the external test set (140/2000), further demonstrating the effectiveness of the model. Thus, high accuracy and low false negative rates in both the internal validation set and the external test set together support the robustness and transferability of the two-stage model.

Table 5.Confusion matrix for the two-stage model on the internal validation set drawn from the Pima Indians Diabetes Dataset (n = 154).

Table 6.Confusion matrix for the two-stage model on the external test set drawn from the Frankfurt Diabetes Dataset (n = 2000).

To improve upon the limitations of the impurity-based GBM importance measure, SHAP (SHapley Additive exPlanations) values were computed using TreeExplainer, which decomposes each individual prediction into additive feature contributions grounded in cooperative game theory [34]. This approach not only ranks feature importance but also reveals the direction and distribution of each feature’s effect across all samples [24].

Figure 5 ranks Glucose first, followed by Insulin, BMI, DiabetesPedigreeFunction, and Age. These variables are all important features in clinical interpretation, which is broadly consistent with established medical knowledge.

Figure 5. SHAP feature importance based on mean absolute SHAP values for the GBM model.

Pregnancies, SkinThickness, and BloodPressure have lower mean absolute SHAP values and contribute relatively less to the overall model predictions. This illustrates that these features are not the main contributors to the model’s predictions.

In Figure 6, the Beeswarm plot further demonstrates the direction and the distribution of each feature’s contribution. Glucose displays a clear directional pattern: as the glucose value increases, SHAP value also increases, with higher glucose values generally corresponding to more positive SHAP values. BMI shows a similar but milder pattern. In contrast, Age and Insulin exhibit a more dispersed color distribution, suggesting their influence on risk is less consistent across all individuals; instead, they may depend on interactions with other variables. The remaining features generally show SHAP values closer to 0, indicating a comparatively weak and inconsistent contribution to individual predictions. These results corroborate the results of the feature-importance plot that Glucose and Insulin are the most important factors.

Figure 6. SHAP beeswarm plot showing the magnitude and direction of feature contributions to individual GBM predictions.

Unlike SHAP analysis in 5.2, the partial dependence (5.3) and interaction plots (5.4) employ the classical partial dependence approach [32]: for each feature being analyzed, all other features remain constant at original values; and the resulting predictions for all the samples are averaged to estimate the feature’s overall effect on the model.

Partial dependence plots illustrate the effect of individual features on the model’s performance, when holding all other variables constant. The y-axis represents the partial dependence value—higher values indicate higher model-predicted probability of diabetes.

As shown in Figure 7, the partial dependence plots reveal nonlinear patterns across Glucose, BMI, Insulin, and Age.

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Figure 7.Partial dependence plots for Glucose, BMI, Insulin, and Age. (a) Glucose; (b) BMI; (c) Insulin; (d) Age.

Glucose: The overall trend shows that there’s a positive correlation between glucose and risk of diabetes. However, the relationship is not a perfect straight line, but increases through several thresholds. Risk first starts to increase from 105 - 110 mg/dL; then it sharply increases at 125 - 130 mg/dL; it finally reaches a very high risk level at 150 - 160 mg/dL.

BMI: The BMI plot shows an initial increase near 23 kg/m² and a second increase around 27 - 30 kg/m². Below BMI at 23 kg/m², risk is constantly low; then the risk progressively rises through (23 kg/m² - 30 kg/m²) and levels out over BMI 30 kg/m² - 45 kg/m².

Insulin: Below approximately 80 μU/mL, risk remains relatively low. It then rises with several fluctuations between approximately 80 and 140 μU/mL, remains at a relatively high level until around 170 μU/mL, declines toward 200 μU/mL, and then stabilizes with a slight increase near the upper end of the plotted range.

Age: From the ages of 20 to 50, risk increases steadily, reaching a local maximum in the early 50s. It then declines through the late 50s and early 60s, followed by a modest rebound around age 70 and a relatively stable pattern at older ages.

Interaction plots visualize the joint effect of two features on predicted diabetes risk through heatmaps. The color gradient represents partial dependence values, with yellow/bright regions indicating high risk and blue/dark regions indicating low risk.

Figure 8 presents the interaction plots for Glucose × Age, Glucose × BMI, Glucose × Insulin, and Age × Insulin.

Glucose × Age: The impact of Glucose is highly significant. As Glucose levels increase from 80 mg/dL to 180 mg/dL, the predicted risk increases significantly, with the highest predicted probabilities at the highest Glucose values. The influence of Age is relatively weak. When Glucose level stays the same, as age increases, the risk does not change significantly. However, in each glucose level, age between 25 - 30 shows a change in the risk, showing a clear interaction effect—Glucose’s impact on the outcome is dependent individual’s age.

Glucose × BMI: In this plot, Glucose still stands out as an important risk factor: as Glucose increases from 80 mg/dL to 180 mg/dL, the risk increases dramatically. The influence of BMI shows a “threshold” characteristic: within the BMI range of approximately 27.5 to 30, the contour lines undergo a sharp transition, indicating a non-linear shift in the model’s response. This shows a clear interaction effect—Glucose’s impact on the outcome is dependent on the individual’s BMI.

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Figure 8.Interaction plots for selected feature pairs in the GBM model. (a) Glucose × Age; (b) Glucose × BMI; (c) Glucose × Insulin; (d) Age × Insulin.

Glucose × Insulin: Similarly, Glucose is an important risk factor: as Glucose increases from 80 mg/dL to 180 mg/dL, the risk increases dramatically. Thresholds occur particularly when Insulin is below 100 and around 200. This shows a clear interaction between Glucose and Insulin.

Age × Insulin: There is a significant increase in risk along the diagonal axis from the bottom-left to the top-right. This means when Age and Insulin Levels both increase simultaneously, the risk increases; when each variable increases independently, the risk almost stays the same. Thus, this plot highlights a strong interaction between Age and Insulin.