Machine learning-based prediction model for 30-day readmission risk in elderly patients with type 2 diabetes mellitus and heart failure: a retrospective cohort study with SHAP interpretability analysis

Figures

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  Figure 1. LASSO regression feature selection analysis. (a) LASSO coefficient path showing the shrinkage behavior of feature coefficients as the regularization parameter (λ) increases. Each colored line represents a different feature, with coefficients approaching zero as λ increases. The red dashed line indicates the optimal λ value selected by cross-validation. (b) LASSO regression deviance plot displaying the cross-validation error (Mean Squared Error) as a function of log (λ). The optimal λ value (λ_min = 0.004687) that minimizes cross-validation error is marked by the red dashed line, resulting in the selection of 14 key variables. Error bars represent standard errors across cross-validation folds. CV, cross-validation; LASSO, least absolute shrinkage and selection operator.

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  Figure 2. Comprehensive model performance evaluation and comparison. (a) Receiver operating characteristic (ROC) curves for all eight machine learning models in the training set, showing discriminative performance with area under the curve (AUC) values. (b) ROC curves for the validation set demonstrating model generalizability. (c) Calibration curves for the training set comparing predicted vs. observed probabilities, with the diagonal dashed line representing perfect calibration. (d) Calibration curves for the validation set. (e) Decision curve analysis for the validation set showing net clinical benefit across different threshold probabilities, with “Treat All” and “Treat None” strategies as references. (f) Model performance comparison heatmap displaying standardized performance metrics (AUC, accuracy, sensitivity, specificity, PPV, F1-score) across all models, with color intensity indicating performance levels. LR, logistic regression; RF, random forest; GBM, gradient boosting machine; SVM, support vector machine; NN, neural network; CNN, convolutional neural network; PPV, positive predictive value.

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  Figure 3. SHAP (SHapley additive exPlanations) interpretability analysis. (a) Feature importance comparison between high-risk and low-risk groups showing mean absolute SHAP values for the top 14 selected features. Red bars represent high-risk patients, blue bars represent low-risk patients. (b) SHAP summary plot for high-risk class showing the distribution of SHAP values for each feature across all patients. Each dot represents one patient, with color indicating feature value (red = high, blue = low) and x-axis position showing the impact on model prediction. (c) SHAP waterfall plot for a representative high-risk individual demonstrating how each feature contributes to the final prediction. Positive SHAP values (red) increase readmission risk, while negative values (blue) decrease risk. The base value represents the model's expected output, and the final prediction probability is shown on the right. CRP, C-reactive protein; eGFR, estimated glomerular filtration rate; BNP/NT-proBNP, B-type natriuretic peptide/N-terminal pro-B-type natriuretic peptide; HbA1c, hemoglobin A1c; BMI, body mass index.

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  Figure 4. Web-based clinical risk calculator interface. Screenshot of the user-friendly 30-day readmission risk calculator developed for point-of-care clinical decision-making. The interface includes input fields for all 14 selected predictive features: laboratory parameters (CRP, eGFR, BNP/NT-proBNP, hemoglobin, HbA1c), clinical characteristics (length of stay, BMI, age, previous hospitalizations), and categorical variables (anemia, diuretic use, alcohol history, chronic kidney disease, smoking history). The right panel displays a color-coded risk gauge with real-time probability calculation, ranging from low risk (green) to high risk (red). The calculator provides immediate risk assessment with visual feedback to facilitate clinical interpretation and intervention planning.