Fig. 3

ROC curves for the training dataset (left) and validation dataset (right), illustrating the model’s discriminatory ability. The area under the curve (AUC) values are 0.771 (95% CI 0.750–0.792) for the training dataset and 0.759 (95% CI 0.727–0.790) for the validation dataset, indicating good predictive performance. The marked points on each curve represent the optimal threshold values, with corresponding sensitivity and specificity