Patients with lumbar disc herniation who underwent percutaneous transforaminal endoscopic discectomy at our hospital were retrospectively collected between May 2021 and May 2023 for the training cohort, and between June 2023 and June 2024 for the validation set. The former served as the training set, while the latter was used as the external validation set. Inclusion criteria were as follows: (1) age between 18 and 75; (2) grade of spinal spondylolisthesis ≤ Grade I; (3) Pfirrmann Grading of Grade II or Grade III; (4) lumbar segments involved were L3–L4, L4–L5, or L5–S1. Patients were divided into a persistent pain group and a non-persistent pain group based on the presence of persistent pain postoperatively. Exclusion criteria included: (1) presence of other diseases affecting the structure or function of the lumbar spine; (2) undergoing other interventions during follow-up that may influence lumbar pain (such as spinal fusion surgery or nerve block therapy); (3) severe hepatic or renal dysfunction; (4) serious systemic diseases such as malignancies; (5) severe mental or psychological disorders (e.g., major depression or severe anxiety) or poor treatment compliance; and (6) missing key data. Persistent pain was defined as a VAS score ≥ 4 and SF-36 scores < 50 in the pain and physical function domains at the 1-month postoperative follow-up. In the training set of 450 cases, 54 experienced postoperative persistent pain.

We collected baseline characteristics and pathological indicators for each patient, including age, gender, BMI, history of lumbar spine trauma, duration of disease (whether more than 6 months), herniation calcification, spondylolisthesis grade, Pfirrmann Grading (14), lumbar segments (L3–L4, L4–L5, L5–S1), sagittal range of motion (sROM), and inflammatory indicators [C-Reactive Protein [CRP], Erythrocyte Sedimentation Rate [ESR], and White Blood Cell Count [WBC]]. These data were obtained from patient medical records and preoperative imaging results.

To predict the occurrence of persistent postoperative pain, we selected four commonly used machine learning models for analysis: Logistic Regression (LR), Support Vector Machine (SVM), XGBoost, and Multilayer Perceptron (MLP). All input features were normalized before training to ensure consistency across different feature scales during model training. The DeLong test was used to perform pairwise comparisons of AUC values between models, with a P-value < 0.05 indicating a statistically significant difference in AUC.

To optimize model performance, we employed grid search combined with 10-fold cross-validation to fine-tune the parameters of each model. In this process, the dataset was split into 10 subsets, with 9 subsets used for training and 1 subset for validation in each iteration. After completing all 10 iterations, the average performance metrics were calculated. The evaluation metrics included the area under the ROC curve (AUC), F1 Score, Accuracy, Recall, and Precision.

To understand the prediction mechanism of the machine learning models, we used SHAP (Shapley Additive Explanations) values to explain the contribution of each feature to the prediction results (15). SHAP values quantify both the positive and negative impacts, as well as the importance of each feature on the prediction outcome, by assessing each feature's influence on the model output across different scenarios. We used SHAP values to analyze the direction and magnitude of each feature's effect on predicting persistent pain.

Based on the most important features identified through SHAP analysis, we constructed a simplified risk model to predict the risk of persistent postoperative pain. The primary formula was:RiskIndex=SHAP∗Feature[1]+SHAP∗Feature[2]+SHAP∗Feature[3]The SHAP values represent the average SHAP values from our chosen machine learning model. The top three important features were selected as input variables, and the model performance was validated on an external validation set. Model performance was evaluated using the AUC to assess its predictive capability.

All statistical analyses were conducted using R software, primarily utilizing the caret (16), iml, and shapviz packages. A P-value less than 0.05 was considered statistically significant. Continuous variables were presented as median (range) and compared using the Mann–Whitney U-test, while categorical variables were expressed as frequency (percentage) and analyzed with the Chi-square test or Fisher's exact test, as appropriate.

The results showed that patients with persistent pain were older, had a higher proportion of lumbar spine trauma history, and a significantly higher percentage of disease duration exceeding 6 months. These patients also had higher rates of herniation calcification, mild spondylolisthesis (Grade I), and Pfirrmann Grade III, with a significant increase in L4-L5 segment involvement. Additionally, levels of inflammatory markers, including C-reactive protein (CRP), erythrocyte sedimentation rate (ESR), and white blood cell count (WBC), were higher in patients with persistent pain compared to those without (Table 1). The training set (n = 316) and external validation set (n = 134) showed a balanced distribution across multiple demographic characteristics such as age and BMI, as well as clinical indicators including disease duration and lumbar spondylolisthesis. There were no significant statistical differences between the two cohorts, indicating good comparability (Supplementary Table S1).

These significant factors were then input as independent variables into four machine learning models. The results showed that the ROC values for these four models were 0.867, 0.888, 0.907, and 0.916, respectively (Table 2) (Figure 1). Among them, the AUC values of the XGBoost and MLP models were both above 0.9, and these models also performed excellently in terms of F1 Score, Accuracy, Recall, and Precision. The DeLong test showed that the AUC values of the XGBoost and MLP models were significantly higher than those of the LR and SVM models (P < 0.05). Therefore, XGBoost and MLP were selected for visualization analysis (Table 3).

For each machine learning model, a sample with persistent pain and a sample without persistent pain were randomly selected for analysis. The x-axis represents the direction of the change in the prediction value, with movement to the left indicating a negative influence and movement to the right indicating a positive influence. In Figure 2A, an age of 46 and CRP (C-Reactive Protein) level of 6.91 had a strong negative impact on the likelihood of persistent pain (−2.3 and −1.88, respectively), while certain lumbar segments and joint degeneration had a positive impact. The final expected prediction value was −2.99, indicating that the model predicts this patient is more likely not to experience persistent pain. In Figure 2B, a history of lumbar spine trauma (value of 1) and herniation calcification (value of 1) had a large positive impact on the prediction, significantly increasing the likelihood of persistent pain, with contributions of +4.68 and +3.3, respectively. Additionally, higher ESR (18.8) and WBC (7.56) levels had a negative impact on the prediction, reducing the risk of persistent pain.

In the MLP visualization results, in Figure 2C, for patients without persistent pain, herniation calcification and no history of lumbar spine trauma had a strong negative impact on the prediction. For patients with persistent pain, lumbar segment L5.S1 and herniation calcification had a significant positive impact on the prediction. In Figure 2D, a history of lumbar spine trauma had a strong positive impact on the prediction of persistent pain, while it showed a negative impact on the prediction of non-persistent pain, indicating that patients with a history of lumbar spine trauma are more likely to be predicted to experience persistent pain. Additionally, younger age also played a negative role in predicting the absence of persistent pain.

The feature value analysis for all samples in Figure 3A shows that the x-axis represents SHAP values, indicating the direction and magnitude of each feature's impact on the prediction. The color gradient from purple to yellow represents the change in feature values from low to high. In the figure, a history of lumbar spine trauma (yellow for high values) and older age have a significant positive impact on the risk of persistent pain, indicating that higher values for these features increase the risk of persistent pain. High values for inflammatory indicators (e.g., CRP, ESR, and WBC) also have varying degrees of impact on the prediction. The MLP model results indicate that a history of lumbar spine trauma and herniation calcification are the most important features affecting the prediction outcome, contributing the most to the prediction of persistent pain, followed by spondylolisthesis, ESR, Pfirrmann Grading, and CRP (Figure 3B). We summarized the SHAP visualization results of the XGBoost and MLP models in Supplementary Table S2 to enhance clarity and interpretability. We also conducted visualization analysis in the external validation cohort, and the results showed that the feature rankings in the external validation set were similar to those in the training set, especially the top three most important features remained consistent. This further supports the stability and generalizability of the model (Supplementary Figure S1).

We constructed a risk model to predict the likelihood of persistent pain based on the top three important features from these two machine learning models, and validated it in an external validation set. The results showed an AUC value of 0.798, indicating that the model has good predictive capability (Figure 4) (Table 2).