Objective To construct a depression risk prediction model for elderly patients with chronic pain in China, and verify the predictive performance of different models.

Methods The national survey data of the China Health and Retirement Longitudinal Survey (CHARLS) in 2020 was adopted. The research subjects were selected according to the inclusion and exclusion criteria, and randomly divided into the training set and validation set at a ratio of 7∶3. The included research variables were demographic information, health status and function, and working status. A risk prediction model for depressive state in elderly patients with chronic pain was constructed based on the decision tree model, random forest model and XGBoost model. The accuracy rate, sensitivity, specificity, F1 score and area under the receiver operating characteristic (ROC) curve (AUC) of each model were compared to evaluate the predictive performance of the models.

Results The detection rate of depressive symptoms among 1037 elderly people was 29.89%. The decision tree model screened out the degree of pain interference, sleep quality, cognitive function, frequency of social activities and self-rated health status as important explanatory variables, among which the degree of pain interference was the root node. The random forest model shows that the degree of pain disturbance (the decrease in Gini coefficient for 0.213), sleep quality (0.186) and frequency of social activities (0.152) are the main influencing factors. The XGBoost model had the highest characteristic gain value of pain interference degree, and the SHAP value analysis shows that there was an interaction effect between pain and sleep, as well as social factors.

Conclusions Among the three constructed prediction models for depression risk in elderly patients with chronic pain, the XGBoost model has the best performance, and can effectively identify high-risk groups for depression. The degree of pain interference, sleep quality and frequency of social activities are the key influencing factors, and their interaction is of great significance for predicting the risk of depression. The research results can provide a scientific basis for the early identification of depression in elderly patients with chronic pain, and the formulation of subsequent risk stratification management strategies.