Random Forest Regression May Become the Optimal Regression Model for Osteoarthritis of the Knee in Elderly, in the Context of Embodied Cognition and Psychosomatic Medicine

Abstract

Background: In the context of embodied cognition and psychosomatic medicine, predicting post-treatment depression in elderly patients with knee osteoarthritis (KOA) is critical for improving psychological outcomes. While regression analysis is widely used in longitudinal medical studies, the optimal model for forecasting complex psychosomatic changes remains unclear.

Objective: This study compared the predictive performance of five regression models in estimating post-treatment depression (D2) among elderly KOA patients, considering variables such as gender, age, pain, anxiety, sleep quality, and baseline depression.

Methods: A total of 106 elderly KOA patients from the Affiliated Hospital of Southwest Medical University were assessed before and after treatment (September 2023 to February 2024). Psychological and physical metrics included the Visual Analog Scale (VAS), Beck Anxiety Inventory (BAI), Geriatric Depression Scale (GDS), and Pittsburgh Sleep Quality Index (PSQI). Five regression techniques-non-negative linear regression, stochastic gradient descent (SGD), AdaBoost, Random Forest, and Gradient Boosting Decision Trees (GBDT)-were evaluated using R², mean squared error (MSE), and mean absolute error (MAE). Bootstrap resampling and the Kruskal-Wallis test were applied to ensure robustness and compare model coefficients.

Results: Random Forest regression achieved the highest performance (R² = 0.687, MSE = 0.589, MAE = 0.785), followed by AdaBoost. Post-treatment anxiety and sleep quality emerged as the strongest predictors. All models showed acceptable multicollinearity (VIF < 10), and Kruskal-Wallis results suggested no significant differences in coefficients across models.

Conclusion: Random forest regression outperformed other models in predicting depression after KOA treatment, demonstrating its strength in capturing complex nonlinear relationships. However, the study's relatively small sample size and predominantly female cohort may limit generalizability. Future research with larger and more diverse samples is recommended to validate these findings.

Keywords: elderly patients; knee osteoarthritis; longitudinal analysis; post-treatment depression; psychosomatic outcomes; random forest; regression models.

Figure 1

Comparison of distributions at two time points.

Figure 2

Correlation heatmap. **Correlation is significant at the 0.01 level (two-tailed). *Correlation is significant at the 0.05 level (two-tailed). P1 is pre-treatment pain; D1 is pre-treatment depression; A1 is pre-treatment anxiety; S1 is pre-treatment sleep; P2 is post-treatment pain; D2 is post-treatment depression; A2 post-treatment anxiety; S2 is post-treatment sleep.

Figure 3

Comparison of R-squared, MSE, and MAE values for five regression models.

Figure 4

Comparison of R-squared, MSE, and MAE confidence intervals for five regression models.