Results
A total of 43 recreational table tennis players were included in this study, with 44 and 42 legs in the non-EOA and EOA groups, respectively ( Table 1 ). There were no significant differences between the groups in terms of sex distribution ( p = 0.22), age ( p = 0.46), height ( p = 0.07), weight ( p = 0.78), BMI ( p = 0.29), or KHD during SD ( p = 0.05). In addition, significant differences were observed in all SU and SD kinematics except for KHD during SD. The EOA group demonstrated significantly higher values for PHD ( p = 0.001), FHD ( p < 0.0001), KHD ( p < 0.0001), LHD ( p < 0.0001), and AHD ( p < 0.0001) during SU and PHD ( p < 0.0001), FHD ( p = 0.016), LHD ( p = 0.015), and AHD ( p < 0.0001) during SD compared with the non-EOA group.

To validate the quality and distinctiveness of the Louvain clustering solution, we calculated widely-used cluster validity indices. The Davies–Bouldin index was 2.09, and the Calinski–Harabasz index was 59.26. While the Davies–Bouldin index was somewhat high (lower values indicate better separation), the Calinski–Harabasz index supported the presence of distinct groupings in our data. The Louvain clustering algorithm identified four distinct clusters (C1–C4) with significant differences in all features (all p < 0.001, except for AHD-SU ( p = 0.017) and portion of EOA ( p = 0.019)) ( Table 2 ). Tukey’s post-hoc analysis revealed that those in C2 had the youngest age (44.80 ± 11.30 years, p < 0.001 vs. all other clusters) and highest BMI (25.59 ± 2.42, p < 0.001 vs. all other clusters). C2 included exclusively males, whereas the other clusters had a mixed sex composition. For SU kinematics, C4 exhibited the largest horizontal displacements for the pelvis, femur, knee, and lower leg, all significantly higher than other clusters ( p < 0.001). During SD, C3 showed the largest pelvis and femur displacements, while C4 had significantly higher ankle displacement ( p < 0.001 vs. all other clusters). C1 exhibited negative mean values for the knee and lower leg displacements during SD, significantly different from other clusters ( p < 0.001). These distinct kinematic profiles suggested potential subgroups within the EOA population, with varying proportions of EOA cases across clusters: C1 (45.6%), C2 (41.2%), C3 (59.5%), and C4 (70.7%).

Notes:

EOA early osteoarthritis EOAQ Early Osteoarthritis Questionnaire PHD pelvic horizontal displacement FHD femur horizontal displacement KHD knee horizontal displacement LHD lower leg horizontal displacement AHD ankle horizontal displacement SU step up SD step down

early osteoarthritis

Early Osteoarthritis Questionnaire

pelvic horizontal displacement

femur horizontal displacement

knee horizontal displacement

lower leg horizontal displacement

ankle horizontal displacement

step up

step down

The performances of the six machine-learning models in classifying groups with and without EOA during model training and testing are summarized in Table 3 and Figure 4 . In the training dataset, the Random Forest (AUC, 0.999 (excellent); accuracy, 0.976; F1, 0.976; precision, 0.976; recall, 0.976), gradient boosting (AUC, 0.983 (excellent); accuracy, 0.940; F1, 0.941; precision, 0.941; recall, 0.940), and decision tree (AUC, 0.964 (excellent); accuracy, 0.935; F1, 0.934; precision, 0.936; recall, 0.935) algorithms demonstrated excellent predictive performance with AUC values exceeding 0.95. The high F1-scores for these algorithms indicate an optimal balance between precision and recall, suggesting that these models correctly identified EOA cases with minimal false positives and false negatives. In the test dataset, the Random Forest, gradient boosting, and decision tree algorithm models achieved perfect classification (AUC = 1.000 (excellent); accuracy = 1.000; F1 = 1.000; precision = 1.000; recall = 1.000), demonstrating exceptional ability to differentiate between EOA and non-EOA cases. This consistent performance across all metrics demonstrates the robust generalizability of our models, particularly the tree-based algorithms (Random Forest and gradient boosting), which maintained their high performance from training to testing set.

Notes:

AUC area under curve Acc Accuracy kNN k-nearest neighbors

area under curve

Accuracy

k-nearest neighbors

Feature importance analysis using both the feature permutation importance and SHAP methods revealed consistent patterns across multiple machine-learning models ( Figure 5 ). For the Random Forest model, the four most important features were AHD-SU, FHD-SU, FHD-SD, and PHD-SD. The SHAP analysis indicated that higher values of AHD-SU, FHD-SU, FHD-SD, and KHD-SU were associated with increased model predictions. The gradient boosting model identified the same top four features, with SHAP analysis showing that higher values of AHD-SU, FHD-SU, and PHD-SD but lower values of FHD-SD influenced the predictions. Similarly, the decision tree model highlighted AHD-SU, FHD-SU, PHD-SD, and FHD-SD as the most important features. The SHAP results for the Decision Tree aligned with those of the gradient boosting model, indicating that higher AHD-SU, FHD-SU, and PHD-SD but lower FHD-SD were associated with increased predictions.