## 3 Results  
Prediction models were developed using the CART algorithm. The training input vectors consisted of the 69 biomechanical parameters (F\({}_{1}\), F\({}_{2}\),...,F\({}_{69}\)), patients' age (F\({}_{70}\)), BMI (F\({}_{71}\)), radiographic OA severity grade measured by the Kellgren-Lawrence scale (F\({}_{72}\)), and the KOOS\({}_{pain}\) (F\({}_{73}\)). The training input measurements were evaluated at baseline as required by the principle of a prediction model. Analyses were undertaken with Matlab R2019b software (Mathworks, MA, USA). Specifically, we used the Toolbox Statistics and Machine Learning Toolbox.  
Table 5 summarizes the classification rates of the three models developed for each validation method. Given that the prediction performances were better when the two sexes were analyzed separately, the prediction model focused on the impact of the physical exercise program for each group independently.  
Figure 4 displays the ROC curve and the AUC for both the male and female prediction models.  
The confusion matrices using the LOOCV are presented in Tables 6 and 7. For instance, the prediction model within the male population reached a sensitivity of 85.4% and a specificity of 70.3%.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & & **Datasets** & \\ \hline
**Validation Techniques** & **Male (N = 78)** & **Female (N = 143)** & **All (N = 221)** \\ \hline
10-Fold & 84.4\% \(\pm\) 13.2 & 75.5\% \(\pm\) 6.8 & 71\% \(\pm\) 9.9 \\ \hline
20-Fold & 84.6\% \(\pm\) 19.2 & 75.7\% \(\pm\) 14.3 & 71\% \(\pm\) 14.6 \\ \hline LOOCV & 78.2\% & 73.4\% & 71\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Classification rates of the three models for each validation technique. Rates for K-fold techniques are presented \(\pm\)standard deviation.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**Predicted Class**} & \multicolumn{1}{c}{**Accuracy**} \\ \hline
**Real Class** & **nI** & **I** & \\ \hline nI & 35 (85.4\%) & 6 (14.6\%) & 85.4\% \\ \hline I & 11 (29.7\%) & 26 (70.3\%) & 70.3\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Confusion matrix of the male prediction model. Accuracy is presented for each class (I and nI).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Feature Id** & **Feature Name** & **Feature Description** \\ \hline \multirow{3}{*}{Male} & F\({}_{4}\) & Varus thrust during & Maximum abduction angle between 10\% and 30\% of the GC \\  & & loading & minus the adduction angle value at 10\% of the GC \\  & F\({}_{26}\) & Flexion at initial swing & Flexion angle value at 69\% of the GC \\  & F\({}_{73}\) & KOOS\({}_{pain}\) & KOOS score on the pain subscale at baseline \\ \hline \multirow{3}{*}{Female} & F\({}_{14}\) & External tibial rotation & Rotation angle value at 1\% of the GC \\  & & at initial contact & Maximum minus the minimum rotation angle \\ \cline{1-1}  & F\({}_{15}\) & Internal tibial rotation & value between 1\% \\ \cline{1-1}  & & during loading & and 20\% of the GC \\ \cline{1-1}  & F\({}_{39}\) & Maximal tibial rotation & Maximum rotation angle value between 1\% and \\ \cline{1-1}  & & during gait & 100\% of the GC \\ \hline \hline \end{tabular}
\end{table}
Table 8: Description of the retained features. All features (except for KOOS\({}_{pain}\)) are expressed in degrees.  
Figure 4: The ROC curves and AUC of the prediction models (**a**) Males and (**b**) Females.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**Predicted Class**} & \multicolumn{1}{c}{**Accuracy**} \\ \hline
**Real Class** & **nI** & **I** & \\ \hline nI & 52 (76.5\%) & 16 (23.5\%) & 76.5\% \\ \hline I & 22 (29.3\%) & 53 (70.7\%) & 70.7\% \\ \hline \hline \end{tabular}
\end{table}
Table 7: Confusion matrix of the female prediction model. Accuracy is presented for each class (I and nI).  
Figure 5 shows the decision trees for each of the prediction models for both the male and female populations. Training and validation were performed independently for each population.