## 2 Materials and Methods
### Evaluation of the Prediction Model  
The evaluation of the classification system was carried out by two cross validation methods. The first is a \(K\)-fold cross validation where the database is divided into two sub-databases: a training database and a test database. This division allows the model to be developed and tested on different data to verify its relevance. In our study, we opted for \(K=10\) and \(K=20\) divisions to evaluate the model's stability.  
The second evaluation method is a the Leave-one-out cross validation (LOOCV) which is a \(K\)-fold cross validation taken to its logical extreme, with \(K\) equal to \(N\), the number of data points in the set, that is to say the number of participants.  
After model training, we considered the classification rate as an evaluation criterion. This rate is the ratio between the total number of well-classified data points and the total number of data points as described in Equation (3). The classification rate is computed for each fold and the average used to evaluate the model.  
\[\text{Classification rate}=\frac{\text{Well-classified observations}}{\text{Total number of observations}}. \tag{3}\]  
The confusion matrix can also be presented for a better interpretation of the results. This is a matrix representation that determines the classification error from a set of test data. The confusion matrix is a square matrix of \([C\times C]\) size where \(C\) is the number of classes. The columns of this matrix correspond to the number of occurrences of an estimated class, while the rows correspond to the number of occurrences of an actual class. Table 4 shows an example of a confusion matrix with two classes. The precision of the classifier is calculated by Formula (4), and the sensitivity and specificity by Formulas (5) and (6), respectively [29].  
True Positive (TP) is the number of patients that improved and were classified in the class I. True Negative (TN) includes the patients that did not improved and were classified as nI patients. False Positive (FP) describes patients that not improved but were classified as I patients. False Negative (FN) is the number of patients that improved but were classified in the class nI.  
To be considered accurate, a classifier must be both highly sensitive and highly specific. The accuracy, sensitivity and specificity were computed according to the following  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Predicted Class** & \\ \hline
**Actual Class** & **I** & **nI** \\ \hline I & True Positive & False Negative \\ \hline nI & False Positive & True Negative \\ \hline \hline \end{tabular}
\end{table}
Table 4: Example of a confusion matrix. I = improved; nI = not-improved.  
mathematical formulas:  
\[\text{Accuracy}=\frac{\text{TN}+\text{FP}}{\text{Total number of observation}} \tag{4}\]  
\[\text{Precision}=\frac{\text{TP}}{\text{TN}+\text{FP}} \tag{5}\]  
\[\text{Sensitivity}=\frac{\text{TP}}{\text{TN}+\text{FP}} \tag{6}\]  
\[\text{Specificity}=\frac{\text{TN}}{\text{TN}+\text{FP}} \tag{7}\]  
Significant differences in 3D knee kinematics between men and women have been reported in the literature, both in healthy and knee OA subjects [30; 31]. Therefore, three different prediction systems were trained: one each for the male and the female population and one for the overall data-set (male and female together) to account for the sex-specific aspects of kinematics. The receiver operating characteristic (ROC) curve was generated to illustrate the performance of the prediction models, using the area under the curve (AUC) [32].