## 2 Materials and Methods
### Statistical Analysis  
Statistical analysis was performed using R (version 4.4.1) and SPSS (IBM SPSS Statistics 27.0). To predict the GMFM-66 using data from gait analysis, multiple linear regression was used. Before evaluating the quality of the model, the assumptions for multiple linear regression were checked. Due to the high number of predictors (s. above), both the overall model and the individual variables were assessed for significance. While the overall model was significant, only a few regression coefficients were. Therefore, variables with high p-values were systematically removed through repeated regression analyses until a model remained in which all coefficients were statistically significant (\(p<0.05\)). Machine learning is increasingly being used to process big data. Used correctly, analyses of big data can quickly lead to research results [34]. Supervised learning is a type of machine learning where a model is trained on a labeled data set. Each example in the training data consists of an input and a corresponding correct output. The model learns to map inputs to outputs by minimizing the error between its predictions and the true labels (training data set). Once trained, it can make predictions on new, unseen data based on the patterns it has learned (validation data set) [35]. We compared four machine learning models, the feed forward neural net (FNN), random forest (RF) and support vector machine (SVM), with the software packages randomForest (version 4.7-1.1) [36], neuralnet (version 1.44.2) [37], nnet (version 7.3-18) [38] and XGboost (version 1.7.11.1) [39] in the software R (version 4.4.1.). For more information, please see the specific literature as this is beyond the scope of this work. The data set was randomly selected and divided into two groups. One group with 70% of the patients in the data set was used to train the algorithms (training data set, Figure 1). The other group with 30% was later used for comparison with the calculated data (validation data set). For the self-learning algorithms, all available parameters of the gait analysis were used as predictors. The tuning process was carried out for RF, FNN and SVM by a grid search with the appropriate hyperparameters. For the XGB model, a Bayesian optimization of the hyperparameters was performed. In the turning process, various statistical models with different combinations of hyperparameters are calculated and an attempt is made to find the best constellation of hyperparameters for each model. This is performed using 5-fold cross-validation. Only the data from the training data was used for this. The models (one for each type: RF, FNN, SVM and XGB) with the best hyperparameter combination determined in this way is then applied to the validation data in order to obtain a prediction of the GMFM-66. SHAP (Shapley Additive Explanations) values were calculated for each individual predictor in the model with the best predictive performance. SHAP values quantify the contribution of each predictor to the model's output for individual observations, based on cooperative game theory [40]. Larger absolute SHAP values indicate a greater influence of a predictor on the model's prediction for a given instance. By averaging the absolute SHAP values across all samples, one can identify the most influential predictors globally. This approach enables an interpretable ranking of feature importance across the examined predictors. The data set was randomly split into a 70% training set and a 30% validation set. Four machine learning models (RF, FNN, SVM and XGB) were trained using all available gait analysis parameters, with hyperparameters tuned via grid search (RF, FNN and SVM) or Bayesian optimization (XGB), based on 5-fold cross-validation. The best-performing models were then applied to the validation data to predict GMFM-66 scores. SHAP values were used to interpret the models by quantifying and ranking the influence of each predictor on the predictions.