## 5 Results
### Explainability Results  
Figure 2 summarizes the most relevant features detected by SHAP and shows the overall features and additive contributions to the probability of being admitted to a ward, using the optimized ANN only. Amongst the features with the greatest contributions, 'Age', 'Heart Rate', 'French Emergency Nurses Classification in Hospital (FRENCH) grade: 2', and 'Reason: multiple severe injuries' increased the patient's likelihood of hospital admission. Since 'Age' and 'Heart Rate' are quantitative variables, the plot shows how much these variables are involved in the algorithm's decision: a young patient (blue color) has a lower likelihood of admission (positive SHAP value, on the right-hand side) than an older patient (red color). Conversely,  
Figure 1: The receiver operating characteristic curves for the data from the test set. The gray dashed line represents the random predictor. \begin{table}
\begin{tabular}{c c c c c} \hline  & **ANN** & **LR** & **KNN** & **RF** \\ \hline AUROC & 83.2\% & 71.5\% & 67.1\% & 71.8\% \\ \hline Accuracy & 77.5\% & 77.2\% & 73.0\% & 77.6\% \\ \hline Precision & 68.9\% & 69.4\% & 60.6\% & 70.4\% \\ \hline Recall & 57.2\% & 54.7\% & 50.0\% & 54.8\% \\ \hline \end{tabular}
\end{table} 
Table 3: Performance of models on the test set. features like 'Waiting mode: wheel chair', 'Reason: chest pain', and 'Reason: fainting' made a considerable negative contribution to the prediction outcome. Even though the (binary) variables 'Arrival mode: Personal', 'FRENCH grade: 5', 'FRENCH grade: 4', and 'Reason: limb trauma' made a small negative contribution to the probability of admission when they were positive, negative values also made a slight positive contribution to the probability of admission (e.g., 'not arriving in the ED by one's own means' increased the likelihood of admission). SHAP also provided local explainability about the predictions for an individual case by depicting the magnitude and direction of each feature's contribution to the final score (red: increasing the likelihood of hospital admission, blue: decreasing the likelihood of hospital admission) and relevance (i.e., the length of the bar in the chart). For instance, Figure 3a,b show the prediction of a true positive case and a true negative case, respectively. In both cases, the prediction started from a baseline Shapley value of 0.378, which corresponds to the model output's average probability of hospital admission for the training data. According to the general attributions in the SHAP summary plots, the patient's age was one of the most relevant features for both true negatives and true positives. It was decisive (\(-0.2\)) for a true negative case (i.e., a discharged patient), as was ED attendance for 'Reason: dyspnea \(<32/\min\)' (\(-0.12\)). For a true positive (i.e., the prediction of hospital admission), 'FRENCH 2' had the highest individual SHAP contribution (+0.11), although 'Age' = 79 (+0.1) and 'Reason: general physical deterioration' (+0.12) increased the probability of hospital admission. Figure 2: The SHAP summary dot plot of the hospital admission model’s overall explainability: the higher the SHAP value (for quantitative variables), the higher probability of hospital admission, and vice versa. With respect to binary features or one-hot coded categorical features, the red and blue colors refer to values of 1 and 0, respectively. The French Emergency Nurses Classification in Hospital (FRENCH) triage scale is detailed in Supplementary Material S1.5 and in [PERSON] et al. [55]. For quantitative features in particular, PDPs quantify the probability contribution as a function of the magnitude. By drawing up a PDP for every feature (to assess how probability changes), we learned that the features associated with the largest increase in the probability of hospital admission were 'Age' and 'Heart Rate' (Figures 4 and 5); this confirmed the SHAP results.