## 7 Discussion
### Explanation of the Models Obtained  
The relation between parameter values and the decision represented by the XGBoost models is difficult to interpret by a human. Logistic regression gives the possibility to estimate the adjusted odds ratio (Table 6), which gives a direct and intuitive interpretation of obtained classifier parameters. However, to give a unified comparison of both approaches, the RPART decision trees [64] were created to provide an explanation of the relationship between symptoms and the outcome predicted by the models. Having two sets of basic features selected for each model, decision trees were generated to explain the behaviour of their representative models. First, two training sets were prepared. The data sets consisted of patients with symptoms (Sick) representing the attributes that were used by the models, and each patient was assigned the decision given by the model. Then, based on these two separate training sets, two RPART decision trees were generated. Finally, it was evaluated how well the decision trees approximate the decisions made by the considered models. For each patient, the decision given by the model was compared with the decision given by its RPART approximation. For the decision tree generated for the logistic regression model approximation, the resulting Balanced Accuracy (BAcc) value was 0.967, and, for the decision tree generated for the XGBoost model approximation, the resulting BAcc value was 0.937. Based on the very high BAcc values, it was possible to use the trees to explain the relationship between symptoms and model outcomes. Furthermore, similar decision trees using training sets based on selected feature interactions were generated. However, since the representation of a tree based on simple (basic) features can be better understood, it was decided to include a simpler version in the manuscript. The generated decision trees are presented in Figures 5 and 6. The colours in the figures represent the classes--COVID-19(+) is represented by red and COVID-19(-) by blue. The more saturated the colour of a node is, the greater the dominance of examples from a given class in this node. The first row of the RPART tree node provides information about the majority class of examples covered by that node; the second provides the percentage of the cases from the node that are classified by the approximated model into the majority class, and the third row provides the percentage of all cases covered by that node. The branches of the tree represent symptoms and their presence or lack thereof (_yes_ means that the patient has a symptom and _no_ means that a symptom is not observed). Please note that since the trees were built to approximate the models, their leaves do not represent the patient outcome, but the decision provided by the model based on the particular set of symptoms. Decision trees can be used to explain which combinations of symptoms and their values are taken into account while predicting diagnosis. For example, it can be noted that, in the case of both models, a long symptom duration _no_of_days_of_symptoms \(\geq\) 13 will result in a negative decision (COVID-19(-)), unless the patient observes the _loss_of_taste_smell_. Figure 5: Decision tree generated to explain the behaviour of logistic regression classifier—red colour represents positive class and blue colour represents negative class. The more saturated the colour of a node is, the greater the dominance of examples from a given class in this node. Figure 6: Decision tree generated to explain the behaviour of XGBoost classifier—red colour represents positive class and blue colour represents negative class. The more saturated the colour of a node is, the greater the dominance of examples from a given class in this node. In general, the decision tree approximating the logistic regression model is less complex and allows for an easy interpretation of the model's decision-making. The decision-making model can be expressed in terms of seven rules containing 2 to 4 conditions (nodes).