## 5 Decision Model Generation
### Proposed Classification Approaches
#### 5.3.1 Logistic Regression-Based Approach  
For the features remaining after the initial data selection, the effect size was calculated (Cramer's V and an estimate for Mann-Whitney non-parametric test for discrete and continuous features, respectively) [59; 60]. Only features with at least a small effect were preserved for further analysis. Hence, during the logistic regression model generation, five attributes were considered: contact with infected person, number of days of symptoms, temperature \(>\) 38 \({}^{\circ}\)C, loss of taste/smell, and dyspnoea. Additionally, for these attributes, all possible pair interactions were constructed (intersections \(\cap\); logical AND), e.g., occurrence of temp. \(>\) 38 \({}^{\circ}\)C and dyspnoea simultaneously will logically result in 1 for the interaction variable. When at least one of the attributes is 0, the interaction value will numerically be 0. Finally, the logistic regression approach does not handle missing values, so patients with incomplete information regarding five considered features were rejected. As a result, the training data set consisted of 572 examples, 185 of which were positive (COVID-19(+)) and 387 were negative (COVID-19(-)). The steps of the analysis presented in the consecutive paragraphs were repeated 100 times within the Multiple Random Cross-Validation (MRCV) process. Patients re  
Figure 4: Distribution of exemplary attributes. Panel (**A**) shows the distribution of the number of days of symptoms in each SARS-CoV-2 infection status (numerical feature). Panel (**B**) shows the proportions of positive and negative answers for binary attributes commonly linked to SARS-CoV-2 infection. maining after filtration were randomly divided into training and validation sets in equal proportions (50:50). The division was balanced in terms of COVID-19 diagnosis, as well as with regard to the considered set of features, so that, for instance, patients with a particular symptom were not underrepresented in the training or test set. Next, the logistic regression model was built with the forward feature selection method. Therefore, in each step, a new attribute was added to the model based on the selection criterion, which, in this case, was the Bayes Factor. New attributes were added until the Bayes Factor value decreased below 1, which is described as \"barely worth mentioning evidence\" [61; 62]. The attributes were either five previously selected features or their pairs' interactions. As the logistic regression model provides the probability that an observation belongs to a particular category (in this case, COVID-19(+)), the cut-off value of the probability must be determined to classify each patient. The cut-off probability was identified in such a way as to maximise the _WHM_ (1) with weight \(w\) equal to 0.85. The enhanced importance of NPV reduces the risk of false negative observations' occurrence for screening test purposes. Moreover, the applied weight reflecting standards in the designed medical screening test were NPV > 90 and PPV > 30 is expected. For medical reasons, it is crucial to avoid COVID-19(+) patients' exclusion from further diagnosis procedures, while molecular testing for SARS-CoV-2 infection of some COVID-19(-) patients is both acceptable and inevitable. The cut-off value could only be selected from the interval 0.1-0.9. Finally, the quality of prediction for the training and validation sets was calculated. After the MRCV procedure, feature ranking was prepared based on the feature significance in the model and the model's quality as characterised by the _WHM_ (1) with a weight \(w\) equal to 0.85. The forward feature selection was again applied for the final model building. However, this time, the feature ranking determined the order in which attributes were added to the model. During each step, the data set was divided into training and validation parts in a 50:50 proportion 100 times, and quality was estimated for each division. The model with the highest average _WHM_ value for validation sets was selected as the final one.