## 5 Decision Model Generation
### Proposed Classification Approaches
#### 5.3.2 Gradient Boosting-Based Approach  
This approach was designed to use all available attributes and binary interactions between binary features. If two features \(a\) and \(b\) were binary ones, then a new binary feature \(a\cup b\) was created, and its value was calculated by applying a logical _OR_ operation. The next steps of the analysis aimed at limiting the number of features involved in the classification in order to better explain the decisions made by the model. For this \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & **Estimate** & **Std. Error** & \(p\)**-Value** & **OR** \\ \hline (Intercept) & \(-0.9299\) & 0.2287 & \(4.77\times 10^{-5}\) & - \\ Days of symptoms & \(-0.1720\) & 0.0486 & \(3.99\times 10^{-4}\) & 0.8420 \\ Loss of smell or taste & 1.4948 & 0.3729 & \(6.11\times 10^{-5}\) & 4.4584 \\ Contact with infected person & 1.1546 & 0.2687 & \(1.73\times 10^{-5}\) & 3.1728 \\ Days of symptoms AND Loss of smell or taste & 0.0112 & 0.0593 & \(8.51\times 10^{-1}\) & 1.0113 \\ Loss of smell or taste AND Contact with infected person & \(-0.9736\) & 0.4135 & \(1.86\times 10^{-2}\) & 0.3777 \\ Days of symptoms AND Temp. > 38 \({}^{\circ}\)C & 0.0763 & 0.0374 & \(4.12\times 10^{-2}\) & 1.0793 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Parameters of the final logistic regression classifier. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**NPV** & **PPV** & **Sensitivity** & **Specificity** \\ \hline
1.0000 & 0.3551 & 1.0000 & 0.1318 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Logistic regression evaluation results—classification results for final model on the whole train set. purpose, all information related to the measurement of body temperature was removed from the set of features, except for the binary feature indicating whether the patient had a temperature greater than 38 \({}^{\circ}\)C. This step was motivated by no significant differences between the values of temperature and maximum temperature in both studied classes. Moreover, the numerical variables that the XGBoost algorithm prefers to construct the tree were removed in this way. Moreover, further feature selection based on 100 draws of a subset of the available data was performed. Each draw selected at least 60% of the examples and 60% of the attributes. On such a limited data set, the XGBoost algorithm was run in the 10-times five-fold cross-validation mode and the ranking of the importance of features in the trained classifier was recorded. Then, the average position of a feature in the ranking was calculated. This average ranking consisted of only those features that occurred at least 60 times in the selected subsets. In this way, the set \(A\) consisting of all features presented in Table 8 and their interactions (OR) between binary features was obtained. The value of the _sum_of_symptoms_ feature was calculated on the basis of 11 disease symptoms included in the training set. The steps of the analysis presented in the consecutive paragraphs were repeated 100 times within the MRCV process. Patients left after filtration were randomly divided into training and validation sets in 60:40 proportions. Within this procedure, the optimisation process based on forward feature selection was performed. The \(WHM\) (1) evaluation measure was used in the optimisation process, and the weight value was set to \(w=0.7\) to enhance the importance of NPV and reduce in this way the risk of false negative observations' occurrence, as the method was developed for the purposes of the screening test. In order to present the complete process of building the classifier, we denote by \(XGB(A,t,m)\) the average value of evaluation measure \(m\) calculated on the basis of the results of the MRCV procedure of the XGBoost algorithm, built based on the set of features \(A\). If \(t=tr\), this means that the average value of \(m\) is given on the training sets; if \(t=ts\), this means that the average value of \(m\) is given on the test sets.