## 3 Results
### Internal Validation  
Table 6 shows the results of the internal validation on the LUNG1 dataset, comparing the classification performance of different feature selection and feature construction methods. For this analysis, the three GP-based models used the best GP_GAIN configuration found previously, i.e., a maximum depth of three levels and two trees; this way, they all have the same configuration to construct two new features. Regarding feature selection methods, FS_FWD and FS_mRMR selected, on average, six and thirteen original radiomic features, respectively.  
Notably, classification models trained with GP_GAIN-based features achieved the highest AUC and accuracy values in every classifier, with LR, LDA, and NB performing the best (AUC equal to 0.69, 0.68, and 0.70, and accuracy equal to 0.65, 0.65, and 0.64, respectively). By observing the K-M survival analysis, the log-rank test revealed that the curves between survival and non-survival patients significantly differed between the two groups, with NB achieving the lowest \(p\)-value (\(9.2\times 10^{-7}\)). In the first column of Table 7, results of the Cox model are reported for the LUNG1 dataset, with the C-index ranging from 0.58 to 0.61, showing a moderate ability to predict survival time.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Index** & **Expression** \\ \hline Accuracy & \(\frac{\text{TP}+\text{TN}}{\text{TP}+\text{FN}+\text{FP}+\text{TN}}\) \\ Recall & \(\frac{\text{TP}}{\text{TP}+\text{FN}}\) \\ Precision & \(\frac{\text{TP}}{\text{TP}+\text{FP}}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: The classification performance indices used to evaluate the methods.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Index**} & \multirow{2}{*}{**Tree Depth**} & \multicolumn{5}{c}{**Number of Trees**} \\  & & **1** & **2** & **3** & **4** & **5** \\ \hline \multirow{5}{*}{**AUC**} & 2 & 0.68 & 0.66 & 0.66 & 0.66 & 0.65 \\  & 3 & 0.67 & **0.69** & 0.63 & 0.65 & 0.67 \\  & 4 & 0.65 & 0.67 & 0.68 & 0.66 & 0.65 \\  & 5 & 0.65 & 0.67 & 0.66 & 0.68 & 0.66 \\  & 6 & **0.69** & 0.65 & 0.66 & 0.63 & 0.67 \\  & 7 & 0.67 & 0.67 & 0.67 & 0.66 & 0.67 \\ \hline \multirow{5}{*}{**Accuracy**} & 2 & 0.59 & 0.62 & 0.58 & 0.61 & 0.59 \\  & 3 & 0.61 & **0.65** & 0.59 & 0.59 & 0.61 \\  & 4 & 0.60 & 0.58 & 0.64 & 0.60 & 0.59 \\  & 5 & 0.61 & 0.60 & 0.62 & 0.61 & 0.60 \\  & 6 & 0.61 & 0.58 & 0.62 & 0.57 & 0.61 \\  & 7 & 0.61 & 0.59 & 0.60 & 0.62 & 0.62 \\ \hline \multirow{5}{*}{**Precision**} & 2 & 0.49 & 0.52 & 0.48 & 0.50 & 0.47 \\  & 3 & 0.52 & **0.56** & 0.49 & 0.49 & 0.52 \\  & 4 & 0.50 & 0.48 & 0.54 & 0.50 & 0.49 \\  & 5 & 0.51 & 0.50 & 0.51 & 0.52 & 0.50 \\  & 6 & 0.51 & 0.46 & 0.51 & 0.46 & 0.51 \\  & 7 & 0.51 & 0.49 & 0.51 & 0.53 & 0.52 \\ \hline \multirow{5}{*}{**Recall**} & 2 & **0.70** & 0.62 & 0.59 & 0.56 & 0.57 \\  & 3 & 0.69 & 0.61 & 0.60 & 0.65 & 0.50 \\  & 4 & 0.51 & 0.61 & 0.55 & 0.56 & 0.64 \\  & 5 & 0.61 & 0.61 & 0.58 & 0.52 & 0.66 \\  & 6 & 0.66 & 0.55 & 0.61 & 0.66 & 0.70 \\  & 7 & 0.59 & 0.65 & 0.62 & 0.61 & 0.67 \\ \hline \end{tabular}
\end{table}
Table 5: The GP_GAIN method’s classification performance results for different configurations. The mean of five cross-validation experiments is presented. The best results are highlighted in bold.  
Figure 4: The best multi-tree configuration determined by GP_GAIN. The first tree constructs the feature \(t_{1}=(x_{79}-x_{75})-x_{66}\), while the second tree constructs the feature \(t_{2}=\max(x_{17},\)\(\max(x_{32},x_{11}\times x_{30}))\).