## 3 Results
### External Validation  
Finally, the external validation results performed on the LUNG2 dataset are summarized in Table 8. In this case, GP_CORR outperformed the other methods in terms of AUC (range 0.65-0.69 for the different classifiers), whereas GP_GAIN was the best for accuracy (range 0.65-0.74) and the second best for AUC (range 0.63-0.68). Nonetheless, GP_GAIN presented the most balanced combination of precision and recall. Feature selection approaches achieved the lowest classification performance, especially for NB, RF, and MLP classifiers.  
The K-M survival analysis showed that GP_AUC reached the lowest \(p\)-values; the curves between survival and non-survival groups were significantly different in almost all cases except for the RF classifier. Moreover, for the LUNG2 dataset, the Cox model revealed higher C-index values than LUNG1, in the range of 0.64-0.69, as shown in the second column of Table 7.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Index** & **Method** & **LR** & **LDA** & **NB** & **RF** & **SVM** & **MLP** \\ \hline \multirow{6}{*}{AUC} & FS\_mRMR & 0.63 & 0.62 & 0.61 & 0.64 & 0.65 & 0.62 \\  & FS\_FWD & 0.65 & 0.65 & 0.63 & 0.60 & 0.66 & 0.63 \\  & GP\_AUC & 0.61 & 0.61 & 0.62 & 0.61 & 0.60 & 0.60 \\  & GP\_CORR & 0.67 & 0.63 & 0.65 & 0.62 & 0.59 & 0.63 \\  & GP\_GAIN & 0.69 & 0.68 & **0.70** & 0.64 & 0.68 & 0.67 \\ \hline \multirow{6}{*}{Accuracy} & FS\_mRMR & 0.57 & 0.57 & 0.59 & 0.62 & 0.57 & 0.58 \\  & FS\_FWD & 0.62 & 0.60 & 0.60 & 0.56 & 0.60 & 0.58 \\  & GP\_AUC & 0.56 & 0.55 & 0.57 & 0.56 & 0.54 & 0.55 \\  & GP\_CORR & 0.60 & 0.57 & 0.58 & 0.58 & 0.56 & 0.58 \\  & GP\_GAIN & **0.65** & **0.65** & 0.64 & 0.59 & 0.62 & 0.64 \\ \hline \multirow{6}{*}{Precision} & FS\_mRMR & 0.47 & 0.46 & 0.48 & 0.53 & 0.49 & 0.48 \\  & FS\_FWD & 0.52 & 0.50 & 0.50 & 0.46 & 0.49 & 0.48 \\  & GP\_AUC & 0.47 & 0.46 & 0.48 & 0.45 & 0.45 & 0.45 \\  & GP\_CORR & 0.50 & 0.47 & 0.48 & 0.48 & 0.46 & 0.47 \\  & GP\_GAIN & **0.56** & 0.55 & 0.55 & 0.39 & 0.52 & 0.54 \\ \hline \multirow{6}{*}{Recall} & FS\_mRMR & 0.52 & 0.52 & 0.65 & 0.56 & 0.61 & 0.63 \\  & FS\_FWD & 0.65 & 0.61 & 0.52 & 0.56 & 0.63 & 0.51 \\  & GP\_AUC & 0.62 & 0.64 & 0.61 & 0.63 & **0.71** & 0.63 \\  & GP\_CORR & 0.60 & 0.55 & 0.63 & 0.62 & 0.52 & 0.55 \\  & GP\_GAIN & 0.61 & 0.59 & 0.63 & 0.53 & 0.59 & 0.61 \\ \hline \multirow{6}{*}{K–M} & FS\_mRMR & 149.829 & 92.688 & 0.538 & 3.188 & 18.356 & 0.230 \\  & FS\_FWD & 0.001 & 0.311 & 2.041 & 33.303 & 0.020 & 4.625 \\ \cline{1-1}  & GP\_AUC & 1.834 & 2.291 & 0.267 & 2.247 & 5.895 & 19.451 \\ \cline{1-1}  & GP\_CORR & 6.176 & 136.507 & 28.744 & 28.731 & 277.792 & 83.912 \\ \cline{1-1}  & GP\_GAIN & 0.012 & 0.205 & **0.000** & 2.116 & 0.951 & 0.019 \\ \hline \end{tabular}
\end{table}
Table 6: The benchmark techniques’ results using different classifiers on the LUNG1 dataset. The mean of five cross-validation experiments is presented. The best results are highlighted in bold.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**Dataset**} \\
**Method** & **LUNG1** & **LUNG2** \\ \hline FS-mRMR & 0.608 & 0.692 \\ FS-SFS-FWD & 0.606 & 0.643 \\ GP-AUC & 0.601 & 0.639 \\ GP-CORR & 0.579 & 0.659 \\ GP-GAIN & 0.586 & 0.644 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The C-index results of the Cox proportional-hazards models considering age, tumor stage, and features selected by each method.