## 4 Discussion  
This paper proposed a GP-based feature construction approach to build new discriminant features for survival prediction in NSCLC patients. A multi-tree representation was used to build a new multi-dimensional feature space from traditional radiomic features, including morphological, volumetric, histogram-based, and texture parameters computed from CT images. The main contribution is applying GP for feature construction in radiomics for the first time to improve the survival prediction of NSCLC patients. The comparison with benchmark methods showed that classification models built from GP features generally outperform traditional feature selection methods for most considered classifiers concerning internal and external validations, confirming its generalizability. In addition, the AUC-based fitness function, which measures the output-to-input AUC gain, guided the GP algorithm to find more accurate solutions than its GP counterparts, especially in the LUNG1 dataset. The differences in classification performances between the internal and external validations can be explained by the different class proportions of the two datasets. The LUNG1 dataset was almost balanced, with 40% of patients surviving more than two years; on the contrary, the LUNG2 dataset was highly unbalanced since almost 80% of patients had a survival higher than two years. This behavior can justify the higher precision values in the second dataset. In this case, GP_GAIN showed the highest values for recall compared to the other methods, making the classification performances more balanced. The experimental results showed relatively low classification performance by all the assessed approaches, suggesting that predicting the two-year survival of NSCLC patients is challenging. Examining the K-M survival curves and the Cox model results, none of the radiomic approaches can give satisfactory results. In particular, the FS_mRMR method achieved the highest C-index, probably due to the larger number of selected features that \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Index** & **Method** & **LR** & **LDA** & **NB** & **RF** & **SVM** & **MLP** \\ \hline \multirow{4}{*}{AUC} & FS\_mRMR & 0.65 & 0.66 & 0.59 & 0.66 & 0.65 & 0.62 \\  & FS\_FWD & 0.65 & 0.65 & 0.65 & 0.58 & 0.67 & 0.62 \\  & GP\_AUC & 0.65 & 0.65 & 0.65 & 0.65 & 0.65 & 0.65 \\  & GP\_CORR & 0.69 & 0.69 & 0.69 & 0.65 & **0.71** & 0.67 \\  & GP\_GAIN & 0.68 & 0.68 & 0.63 & 0.68 & 0.67 & 0.67 \\ \hline \multirow{4}{*}{Accuracy} & FS\_mRMR & 0.63 & 0.64 & 0.52 & 0.39 & 0.64 & 0.69 \\  & FS\_FWD & 0.66 & 0.56 & 0.61 & 0.52 & 0.65 & 0.64 \\  & GP\_AUC & 0.58 & 0.58 & 0.58 & 0.62 & 0.58 & 0.58 \\  & GP\_CORR & 0.58 & 0.58 & 0.58 & 0.62 & 0.55 & 0.54 \\  & GP\_GAIN & **0.74** & 0.68 & 0.65 & **0.74** & 0.54 & **0.74** \\ \hline \multirow{4}{*}{Precision} & FS\_mRMR & 0.86 & 0.86 & 0.80 & 0.87 & 0.84 & 0.83 \\  & FS\_FWD & 0.87 & 0.87 & 0.86 & 0.83 & 0.85 & 0.83 \\  & GP\_AUC & 0.86 & 0.86 & 0.86 & 0.87 & 0.88 & 0.88 \\  & GP\_CORR & 0.89 & 0.89 & 0.89 & 0.83 & 0.89 & **0.92** \\  & GP\_GAIN & 0.85 & 0.87 & 0.86 & 0.82 & 0.88 & 0.84 \\ \hline \multirow{4}{*}{Recall} & FS\_mRMR & 0.63 & 0.65 & 0.52 & 0.26 & 0.67 & 0.76 \\  & FS\_FWD & 0.67 & 0.52 & 0.60 & 0.49 & 0.68 & 0.68 \\  & GP\_AUC & 0.56 & 0.56 & 0.56 & 0.60 & 0.55 & 0.55 \\  & GP\_CORR & 0.54 & 0.54 & 0.54 & 0.65 & 0.48 & 0.45 \\  & GP\_GAIN & 0.81 & 0.70 & 0.66 & **0.85** & 0.48 & 0.82 \\ \hline \multirow{4}{*}{K–M (\(\times 10^{-2}\))} & FS\_mRMR & 1.67 & 1.77 & 7.46 & 42.23 & 5.88 & 6.73 \\  & FS\_FWD & 0.03 & 1.94 & 1.02 & 22.75 & 0.77 & 1.33 \\ \cline{1-1}  & GP\_AUC & 0.20 & 0.20 & 0.20 & **0.09** & 0.05 & 0.05 \\ \cline{1-1}  & GP\_CORR & 1.75 & 1.75 & 0.66 & 18.77 & 5.16 & 5.23 \\ \cline{1-1}  & GP\_GAIN & 2.65 & 1.93 & 0.61 & 8.58 & 13.28 & 0.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The benchmark techniques’ results using different classifiers on the LUNG2 dataset. The mean of five cross-validation experiments is presented. The best results are highlighted in bold.