## 2 Materials and Methods
### Experimental Setup
#### 2.4.2 Experiments  
First, different GP_GAIN configurations were tested by varying the number of trees, \(m\), from 1 to 5, and the depth levels, \(l_{\text{max}}\), from 2 to 7, using the 5-fold cross-validation method on the LUNG1 dataset. All the pairwise combinations of the number of trees and depth levels were assessed to identify the best configuration for survival prediction in NSCLC, where LR was the base classifier.  
Next, two experiments were defined to evaluate the survival prediction of distinct prediction models. The first experiment is internal validation, which uses the LUNG1 dataset split into training and test sets using the 5-fold cross-validation method. This experiment aims to identify the best survival prediction models for feature selection and feature construction using distinct classifiers. The second experiment is external validation, which uses the entire LUNG2 dataset as a test set. This experiment aims to assess the generalization capabilities of the prediction models obtained in the first experiment using an independent test set external to the LUNG1 dataset.  
The classification performance was evaluated regarding accuracy, precision, and recall, as summarized in Table 4. These indices were calculated from the binary confusion matrix \(\left(\begin{smallmatrix}\text{TP FN}\\ \text{FP TN}\end{smallmatrix}\right)\), where TP is true positive, TN is true negative, FP is false positive, and FN is false negative. The AUC index in (1) also measured the separability between survivor and non-survivor predicted scores [49].  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Classifier** & **Hyperparameter** & **Value** \\ \hline \multirow{3}{*}{RF} & Features to sample & \(\sqrt{d}\) \\  & Decision trees & \([5,1000]\) \\  & Leaf node samples & \([1,150]\) \\ \hline \multirow{3}{*}{MLP} & Hidden units & \([2,4\sqrt{d}]\) \\  & Learning rate & \([10^{-6},10^{-2}]\) \\  & Momentum factor & \([0.5,0.9]\) \\ \hline \multirow{3}{*}{SVM} & Margin penalty & \([2^{-5},2^{5}]\) \\  & Gaussian bandwidth & \([2^{-5},2^{5}]\) \\ \hline \(d\) stands for the number of input features. & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: The classifier’s hyperparameter values.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Population size & 50 \\ Number of generations (\(g_{\text{max}}\)) & 100 \\ Mutation probability (\(p_{\text{m}}\)) & 0.10 \\ Crossover probability (\(p_{c}\)) & 0.90 \\ Tournament size & 5 \\ Number of trees (\(m\)) & 1 to 5 \\ Maximum tree depth (\(l_{\text{max}}\)) & 2 to 7 \\ Function set & \(\{+,-,\times,\div,\min,\max\}\) \\ Terminal set & 105 radiomic features \\ \hline \hline \end{tabular}
\end{table}
Table 3: The GP parameter settings.  
Survival analysis was also performed on LUNG1 and LUNG2 datasets, considering the best GP configuration and comparing the selected methods. First, the Kaplan-Meier (K-M) survival analysis is performed to associate the predicted binary classification with the survival information by splitting the survival curves into high- and low-risk groups. The log-rank test assesses significant differences between the two survival curves [50].  
Next, the Cox proportional-hazards model was fitted considering the radiomic features selected by FS_FWD, FS_mRMR, and the constructed features obtained by the GP-based approaches. Also, age and tumor stage information were considered to adjust for potential confounding variables. As in previous works, C-Index was used as the evaluation metric for the Cox model [33; 35].  
To provide a quantitative tool that could be helpful in clinics and to enhance feature interpretability, a nomogram of the proposed approach was built based on multivariate logistic regression analysis in the training cohort by considering the best configuration for GP-based features, age, and TN tumor stage, as in [14].