## 2 Materials and Methods
### Survival Prediction  
We applied penalized Cox and random survival forest (RSF) models for the prediction of patients' overall survival. The Cox and RSF models were applied on the CT and PET feature sets selected by the GA separately and on their union. The RSF is an ensemble model and, therefore, it should not require a prior feature selection step. Figure 2: Trend of genetic algorithm fitness values for 200 iterations. The fitness of each genome is the partial AIC of a Cox model fitted with the features selected by that genome. The image shows the fitness minimization of the PET feature set. The minimum and average fitness values are shown in red and green, respectively. The main parameter required to tune the Cox model is the regression penalty. One hundred Cox models were trained with different \(\mathrm{l}_{2}\) penalization values ranging from \(10^{-3}\) to \(1\). The models were evaluated using a 5-fold cross-validation repeated five times. The parameters yielding the best cross-validation results were chosen as the optimal ones. A grid-search strategy was employed to find the optimal parameters for the RSF model. The grid-search algorithm tests different parameter configurations and selects the one that maximizes the repeated 5-fold cross-validation. We used the concordance index as a metric for cross-validation evaluation. Each configuration considered the number of estimators in the forest, the minimum number of samples required to split a node, and the maximum number of features to consider when looking for the  
The results obtained by the best models on the test data are shown in Table 6. The addition of recurrence as an extra feature produced a general improvement in all model performances. The results obtained on the test data using recurrence as an extra feature are shown in Table 7.  
The results obtained by the models trained with only radiomic features, i.e., without the recurrence feature, evaluated on the test sets. The metric used for evaluation was the concordance index. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model (without Recurrence)** & **No. Concordant Pairs** & **No. Discordant Pairs** & **Concordance Index** \\ \hline Cox (CT) & 41 & 17 & 0.707 \\ Cox (PET) & 17 & 41 & 0.293 \\ Cox (PET + CT) & 32 & 26 & 0.552 \\ RSF (CT) & 16 & 42 & 0.276 \\ RSF (PET) & 30 & 28 & 0.517 \\ RSF (PET + CT) & 30 & 28 & 0.517 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results obtained by the models trained with only radiomic features, i.e., without the recurrence feature, evaluated on the test sets. The metric used for evaluation was the concordance index. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Feature (CT)** & **Coef.** & **Std. Err.** & **Coef. lower 95\%** & **Coef. Upper 95\%** & _p-Value_ \\ \hline SmallDepHighGLEmph & 2.579 & 0.781 & 1.048 & 4.109 & \textless{}0.005 \\ LargeDepLowGLEmph & \(-1.069\) & 0.546 & \(-2.139\) & 0.001 & 0.050 \\ JointAverage & \(-4.234\) & 1.240 & \(-6.665\) & \(-1.803\) & \textless{}0.005 \\ DifferenceEntropy & \(-1.124\) & 0.527 & \(-2.157\) & \(-0.901\) & 0.033 \\ Imc2 & \(-1.258\) & 0.911 & \(-3.044\) & 0.529 & 0.168 \\ Imc1 & \(-2.679\) & 1.339 & \(-5.304\) & \(-0.054\) & 0.045 \\ Skewness & \(-1.458\) & 0.603 & \(-2.640\) & \(-0.276\) & 0.016 \\ Energy & 1.054 & 0.295 & 0.476 & 1.632 & \textless{}0.005 \\ Contrast & \(-2.093\) & 1.122 & \(-4.292\) & 0.106 & 0.062 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Selected CT features and corresponding Cox coefficients, standard errors, 95% confidence intervals, and _p_-values. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model (without Recurrence)** & **No. Concordant Pairs** & **No. Discordant Pairs** & **Concordance Index** \\ \hline Cox (CT) & 45 & 13 & 0.776 \\ Cox (PET) & 36 & 22 & 0.621 \\ Cox (PET + CT) & 45 & 13 & 0.776 \\ RSF (CT) & 26 & 32 & 0.448 \\ RSF (PET) & 30 & 28 & 0.517 \\ RSF (PET) & 30 & 28 & 0.517 \\ \hline \hline \end{tabular}
\end{table}