## 2 Materials and Methods
### Analysis Strategy and Pipeline  
The workflow consisted of four major steps: the collection and curation of imaging dataset; the division of the data into three datasets as described in Section 2.1; the extraction of RFs; and the statistical analysis. Figure 1 describes the workflow of the study. Fifteen different experiments were performed, and the performance of the different approaches is compared accordingly.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Vendor** & **Number of Scans** & **Convolution Kernels** & **Slice Thickness (mm)** & **Pixel Spacing (mm2)** \\ \hline GE & 154 & Standard, Soft & 1.25–7.5 & 0.7 \(\times\) 0.7–0.78 \(\times\) 0.78 \\ Philips & 3 & A, B & 5 & 0.74 \(\times\) 0.74–0.86 \(\times\) 0.86 \\ Siemens & 22 & B30\(\ell\), B30s, B31f, B31s & 3, 5 & 0.54 \(\times\) 0.54–0.98 \(\times\) 0.98 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Description of the data included.  
Each dataset was analyzed using five different approaches. In the first approach, RFs extracted from the CT scans were directly used to assess overall survival (Ori). In the second approach, the clinical variable \"percentage of tumor tissue necrosis\" was used to assess overall survival (Necrosis) [39]. In the third approach, the percentage of tumor tissue necrosis and RFs were combined to assess overall survival (Ori_Necrosis). In the fourth approach, RFs were harmonized using ComBat harmonization, with the slice thickness being the batch, in order to assess overall survival. In the fifth approach, pixel spacing was used as the batch to harmonize RFs with ComBat, and the harmonized RFs were used to predict overall survival. To avoid reporting significant results by chance, the analysis was repeated 1000 times in each of the approaches. In each repeat, the data are split randomly into 70% training and 30% validation sets. Feature selection and cox regression are performed in each repeat. The concordance index (C-index) was used to evaluate the performance of developed cox regression models [40]. The C-index of each of the final developed models on the validation set is kept in each repeat, and an average is calculated on the indices saved per approach. By performing the analysis 1000 times, we investigate whether the selected radiomic features and calculated performances are robust.  
The set of features to be included in the modeling was contingent upon which of the five approaches (explained above in strategy) was utilized. In each of the repeats, following the division of data into training and validation sets, highly correlated features (identified using Spearman's correlation [41] with a cut-off of R > 0.90) were removed. If two RFs were found to be highly correlated, the RF that was removed was the one with higher average correlation with the other RFs. The remaining RFs were then used to build a cox regression model [42]. Backward feature selection [43] was applied on the generated cox model to select the important features. The selected features were then used to build the final cox regression model. Due to the small dataset size, if the number of the selected features was higher than 5, the 5 features with the most contributions to the model were used to build the final model. The model performance was then validated on the validation set using the C-index. Student \(t\)-test [44] was used to assess the difference on average between the different approaches used. All statistical were performed using R [45] language on RStudio (Version 2022.2.1.461, RStudio Inc., Boston, MA, USA) [46].