## 2 Materials and Methods
### Radiomics Analysis  
The volumetric segmentations were performed with the freely available texture analysis LIFEx platform [13] that is the most widely used IBSI (Image Biomarker Standardization Initiative) compliant software in PET imaging to obtain reproducible and robust radiomics features. Specifically, two board-certified nuclear physicians evaluated and segmented PET/CT lesions by consensus and blinded to the purpose of the study and to the pathology information. Signal intensity on PET images was judged as hyperintense when the signal intensity of the tumor was higher than the signal intensity of non-tumoral tissue. SUV\({}_{\text{max}}\) was used as a PET parameter to select the most avid lesion for the global evaluation of disease status and for the most avid liver lesion in every patient. The same volume was transposed in the same region on CT images for extraction of morphological features. Successively, 105 and 66 features were automatically extracted using LifeX starting from the above-mentioned volumes of interest (VOI) from each lesion in PET and CT images, respectively. The extracted features were classified into two categories based on their information type: (I) shape features, which consider the geometric aspects of the VOI, such as shape and volume, (II) statistical features including first-order statistic (histogram-based) features describing intensity values within the target and higher-order statistics (texture) features that are designed to quantify the perceived texture of an image and to provide spatial information of intensities in a VOI. In the last case, five texture classes were considered:(i) gray-level cooccurrence matrix (GLCM), (ii) gray-level run-length matrix (GLRLM), (iii) gray-level dependence matrix (GLDM), (iv) gray-level zone length matrix (GLZLM), and (v) neigh-boring gray-level dependence matrix (NGLDM). Specifically, (i) GLCM evaluates the incidence of voxels with the same intensities at a predetermined distance along a fixed direction; (ii) GLRLM assesses consecutive voxels with the same intensity along fixed directions; (iii) GLDM counts the number of voxel segments having the same intensity in a given direction; (iv) GLZLM is defined as the number of connected voxels that have equal gray-level intensity; (v) NGTDM assesses the spatial interrelationships between 3 or more voxels [14]. In the work of [13], there is an extensive description of each extracted feature. Successively, the mixed descriptive-inferential sequential approach, as described in two complementary studies [15; 16], was used to identify a small set of radiomics features with valuable association with patients' outcomes for better predictive performance, leading to the exclusion of non-reproducible, redundant, and nonrelevant features from the initial feature data set. After the selection and reduction process, the predictive model was implemented using the discriminant analysis (DA) [17]. The training step was performed only once, and when completed, the DA was capable of classifying new PET lesions. Using the k-fold cross-validation strategy, data were divided into training and validation sets using a random partition. Specifically, data were divided into k-folds: one-fold was used as the validation set while the others folds were used as the training set. The folds were created in such a way that the training and validation sets maintained the same percentage of patient status as the original data set. After applying the trial-and-error methodology, k = 5 was determined as the best value for our analyses (k range: 5-15, step size of 5). Consequently, this process was repeated 5 times, and the mean error was calculated (i) to avoid the over-fitting and asymmetrical sampling by increasing the accuracy of the final results, (ii) to test different models, and (iii) to obtain more robust results [18; 19; 20; 21; 22].