## 4 Discussion  
The procedure proposed in Pipeline 3 obtained an ROC AUC score of 0.61. This result was in agreement with the hypothesis that radiomic features extracted from tumor VOIs and the ZOT allowed identifying the presence of MVI from CT images. However, the results obtained were not as good as other state-of-the-art results [18; 19; 21]. According to the authors, this limit could have been due to the limited number of samples involved in the study. This limit was a direct consequence of the single-center nature of the present study, which reduced the possible heterogeneity of the samples and affected the generalization capabilities of the pipelines in this study. Novel techniques capable of increasing the  
Figure 2: The importance of the 15 features selected according to the absolute value of the ridge coefficients. For each feature selected, it is reported whether it belonged to the original image (O), wavelet (W), or Laplacian of Gaussian (LoG). Moreover, whether they were computed from the CECT in the arterial (A) or the portal (P) phase is specified as the tumor (VOI) or zone of transition (ZOT) volumes. The features from the arterial phase, the portal phase, and the ZOT volume are highlighted in red, blue, and bold, respectively. (**a**) Absolute values of the ridge coefficients for the 15 selected features by Pipeline 1, i.e., computed considering the entire dataset. (**b**) The mean and standard deviation of the absolute values of the ridge coefficients for the 15 most-frequent features selected by Pipeline 2. (**c**) The mean and standard deviation of the absolute values of the ridge coefficient for the 15 most-frequent features selected by Pipeline 3.  
amount of data based on synthetic image generation have already been proposed in the literature [35]; however, their use could introduce unpredictable biases in the radiomic analysis and go beyond the aim of the present study. Furthermore, the dataset used in this study involved small tumor VOIs, making the radiomic analysis more difficult [20]. Moreover, many studies have considered not only radiomic features, but also clinical features [18; 19; 21]. The authors obtained notably better results using the scheme proposed in Pipelines 1 and 2, achieving an ROC AUC score of 0.89 and 0.84, respectively. These results are in agreement with the current state-of-the-art results [20; 23] obtained with equivalent pipelines. The results obtained highlighted the criticality of the pre-processing step inside a radiomic pipeline. The application of Pipeline 1 led to results 45% higher than Pipeline 3, by simply excluding the pre-processing steps from the cross-validation procedure. In fact, Pipeline 1 carried out the feature selection and oversampling using the entire set of available data, introducing a putative source of cross-contamination of the training and the test samples. The same behavior was observed when comparing Pipelines 2 and 3. Pipeline 2 obtained results 37% higher than Pipeline 3, by excluding the oversampling step from the cross-validation. The pipeline designs that carried out the oversampling before splitting could show the contamination of the test set with the training data. In both Pipeline 1 and Pipeline 2, the presence of almost redundant data in both the training and the test sets introduced the probability of overfitting, producing classification results that were too optimistic. [PERSON] et al. and [PERSON] et al. [19; 21] assessed model performance with configurations equivalent to those presented in this study, i.e., they evaluated the pipeline performances using both the training and the test datasets. Their results showed a higher ROC AUC score for the pipeline tested on the training set, i.e., with a design equivalent to the one presented in Pipelines 1 and 2. This behavior validated the authors' hypothesis regarding cross-contamination and its effect on evaluating pipeline performance and generalization capabilities.