## 3 Results
### Does the Model Identify Tumor Budding as the Distinctive Feature? Although the used evaluation method for the budding score is outdated (see Section 2.1.1), it is prognostically relevant concerning nodal status, as described in previous works on this data set [12]. For the data set used here, a chi-square analysis shows a strong correlation between the tumor budding score (as described above and assessed based on an outdated system) and the nodal status (\(p\)-value < 10 \(\times\) 10\({}^{-8}\)). In addition to this correlation, we tested the predictive power of the budding score per case. Therefore, the same splitting into a training and validation set as for the above-described MIL approach is used. By doing so, a logistic regression model trained to predict N\(-\) and N+ based on the budding score per case has an accuracy of 0.725 and an AUC of 0.802 for the validation set (compared to the AUC-values for the MIL approach in Table 2). Despite these prognostic capabilities, the budding score is not an independent parameter in the outdated system. For the used data set, there is a strong correlation between the expert-based tumor budding score [47] and the at this time used 3-tired tumor grading [48] per case. In the chi-square test, the \(p\)-value is also <10\({}^{-5}\). Thus, tumor budding is not independent of tumor grading. Testing the grading as a predictive marker for nodal status using again a logistic regression model results in an accuracy of 0.725 and an AUC of 0.690 for the validation set. In conclusion, the predictive power of grading for the nodal status seems comparable to tumor budding. In summary, the budding score in this data set is not an independent marker but harbors a predictive power. Utilizing the metrics employed (namely accuracy and AUC) to assess the predictive reliability of the tumor budding score and the previously outlined MIL approach, both exhibit comparability (compare Section 3.3 above). Besides the comparable prediction quality, both approaches show similarities in other respects so that it can be argued that the same features underlie them. From the false predicted cases in the validation data set, six cases are false in both models. Looking at the budding score values in the wrong predicted cases for both models, the MIL model and the logistic regression model, the assigned budding scores have a median of 3 (compare Figure 4. Thus, these cases show a high budding score, known as being predictive for nodal positivity, albeit both are nodal negative. The location of the relevant image tiles is also an argument that tumor budding is the underlying feature. Looking at the location of the 20% most predictive image tiles per N+ case, 84.0% of these tiles are in the border region and 16.0% are in the central tumor regions. Of the N\(-\) cases 65.3% are in the tumor border region and 34.7% are in the central regions (compare B in Figure 4). Since tumor budding is defined as taking place in the border regions, this can be used as an argument that the model at least recognizes similar features in the image. Figure 3: **Cluster map analysis of the bag feature vectors produced by the MIL model. ** Prior to the final fully connected layer for the decision the MIL model produces a feature vector per bag based on all input instances. (**A**) The feature vector per bag is clustered against the nodal status. On the left the true status of a bag is shown with nodal negative as blue bar and nodal positive as red bar. The feature vector of one bag is split along the x-axis and different bags along the y-axis. The instances of a feature vector are depicted with color-coding representing the N+ probability (black bars equal zero). (**B1**) For the entire dataset, comprising the training and validation set, a PCA of the bag feature vectors are plotted in the latent space. The nodal status (nodal negative (0) or positive (1)) is used as a label. (**B2**) Comparable to Figure 2(B2) the pseudo-probability is shown in the L-space.