## 4 Technical Contribution
### Example Study Case, Technical Approach  
At this point, we have all the tools in place to provide the system response to the medical use case presented in Section 3.1 and to also formalize the technical contribution, in addition to the medical one, which in the combined form offered an overall 7% improvement, representing three novel correlations not observed by the surgeon out of a total of 45 cases.  
The summary plot combines feature importance with feature effects. Each point on the summary plot is a Shapley value for a feature and an instance. The position on the y-axis is determined by the feature and on the x-axis by the Shapley value. The color represents the value of the feature from low to high. The overlapping points are jittered in the y-axis direction, so we achieve a sense of the distribution of the Shapley values per feature.  
The features are ordered according to their importance. In the summary plot, we see the first indications of the relationship between the value of a feature and the impact on the prediction. The parameters are ordered automatically with respect to the impact on the decision of the network. As can be seen in Figure 8, the Size parameter was considered the most important for the overall result of the network computation. By correlating the features' inter-dependencies, see Figures 6 and 7, with the feature importance given by the global SHAP, see Figure 8, we were able to reduce the number of relevant features for a particular prediction.  
The explainability can also be performed for each individual at once due to the fact that we are interested in deciding the diagnostic for particular persons.  
The explainable representation for one individual, i.e., our case study can be seen in Figure 9 for SHAP and in Figure 10 for LIME. In this case, we drastically reduced the  
Figure 8: Global feature importance. SHAP explainable plot.  
number of independent relevant features for explanation to five. Furthermore, the LIME post-hoc application was stabilized, as proposed in paper [6], and we obtained a compound stability-fit index of 85, which is considered acceptable for the explanations.  
The first correlation is to be read from Figure 8: from the global SHAP representation, we found out that the variables Size, HUavg, age, PeHi, and Sem0l2 have the overall highest impact on the system's decisions. The second correlation can be found in Figures 9 and 10: given the importance of global SHAP features, we reduced the construction of the Shapley values and the ridge regression for the local explainability to only five variables, respectively.  
Given the positive factors for the decision, such as PeHi, size, and HUavg, and the negative factor for the decision, such as sex and Sem0l2, for the particular case according to Figure 10, the system explanation opened a novel perspective for the surgeon who considers that now that the person is unlikely to have cancer, even though the system inferred with a 56% accuracy that they have cancer, as suggested by the original surgeon in charge with the case. This represents the third novel correlation.  
The improvement refers to the cases for which the post-hoc agnostic explanations are found useful to increase the trustworthiness of the AI system's inference. We had 45 patients in the test set after SMOTE balancing, and for three of them, including the case study explained from both technical and medical perspectives in the manuscript, the explainability models provided to the surgeon an interpretation of the variables contribution, on which the decision is based, which changed his original opinion, as was described above for the case study presented. Hence, we obtained a 7% improvement over the network accuracy alone. Since this is a cumulative value, we computed for statistical analysis the \(p\)-value under k-fold validation with k = 2, k = 3, and k = 5, and we obtained in the all the cases a \(p<0.05\), which is considered to be statistically significant.