## 4 Discussion
### Computational Performance Evaluation of the EC-Nomenclature-Based G-S-M Model  
The EC-nomenclature-based G-S-M approach demonstrates its efficacy in predicting disease-causing enzymes by modeling and analyzing enzyme abundance data utilizing EC numbers. Within the G-S-M framework, a machine learning algorithm was employed to identify the most significant EC groups. The EC-nomenclature-based G-S-M method was evaluated using 1262 CRC-associated metagenomic samples, including the relative abundance values of enzymes. In Table 2, we present the performance metrics of the EC-nomenclature-based G-S-M model averaged over 10-fold MCCV iterations for the aggregated top 10 scoring EC groups identified for the CRC-associated metagenomic dataset, including a functional profile of the samples. Table 2 also demonstrates the effect of cumulatively adding the top scoring EC groups in terms of model performance. For example, the EC-nomenclature-based G-S-M model has an AUC value of 0.729 when on average 59.5 enzymes are used, as shown in the first row of Table 2 (using only the enzymes found in the top scoring EC group). On the other hand, the AUC value of the EC-nomenclature-based G-S-M model is reported as 0.769 when 90.7 enzymes from the top two scoring EC groups are used (as shown in the second row of Table 2). Additionally, the AUC value of the EC-nomenclature-based G-S-M model becomes 0.763 when 457 enzymes from the top-10 scoring EC groups are cumulatively used (as shown in the last row of Table 2). Instead of checking the functional profile values of 457 enzymes, one could check the functional profile values for only 90 enzymes to predict with high AUC values. The model that is generated via only using the enzyme abundance value of 90 can successfully predict CRC-associated enzymes with an AUC score of 0.769, which is quite satisfying. As shown in Table 2, the inclusion of additional EC groups did not show a statistically significant improvement in performance metrics. Consequently, constructing a model with a reduced number of enzymes becomes feasible, thereby facilitating the interpretation of the resultant model. In order to evaluate population-based differences, we have applied the EC-nomenclature-based G-S-M method to population-specific CRC-associated metagenomic datasets, including the relative abundance values of the enzymes. Figure 5 presents the number of selected enzymes and AUC values recorded in this experiment. Moreover, when the EC-nomenclature-based G-S-M method is applied, we assess the correlation among the identified EC groups between different population datasets using the Jaccard index (asshown in Figure 15). The Jaccard index refers to the number of enzyme groups that are commonly identified in two different populations divided by the total number of enzyme groups detected by either one of these populations. The maximum Jaccard index value between the identified enzyme groups from different populations is calculated as 0.25 between the French and Indian datasets. Figure 16 presents the commonalities among the top 10 enzyme groups that are selected for different datasets obtained from different populations. The methyltransferases (EC: 2.1.1) group has been identified among the top 10 groups for the five different population datasets obtained from Germany (DEU), France (FRA), India (IND), Italy (ITA), and Japan (JPN). Figure 16: Commonalities among the top 10 enzyme groups that were selected by the EC-nomenclature-based G-S-M for different CRC-associated metagenomic datasets, including the relative abundance values of the enzymes obtained from the samples belonging to different populations. Figure 15: Correlations among the top 10 enzyme groups that were selected by the EC-nomenclature-based G-S-M for different CRC-associated metagenomic datasets, including the relative abundance values of the enzymes obtained from the samples belonging to different populations. The Jaccard index is used to calculate the correlation between the identified EC groups among two populations.