## 3 Results
### Performance Evaluation of the Proposed EC-Nomenclature-Based G-S-M Approach  
EC-nomenclature-based G-S-M was tested on a CRC-associated metagenomic relative enzyme abundance dataset including 1262 samples, where 600 belong to CRC patients and 662 belong to controls. For each dataset, for different numbers of groups, accuracy, sensitivity, specificity, and AUC values have been calculated as the mean of the values obtained in 10 iterations of the cross-validation procedure. For each group, G-S-M reports the number of enzymes included in the group. Also, the average enzyme numbers over 10 iterations are reported. Table 2 shows the performance metrics of the EC-nomenclature-based G-S-M method applied to the CRC-associated metagenomic dataset, including relative enzyme abundance values. For example, there are 59.5 enzymes on average, as shown in the # (number) of enzymes column of the top row (highest scoring group) in Table 2. There are 90.7 enzymes on average, as shown in the # of features in the column of the 2 nd row (the top two groups are combined). In other words, the model that is generated via using the enzyme values of 90.7 can successfully predict CRC with a 0.769 AUC score. Upon scrutinizing different performance metrics of EC-nomenclature-based G-S-M, it becomes evident that our proposed method consistently excels, as delineated in Table 2. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**\# of** **Groups** & **\# of Enzymes** & **AUC** & **Accuracy** & **Specificity** & **Sensitivity** \\ \hline
1 & 59.5 \(\pm\) 26.517 & 0.728 \(\pm\) 0.031 & 0.673 \(\pm\) 0.028 & 0.749 \(\pm\) 0.08 & 0.588 \(\pm\) 0.058 \\ \hline
2 & 90.7 \(\pm\) 38.257 & 0.769 \(\pm\) 0.041 & 0.695 \(\pm\) 0.037 & 0.767 \(\pm\) 0.050 & 0.615 \(\pm\) 0.049 \\ \hline
3 & 147.9 \(\pm\) 45.261 & 0.763 \(\pm\) 0.031 & 0.704 \(\pm\) 0.032 & 0.769 \(\pm\) 0.054 & 0.632 \(\pm\) 0.033 \\ \hline
4 & 200.9 \(\pm\) 52.821 & 0.765 \(\pm\) 0.032 & 0.704 \(\pm\) 0.035 & 0.773 \(\pm\) 0.039 & 0.627 \(\pm\) 0.052 \\ \hline
5 & 244.9 \(\pm\) 64.824 & 0.770 \(\pm\) 0.029 & 0.706 \(\pm\) 0.029 & 0.773 \(\pm\) 0.034 & 0.630 \(\pm\) 0.057 \\ \hline
6 & 281.9 \(\pm\) 68.709 & 0.763 \(\pm\) 0.033 & 0.694 \(\pm\) 0.026 & 0.766 \(\pm\) 0.024 & 0.613 \(\pm\) 0.046 \\ \hline
7 & 330.4 \(\pm\) 79.269 & 0.761 \(\pm\) 0.029 & 0.683 \(\pm\) 0.036 & 0.760 \(\pm\) 0.034 & 0.598 \(\pm\) 0.060 \\ \hline
8 & 372.1 \(\pm\) 82.131 & 0.766 \(\pm\) 0.034 & 0.692 \(\pm\) 0.037 & 0.755 \(\pm\) 0.038 & 0.622 \(\pm\) 0.050 \\ \hline
9 & 391.1 \(\pm\) 84.069 & 0.767 \(\pm\) 0.026 & 0.706 \(\pm\) 0.032 & 0.772 \(\pm\) 0.030 & 0.633 \(\pm\) 0.048 \\ \hline
10 & 457.0 \(\pm\) 79.538 & 0.763 \(\pm\) 0.035 & 0.688 \(\pm\) 0.045 & 0.739 \(\pm\) 0.047 & 0.632 \(\pm\) 0.062 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Averages over 10-fold MCCV and standard deviations are presented for different performance metrics. These were obtained cumulatively for the top 10 ranked enzyme groups, when applied to the CRC-associated metagenomic dataset, including relative abundance values of the enzymes. The robust rank aggregation approach was applied (i.e., ranked enzyme groups and enzymes) to aggregate them into a final list, as shown in Table 3. The ranked enzyme groups and the enzymes that are annotated with these enzyme groups are shown in the final list. All of those final lists are visualized in the output panel of the G-S-M approach, as shown in Figure 4. The EC-nomenclature-based G-S-M approach identified glycosidases (3.2.1), CoA-transferases (2.8.3), and hydro-lyases (4.2.1) as the top three most important enzyme groups when the CRC-associated metagenomic dataset was analyzed (as shown in Figure 4A). Oligo 1,6 glucosidase, crotonobetainyl-CoA hydratase, and citrate CoA-transferase are found to be the top three important enzymes when the EC-nomenclature-based G-S-M approach was applied to the CRC-associated metagenomic dataset (as shown in Figure 4B).