## 4 Empirical Results  
In this study, colorectal cancer datasets provided by three hospital cancer registries were used to verify the proposed medical diagnostic scheme for predicting the occurrence of SPC in colorectal cancer patients. Each patient in the dataset had 14 predictor variables, with one response variable indicating SPC or not. Excluding incomplete records, there were a total of 4287 patients in the dataset. The 10-fold cross-validation method was used in this study for evaluating the performance of the proposed scheme. This received institutional review board (IRB) approval by the Chung-Shan Medical University Hospital (CSMUH number: CS18116).  
For modeling the ten models, including the S-SVM, S-RF, S-MARS, S-ELM, S-XGboost, A-SVM, A-RF, A-MARS, A-ELM, and A-XGboost models for predicting SPC in colorectal cancer patients, the process mentioned in Section 3 was used. Table 3 shows the classification results of the five single methods, including the S-SVM, S-RF, S-MARS, S-ELM, and S-XGboost models. From Table 3, it can be observed that the AUC values of the S-SVM, S-RF, S-MARS, S-ELM, and S-XGboost models were 0.711, 0.618, 0.640, 0.710, and 0.550, respectively. The single SVM model provided the highest AUC value, followed by the single XGboost model with a slightly smaller AUC value. However, it also can be seen from Table 3 that the accuracy value of the S-XGboost model was 0.641, which is significantly greater than that of the single SVM model at 0.408. Figure 3 shows the ROC (Receiver Operating Characteristic) curves of the five single classification methods for the occurrence of SPC in colorectal cancer patients. Thus, among the five single classification methods, the single XGboost model provided the best classification results.  
For comparing the classification performances between the five single methods and the five two-stage models, Figure 5 depicts the AUC values of the ten models in decreasing order. It can be observed from Figure 5 that the A-XGboost model generated the best AUC value, followed by the S-SVM and S-XGboost models. These results indicated that the A-XGboost method is a good alternative for constructing a classification model for diagnosing the occurrence of SPC in colorectal cancer. Moreover, the A-XGboost method can be used to select important risk factors that are more influential on patients with SPC of colorectal cancer.  
In order to evaluate the robustness of the ten models, we randomly repeated 10-fold cross-validation 100 times and averaged the classification accuracy metrics; i.e., accuracy, sensitivity, specificity, and AUC. The averaged accuracy, sensitivity, specificity, and AUC values are shown in Table 5. From the Table, it can be observed that the A-XGboost model still generated the highest AUC value, 0.723, and is the most promising model in this study for predicting the SPC in colorectal cancer.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Methods** & **Accuracy** & **Sensitivity** & **Specificity** & **AUC** \\ \hline A-SVM & 0.294 & 0.407 & 0.281 & 0.672 \\ A-RF & 0.615 & 0.558 & 0.622 & 0.604 \\ A-MARS & 0.731 & 0.361 & 0.772 & 0.566 \\ A-XGboost & 0.611 & 0.767 & 0.593 & 0.714 \\ A-ELM & 0.425 & 0.442 & 0.424 & 0.546 \\ \hline \end{tabular}
\end{table}
Table 4: Classification results of the five two-stage methods.  
Figure 5: Comparison of the area under the curve (AUC) values of the ten models.