## 3 Proposed Prediction Scheme  
In this study, the five machine learning classification techniques described above were integrated to propose a scheme for predicting SPC in colorectal cancer patients. The flowchart of the proposed scheme is shown in Figure 1.  
The first step of the proposed scheme was to collect the data. The second step was to collect candidate risk factors as predictor variables. In addition, this paper reviews the available literature on what variables are associated with the risk factors for the recurrence of ovarian cancer [13]. As shown in Table 1, the 14 risk factors for SPC in colorectal cancer patients are represented as X1 to X14. The target variable is SPC or not (Y). In the third step, we constructed classification models for predicting SPC in colorectal cancer patients. In building the classification models, we used two types of modeling processes. One was a single model and the other was a two-stage model. In modeling the single models, all 14 risk factors were directly used as predictors for SVM, RF, MARS, ELM, and XGboost for constructing five single classification models. These were termed single SVM (S-SVM), single RF (S-RF), single MARS (S-MARS), single ELM (S-ELM), and single XGboost (S-XGboost) models. \begin{table}
\begin{tabular}{l l} \hline \hline
**Variables** & **Description** \\ \hline X1. Sex & Male/female \\ X2. Age at diagnosis & Age at diagnosis \\ X3. Primary site & Colon/recal \\ X4. Grade/differentiation & Grade of tumor differentiation \\ X5. Tumor size & Distinguish by unit size (in center meter) \\ X6. Regional lymph nodes positive & Regional lymphoid node involved by tumor \\ X7. Combined stage & Combined pathological and clinical stage as mixed stages \\ X8. Surgical margins of the primary site & Residual/no residual \\ X9. Radiation therapy/no radiation therapy & Radiation therapy/no radiation therapy \\ X10. Chemotherapy/no chemotherapy & Chemotherapy/no chemotherapy \\ X11. BMI & BMI (Body Mass Index) \\ X12. Smoking behavior & Smoking behavior/no smoking behavior \\ X13. Betel nut chewing & Betel nut chewing/no betel nut chewing \\ X14. Drinking & Drinking/no drinking \\ Y: SPC & 1: No, 2: yes \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The fourteen candidate risk factors for SPC in colorectal cancer patients. Figure 1: The flowchart of the proposed second primary cancer (SPC) prediction scheme in colorectal cancer patients. The two-stage model integrating the feature selection method and classifier were used in the third step of the proposed scheme, as important disease risk factors are often fundamental indicators that provide useful information for modeling effective disease predictions. In modeling the two-stage model, a feature selection method was first used to select the important risk factors. Among the five machine learning methods, only RF, MARS, and XGboost can be used to select important risk factors based on their fundamental algorithms; thus, these were used as the three feature selection methods to identify and rank important risk factors for predicting SPC in colorectal cancer patients. Each feature selection method generated one set of important risk factors. Using only one feature selection technique may not provide stable and effective selection results. A simple average rank method was used to combine the risk factor selection results of the three methods. Table 2 shows the selected and ranked risk factors using the RF, MARS, and XGboost methods. Note that a risk factor with a rank of 1 indicates that it is the most important risk factor, while one with a rank of 14 indicates that it is a risk factor not selected by the method. For each risk factor, the average rank was obtained by calculating the average value of its rankings in the RF, MARS, and XGboost methods. Table 2 shows, also, the average rank of every risk factor. The ranked overall variable importance of all the risk factors is shown in Figure 2. It can be observed that X7, with an average rank of 1, is the most important risk factor, followed by X2 and X11.