## 3 Results and Discussion
### Grouping Predictors  
For our machine learning (ML) model, we performed several experimental analyses to group interacting predictors into the same subset to identify which one of them better predicts CKD in the models with or without creatinine. To group our predictors into subsets, we first trained the models inputting all the 13 variables in Table 2. Applying the backward elimination feature selection technique, variables with the least significance to the models were removed according to their decreased AUC value in Table 2. This was important for the ML models to make an accurate and quick judgment on the predictors. Furthermore, it helped to control the impute variables and training time. The predictors with higher computing power to the models were retained for the grouping. Age, gender, creatinine, and the novel metabolic indices including TyG-Index, TG/HDL-C ratio, and VAI, were the most significant predictors for the grouping and modeling. Among the conventional CKD risk factors, age, gender, and creatinine were the most consistent and had better interaction with the NML. To fit our models with fewer variables, we combined age, gender, and a novel metabolic index to form a distinct subset. Age and gender are non-modifiable conventional risk factors, which play a crucial role in the prediction of CKD [19]. Each ML model was trained and tested using the subsets. We discovered that conventional features with high affinity for the NMI accurately predicted CDK. Those with low affinity, on the other hand, predicted CKD moderately. In total, three subsets were identified as the best predictors, and each subset constituted three features as represented in Table 3. Integrating age and gender with TyG-Index, TG/HDL-C ratio or VAI generated high performance in the model. To further maximize the model performance, we subsequently added creatinine.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Variable** & **HR (95\% CI)** & **AUC (95\% CI)** & \(\mathbf{p}\)**-Value** \\ \hline Non-laboratory examination & & & \\ Age & 1.04 (1.032–1.038) & 0.633 (0.62–0.645) & \textless{}0.001 \\ Gender & 5.6 (5.208–6.083) & 0.756 (0.745–0.768) & \textless{}0.001 \\ BMI (kg/m\({}^{2}\)) & 1.07 (1.06–1.077) & 0.606 (0.593–0.618) & \textless{}0.001 \\ Waist circumference (cm) & 1.05 (1.043–1.05) & 0.676 (0.663–0.687) & \textless{}0.001 \\ \hline Laboratory examination & & & \\ Triglyceride (mmol/L) & 1.3 (1.255–1.42) & 0.603 (0.59–0.615) & \textless{}0.001 \\ Cholesterol (mmol/L) & 1.1 (1.073–1.155) & 0.54 (0.527–0.553) & \textless{}0.001 \\ HDL-cholesterol (mmol/L) & 0.41 (0.366–0.455) & 0.377 (0.364–0.389) & \textless{}0.001 \\ LDL-cholesterol (mmol/L) & 1.23 (1.187–1.284) & 0.571 (0.558–0.583) & \textless{}0.001 \\ Blood urea nitrogen (BUN, mg/dL) & 1.06 (1.05–1.07) & 0.618 (0.605–0.629) & \textless{}0.001 \\ Creatinine & 1.7 (1.535–1.968) & 0.909 (0.903–0.915) & \textless{}0.001 \\ \hline Metabolic indices & & & \\ TyG-Index & 2.53 (2.269–2.816) & 0.605 (0.592–0.617) & \textless{}0.001 \\ TG/HDL-C ratio & 1.15 (1.121–1.186) & 0.625 (0.613–0.638) & \textless{}0.001 \\ VAI & 1.35 (1.291–1.407) & 0.716 (0.705–0.727) & \textless{}0.001 \\ \hline \hline \end{tabular} BMI, body mass index; HDL-cholesterol, high-density lipoprotein cholesterol; LDL-cholesterol, low-density lipoprotein cholesterol; eGRR, estimated glomerular filtration; TyG-Index, triglyceride glucose index; TG/HDL-C ratio, triglyceride to high-density lipoprotein cholesterol ratio; VAI, visceral adiposity index.  
\end{table}
Table 2: Predictors of CKD in univariate Cox proportional hazard regression and ROC curve analysis.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Group** & **Predictors** \\ \hline Subset A & Age + Gender + TyG-Index \\ Subset B & Age + Gender + TG/HDL-C ratio \\ Subset C & Age + Gender + VAI \\ \hline \hline \end{tabular}
\end{table}
Table 3: Best groups of predictors.