# Development of a Metabolic Syndrome Prediction Model Using HOMA-IR and Multivariate Factors
## 2 Materials and Methods
### Statistical Analysis  
Descriptive statistics were employed to summarize the demographic and clinical characteristics of the study population. Gender distribution and the presence or absence of metabolic syndrome (MetS) were presented as frequencies and standard deviations. Continuous variables such as age and HOMA-IR levels were described using means and standard deviations. This initial descriptive overview provided a foundation for further analyses.  
We also conducted a stratified ROC analysis by dividing participants into approximately 10-year intervals (20-29, 30-39, 40-49, 50-59, and \(\geq\)60 years). This was to explore any age-dependent variations in model performance.  
To assess the associations between Diabetes Mellitus status and other variables, chi-square tests were utilized for categorical variables and independent \(t\)-tests for continuous variables. These tests helped identify significant differences across groups, which were crucial for subsequent modeling.  
Multiple logistic regression analysis was conducted to predict the occurrence of MetS. Variables included in the model--HOMA-IR levels, gender, age, and DM status--were selected based on their known associations with MetS from previous studies. This selection was aimed at understanding the unique contributions of these factors to MetS risk. The model estimated regression coefficients for each predictor to assess their individual impact and interaction within the model. This approach allowed for a detailed interpretation of how each variable influences the likelihood of MetS, aligning the analysis with the objectives of predicting and managing MetS effectively. Because KNHANES employs a complex, multi-stage sampling design, we applied the sampling weights provided by the survey to ensure national representativeness. All logistic regression analyses, including ROC evaluations, were performed using these weights. Prior to logistic regression, we evaluated the distribution of HOMA-IR using the Shapiro-Wilk test. The data exhibited a right-skewed (long-tailed) distribution, and log transformation did not substantiallyimprove normality. However, because logistic regression does not require normality of the predictor variables, we proceeded without further transformations. We also conducted a multicollinearity check using variance inflation factors (VIF) for all independent variables (HOMA-IR, gender, age, and DM status), and each showed a VIF value of 1.000, indicating no significant multicollinearity.  
The predictive accuracy of the logistic regression model was evaluated using a receiver operating characteristic (ROC) curve analysis. The model's performance was detailed through the area under the curve (AUC), with sensitivity and specificity calculated to reflect its diagnostic ability. To address variations in MetS risk across different age groups, the ROC analysis was stratified by age. This stratification was based on the premise that risk factors for MetS, such as hormonal changes and lifestyle modifications, differ significantly among age groups, potentially affecting the model's performance.  
The results were discussed in terms of AUC values for each age group, highlighting the model's strengths and limitations in different demographic segments. All statistical analyses were conducted using SPSS software (version 25.0), with a significance level set at \(p<0.05\), ensuring the robustness and reliability of the findings.