MODELING THE RELATIONSHIP BETWEEN HBA1C, TC, AND TG: A GENERALIZED ADDITIVE MODEL AND RESPONSE SURFACE METHODOLOGY APPROACH

This study aims to model the relationship between Hemoglobin A1c (HbA1c) levels and two key metabolic indicators-Triglycerides (TG) and Total Cholesterol (TC)-using advanced statistical methods. By leveraging nonparametric regression techniques, this research explores complex, nonlinear interactions between these variables, providing a more nuanced analysis than traditional linear models. Objective: The primary objective is to construct and validate an analytical framework that combines Generalized Additive Models (GAM) and Response Surface Methodology (RSM) to understand the effects of TG and TC on HbA1c. The dataset comprises HbA1c, TC, and TG as variables of interest. The data were split into a training set (70%) and a testing set (30%). A GAM model was used to capture the smooth, nonlinear relationships between the predictors and the response variable, while RSM was employed to generate response surface plots for further interpretation. Model performance was evaluated using Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Root Mean Squared Percentage Error (RMSPE), and Median Absolute Error (MedAE). The GAM model demonstrated strong predictive performance with an RMSE of 3.73, MAE of 2.33, and RMSPE of 54.80%. The RSM model highlighted the significant contributions of TC and TG, showing that both variables significantly affect HbA1c levels. The integration of GAM and RSM provides an effective approach for modeling complex health data and understanding the relationship between HbA1c, TC, and TG. This methodology offers valuable insights for healthcare professionals in predicting metabolic disorders and informs strategies for better managing patient health outcomes.