A Comparative Study of Linear and Quadratic Spline Regression Models for Predicting HbA1c Levels in Patients with Diabetes Mellitus - Arifin, Samsul; Anggraini, Dewi; Salam, Nur (Jambura Journal of Mathematics, 2025)
HbA1c is widely recognized as a key clinical indicator for monitoring and controlling diabetes, as it reflects average blood glucose levels over the preceding 2–3 months and is closely linked to the risk of complications. This study compares linear and quadratic truncated spline regression models for predicting HbA1c levels in patients with diabetes mellitus. The analysis used retrospective medical record data from a hospital in Makassar, Indonesia, collected in 2023. Fasting blood glucose and LDL cholesterol were included as predictors, with HbA1c as the response variable. Truncated spline regression was applied to capture nonlinear associations between predictors and HbA1c, and the comparison focused on linear versus quadratic specifications. The selection of the best model was based on the minimum GCV value. The model selection process indicated that the best specification was the linear truncated spline regression with two knot points. For FBG, the optimal knots were located at 159 mg/dL and 368 mg/dL, yielding the lowest GCV value of 3.5798. For LDL cholesterol, the best fit was achieved with knots at 183 mg/dL and 191 mg/dL, resulting in a GCV value of 4.3325. The predictive performance of this model was further supported by an R² value of 0.3861, indicating that the linear spline with two knots provides a better fit compared with the quadratic spline alternative. The spline approach showed a better fit based on GCV in depicting the changes in the influence of predictors on HbA1c, suggesting its potential as a more accurate predictive model for clinical and epidemiological purposes.