COMPARISON OF BINARY PROBIT REGRESSION AND FOURIER SERIES NONPARAMETRIC LOGISTIC REGRESSION IN MODELING DIABETES STATUS AT HAJJ GENERAL HOSPITAL SURABAYA

Abstract

Diabetes mellitus is a chronic disease with a rising global prevalence, including in Indonesia. Early detection and accurate modeling are crucial for effective prevention and management. Binary Logistic Regression (BLR) is commonly used for binary outcome modeling; however, in practice, the relationship between binary outcomes and continuous predictors is often nonlinear, making BLR less suitable. To address these limitations, alternative methods such as Binary Probit Regression (BPR) and Flexible Semiparametric Nonlinear Binary Logistic Regression (FSNBLR) have been developed. This study aims to compare the performance of BLR, BPR, and FSNBLR models in classifying diabetes mellitus cases at Hajj General Hospital Surabaya. All three models were estimated using the Maximum Likelihood Estimation (MLE) method. Since the resulting estimators do not have closed-form solutions, numerical iteration using the Newton-Raphson method was applied. Model performance was assessed using Area Under the Curve (AUC), accuracy, sensitivity, and specificity. The FSNBLR model outperformed both the BLR and BPR models. It achieved the highest AUC value of 81.86%, while BLR (66.30%) and BPR (66.30%). That is indicated FSNBLR superior discriminative ability. In addition, the FSNBLR model recorded higher accuracy, sensitivity, and specificity compared to the other two models. The FSNBLR model demonstrated better predictive performance in identifying diabetes mellitus cases, especially in scenarios involving nonlinear relationships between predictors and the outcome variable. These findings suggest that flexible semiparametric approaches offer greater effectiveness in medical classification tasks, particularly for chronic conditions like diabetes mellitus.