Nonparametric Bi-Response Ordinal Logistic Regression Model for Diabetes Mellitus and Hypertension Risks Based on Multivariate Adaptive Regression Spline

Abstract

This study discusses the application of nonparametric regression for bi-response ordinal logistic modeling based on the Multivariate Adaptive Regression Spline (MARS) estimator in assessing the risk of diabetes mellitus and hypertension. The MARS estimator provides greater flexibility by allowing for nonlinearity and interactions among predictors, making it well-suited for modeling health-related risk factors. Parameter estimation in this study is conducted using the Maximum Likelihood Estimation (MLE) method. However, due to the non-linearity of the first derivative of the log-likelihood function, the Berndt-Hall-Hall-Hausman (BHHH) numerical iteration method is applied to obtain parameter estimates. The complexity of the likelihood function poses challenges in constructing the Hessian matrix, necessitating an approximation of the second derivative using the first derivative in the BHHH method. The analysis identifies Age, Body Mass Index (BMI), and Total Cholesterol as significant predictor variables influencing the risk of diabetes mellitus and hypertension. Model evaluation is carried out using accuracy, the Area Under the Curve (AUC), and the Apparent Error Rate (APER). The results demonstrate an accuracy of 82.44%, indicating strong classification performance. Additionally, the AUC value of 73.42% suggests the model falls within the good category, while the APER value of 17.56% confirms the model’s stability and reliability. The findings suggest that the MARS-based bi-response ordinal logistic regression model effectively captures the relationship between significant risk factors of diabetes mellitus and hypertension.