Hypertension modelling using nonparametric ordinal logistic regression based on multivariate adaptive regression spline

Abstract

Hypertension is one of the most common diseases in the world and is an important risk factor for heart disease and a significant contributor to mortality and morbidity in both developed and developing countries. Systematic reviews have been conducted to assess the prevalence of hypertension and its risk factors. To model the hypertension status, in this study we developed an ordinal logistic regression model into a nonparametric regression model and called it a Nonparametric Ordinal Logistic Regression (NOLR) model. Therefore, this study aims to model hypertension status based on several influencing factors, and identify these factors that the most influential on hypertension status using the NOLR model approach, because we assume an ordinal scale response variable with q categories to have an asymmetric distribution, namely a multinomial distribution. Next, to estimate the NOLR model of Hypertension status, we use a Multivariate Adaptive Regression Spline (MARS) estimator, because it can accommodate interactions between risk factors expressed in basis functions, making it suitable for high-dimensional data cases. Furthermore, selection of the best model is based on minimum value of Generalized Cross-Validation (GCV). The results are that the best MARS model of hypertension status has BF = 16, MI = 3, and MO = 1 with GCV value of 0.0353874, and R² value of 49.13508%. Also, there are three predictor variables, namely age, body mass index and total cholesterol that significantly affect the hypertension status. In addition, the obtained estimation of nonparametric ordinal logistic regression model using the MARS estimator is valid for predicting the hypertension status with an accuracy value of 69.25%, sensitivity value of 66.47% and specificity value of 84.06%.