Multivariate adaptive regression spline (MARS) methods with application to multi drug-resistant tuberculosis (mdr-tb) prevalence

Abstract

Tuberculosis (TB) is the main public health problems 111 the world and Indonesia. The WHO report states that Indonesia is one of the countries contributing to TB in the world. If a TB patient is not successfully cured, it causes a double immunity of TB bacteria against Anti-TB Drugs (OAT), so-called multi-drug resistant (MDR). One of the Efforts to reduce the MDR-TB prevalence has been made based on information obtained from mathematical modeling, for example, using regression analysis that includes parametric, semi-parametric, and non-parametric approaches. Multivariate Adaptive Regression Spline (MARS) is one of the non-parametric regression approaches. The MARS model can overcome the problem of high dimensional data, produce an accurate prediction of response variables, and can overcome the weaknesses of recursive partition regression (RPR). The MARS has been built by a stepwise algorithm, which is a combination of forward and backward technique, according to a Generalized minimum Cross-Validation (GCV) value. The minimum GCV value 0.000015 is obtained from the best model that has a combination of Basis Function (BF) = 28, Minimum Interaction (MI) = 3, and Minimum Observation (MO) = 2. The result shows that all of the basis functions in the model have a significant effect on the response. The highest contribution of the basis function coefficient has given by BF6, which means the coefficient of BF6 will be statistically significant when the ratio of primary health facilities is more than 28.44. If the ratio of primary health facilities is more than 28.44, then the increase of one unit (other variables is considered constant) the MDR-TB prevalence increase by 0.171.