Advancing dengue morbidity prediction in Indonesia: a hybrid MARS–random forest framework for Java and Bali

Abstract

Dengue hemorrhagic fever (DHF) is an endemic disease in Indonesia with a steadily rising number of cases, particularly on the islands of Java and Bali, which account for the highest number of cases nationwide. The complexity of the relationships between environmental, social, and health factors means that modeling DHF morbidity rates requires methods capable of capturing nonlinear relationships. This study aims to compare the performance of the Multivariate Adaptive Regression Splines (MARS), Random Forest, and MARS-Random Forest hybrid methods in modeling DBD morbidity rates on the islands of Java and Bali. The data used are aggregated regency/city-level data from 2024 sourced from the Central Statistics Agency, with the response variable being the DBD morbidity rate and seven predictor variables. The preprocessing stage included handling missing data, removing outliers, applying a natural logarithmic transformation to the response variable, Z-score standardization, and splitting the data using a stratified split with an 80:20 ratio. The MARS model was built using a combination of basis function parameters, interaction order, and minimum observations, while the Random Forest and hybrid models were optimized via grid search based on the Out-of-Bag Mean Squared Error (OOB MSE) value. The results of the study show that the MARS model produces four basis functions that describe the nonlinear relationships among the variables. On the test data, Random Forest delivered the best performance with an MSE of 0.9675, an RMSE of 0.9836, an MAE of 0.8014, and an R² of -0.0258. Meanwhile, the MARS-Random Forest hybrid model produced an MSE of 1.2454, and the MARS model produced an MSE of 1.7225. Thus, Random Forest is the best model for modeling dengue fever incidence on the islands of Java and Bali, while MARS retains an advantage in terms of interpretability through the basis functions it generates.