Flexible statistical approaches for modeling nonlinear relationships in diabetes prediction using splines, Bayesian kernel regression and Bayesian regression trees

Modeling nonlinear relationships is a fundamental challenge in statistical analysis, particularly when predictors exhibit complex and interacting effects on outcomes. This study compares three flexible methods for capturing such structures: restricted cubic spline regression (RCS), Bayesian kernel machine regression (BKMR), and Bayesian additive regression trees (BART). RCS enables explicit modeling of nonlinear associations via spline basis functions, BKMR leverages kernel functions within a Bayesian framework to capture nonlinear and non-additive effects, and BART provides a nonparametric ensemble approach that flexibly accommodates interactions and nonlinearities without prior specification. To demonstrate the utility of these methods, we apply them to the Pima Indians diabetes dataset, consisting of 768 observations of women at high risk of type II diabetes. After data preprocessing, including imputation and outlier handling, each method was fitted and evaluated using six performance measures. RCS and BKMR identified glucose, insulin, age, and skin thickness as significant predictors, while BART yielded the best predictive performance (AUC 97%). Predictor-response functions were used to enhance clinical interpretability. These findings illustrate that a methodology capable of capturing nonlinear effects can substantially improve prediction accuracy in epidemiological studies.