Bayesian Additive Regression Trees for Modeling Multiple Exposures With Measurement Error

We develop a Bayesian Additive Regression Trees with Measurement Error (BART-ME) model for flexibly estimating exposure-response functions when multiple covariates are measured with classical error. Unlike existing approaches, BART-ME accommodates nonlinearities, interactions, correlated exposures, and correlated measurement errors, while exploiting replicate measurements to estimate the error variance-covariance structure. Posterior inference is obtained via a Metropolis-within-Gibbs algorithm, yielding estimates of exposure-response functions, variable importance, and measurement reliability. Simulation studies demonstrate that BART-ME reduces bias and improves coverage compared with Naïve BART analyses that ignore measurement error, even with sparse replication. In an application to first-trimester ultrasound data from the NICHD Fetal Growth Studies, BART-ME identified crown-rump length as the most reliable predictor of gestational age at delivery and revealed nonlinear patterns attenuated by Naïve methods. These results illustrate the potential of BART-ME as a general framework for correcting measurement error in complex exposure settings.