Estimating Perinatal Critical Windows to Environmental Mixtures via Structured Bayesian Regression Tree Pairs

Maternal exposure to environmental chemicals during pregnancy can alter birth and children's health outcomes. Research seeks to identify critical windows, time periods when the exposures can change future health outcomes, and estimate the exposure-response relationship. Existing statistical approaches focus on estimation of the association between maternal exposure to a single environmental chemical observed at high-temporal resolution, such as weekly throughout pregnancy, and children's health outcomes. Extending to multiple chemicals observed at high temporal resolution poses a dimensionality problem and statistical methods are lacking. We propose a tree-based model for mixtures of exposures that are observed at high temporal resolution. The proposed approach uses an additive ensemble of structured tree-pairs that define structured main effects and interactions between time-resolved predictors and variable selection to select out of the model predictors not correlated with the outcome. We apply our method in a simulation and the analysis of the relationship between five exposures measured weekly throughout pregnancy and resulting birth weight in a Denver, Colorado birth cohort. We identified critical windows during which fine particulate matter, sulfur dioxide, and temperature are negatively associated with birth weight and an interaction between fine particulate matter and temperature. Software is made available in the R package dlmtree.