Estimating perinatal critical windows of susceptibility 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 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 (e.g., 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 regression tree–based model for mixtures of exposures observed at high temporal resolution. The proposed approach uses an additive ensemble of tree pairs that defines structured main effects and interactions between time‐resolved predictors and performs variable selection to select out of the model predictors not correlated with the outcome. In simulation, we show that the tree‐based approach performs better than existing methods for a single exposure and can accurately estimate critical windows in the exposure–response relation for mixtures. We apply our method to estimate the relationship between five exposures measured weekly throughout pregnancy and 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.