  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 define 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 spline-based 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 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.
