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

Abstract

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 exposureresponse 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 splinebased 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.

Heterogeneous Distributed Lag Models to Estimate Personalized Effects of Maternal Exposures to Air Pollution

“…The horseshoe variance prior will shrink the effects of misspecified trees reducing variance and false window detection. A similar prior specification was shown to improve DLM estimation in the treed DLM method of Mork and Wilson (2021a). We restrict the range of φ to exp{−φ} ∈ (0.05, 0.95) and assign prior φ ∼ Gamma(1/2, 1/2), which gives higher probability to smoother distributed lag effects.…”

“…These constraints yield effect estimates that are more biologically plausible as well as add stability to the estimator in the presence of high autocorrelation in the exposure data, which is typical with repeated measures of environmental exposures, such as the air pollution exposure considered in this paper. Methods for constraining DLMs include splines (Zanobetti et al, 2000;Gasparrini et al, 2010), Gaussian processes (Warren et al, 2012), principal components (Wilson et al, 2017), and regression trees (Mork and Wilson, 2021a). The majority of studies that apply these methods assume a homogeneous exposure-response relationship across the population.…”

“…The BART framework of Chipman et al (2010) is a popular method for estimating non-parametric functions. Extensions of BART allow for estimating distributed lag nonlinear (Mork and Wilson, 2021b) and mixture models (Mork and Wilson, 2021a). The treed DLM approach of Mork and Wilson (2021a) outperforms competing spline and Gaussian process methods when the goal is distributed lag effect estimation and critical window identification.…”

“…Extensions of BART allow for estimating distributed lag nonlinear (Mork and Wilson, 2021b) and mixture models (Mork and Wilson, 2021a). The treed DLM approach of Mork and Wilson (2021a) outperforms competing spline and Gaussian process methods when the goal is distributed lag effect estimation and critical window identification. However, both of these approaches assume a common distributed lag effect for all individuals.…”

“…The first considers a Gaussian process DLM for each subgroup and assumes the same smoothness in the distributed lag effects for all observations. The second method incorporates the treed DLM method of Mork and Wilson (2021a) and defines a nested tree structure where the treed DLM is used to estimate unique critical windows and effect sizes for the subgroup at each terminal node of the modifier tree. This approach relaxes the smoothness assumption imposed by Gaussian processes and improves performance when the magnitude of the effect varies over the population or there are subgroups with no exposure effect.…”