Multi-Tree Model for Precision Environmental Health with Longitudinally Assessed Mixture Exposure

Precision environmental health seeks to estimate how the effects of the environment vary across the population to inform targeted interventions and public health policy. However, there is a lack of statistical methods to estimate the heterogeneous effects of environmental exposures, particularly mixture exposures that are assessed longitudinally. We examine the heterogeneous exposure effect of weekly-average fine particulate matter (PM_2.5) and maximal daily temperature during gestation on birth weight using birth registry data in Colorado. We develop a Bayesian additive model represented by an ensemble of tree triplets where a tree triplet consists of two types of binary trees, interacting to model heterogeneous time-structured exposure effects. Our framework provides a tool to estimate individualized and subgroup-specific distributed lag effects of longitudinally assessed mixture exposures. Our method can accommodate a high-dimensional set of candidate modifiers with modifier selection and allows for mixture exposures with time-sensitive interactions. Through simulation, we demonstrate that our model can estimate individualized exposure effects and identify important mixture components and modifying factors. From the Colorado birth registry data, we find evidence of an association between PM_2.5 and birth weight with larger effects among mothers younger than 25 years with low income.