Bayesian treed distributed lag models - Mork, Daniel S., author; Wilson, Ander, advisor; Sharp, Julia, committee member; Keller, Josh, committee member; Neophytou, Andreas, committee member (Colorado State University. Libraries, 2021)
In many applications there is interest in regressing an outcome on exposures observed over a previous time window. This frequently arises in environmental epidemiology where either a health outcome on one day is regressed on environmental exposures (e.g. temperature or air pollution) observed on that day and several proceeding days or when a birth or children's health outcome is regressed on exposures observed daily or weekly throughout pregnancy. The distributed lag model (DLM) is a statistical method commonly implemented to estimate an exposure-time-response function by regressing the outcome on repeated measures of a single exposure over a preceding time period, for example, mean exposure during each week of pregnancy. Inferential goals include estimating the exposure-time-response function and identifying critical windows during which exposures can alter a health endpoint. In this dissertation, we develop novel formulations of Bayesian additive regression trees that allow for estimating a DLM. First, we propose treed distributed lag nonlinear models to estimate the association between weekly maternal exposure to air pollution and a birth outcome when the exposure-response relation is nonlinear. We introduce a regression tree-based model that accommodates a multivariate predictor along with parametric control for fixed effects. Second, we propose a tree-based method for estimating the association between repeated measures of a mixture of multiple pollutants and a health outcome. The proposed approach introduces regression tree pairs, which allow for estimation of marginal effects of exposures along with structured interactions that account for the temporal ordering of the exposure data. Finally, we present a framework to estimate a heterogeneous DLM in the presence of a potentially high dimensional set of modifying variables. We present simulation studies to validate the models. We apply these methods to estimate the association between ambient pollution exposures and birth weight for a Colorado, USA birth cohort.