Treed distributed lag nonlinear models

TL;DR

This paper introduces a Bayesian additive regression trees approach for distributed lag nonlinear models, improving the estimation of exposure effects over specific time windows in environmental health studies.

Contribution

It proposes a novel Bayesian tree-based framework for DLNMs that better captures non-smooth exposure-response surfaces and identifies critical exposure windows.

Findings

Outperforms spline-based models in non-smooth settings

Achieves lower variance in estimates

More accurately identifies critical exposure windows

Abstract

In studies of maternal exposure to air pollution a children's health outcome is regressed on exposures observed during pregnancy. The distributed lag nonlinear model (DLNM) is a statistical method commonly implemented to estimate an exposure-time-response function when it is postulated the exposure effect is nonlinear. Previous implementations of the DLNM estimate an exposure-time-response surface parameterized with a bivariate basis expansion. However, basis functions such as splines assume smoothness across the entire exposure-time-response surface, which may be unrealistic in settings where the exposure is associated with the outcome only in a specific time window. We propose a framework for estimating the DLNM based on Bayesian additive regression trees. Our method operates using a set of regression trees that each assume piecewise constant relationships across the exposure-time space. In a simulation, we show that our model outperforms spline-based models when the exposure-time surface is not smooth, while both methods perform similarly in settings where the true surface is smooth. Importantly, the proposed approach is lower variance and more precisely identifies critical windows during which exposure is associated with a future health outcome. We apply our method to estimate the association between maternal exposure to PM$_{2.5}$ and birth weight in a Colorado USA birth cohort.