[Paper Review] Kernel Machine and Distributed Lag Models for Assessing Windows of Susceptibility to Mixtures of Time-Varying Environmental Exposures in Children's Health Studies

Ander Wilson, Hsiao‐Hsien Leon Hsu+4 more|arXiv (Cornell University)|Apr 29, 2019

Air Quality and Health Impacts4 citations

TL;DR

This paper proposes a novel Bayesian kernel machine regression method that simultaneously models exposure-timing, nonlinear associations, and interactions for multiple time-varying environmental exposures in children's health studies. By integrating a functional weight component into the kernel, the method identifies windows of susceptibility during development, demonstrating its utility in linking prenatal exposure to four ambient pollutants with birth weight in a Boston-area cohort.

ABSTRACT

Research has shown that early life exposures to environmental chemicals, starting as early as conception, can reprogram developmental trajectories to result in altered health status later in life. These principles likely apply to complex mixtures as well as individual chemicals. We thus consider statistical methods to estimate the association between mixtures of multiple time-varying exposures and a future health outcome, e.g. exposure to multiple air pollutants observed weekly throughout pregnancy and birth weight. First, we illustrate how to use traditional distributed lag models, distributed lag nonlinear models, and Bayesian kernel machine regression to estimate the association between multiple time-varying exposures and a health outcome. While none of these methods simultaneously account for exposure-timing, nonlinear association, and interactions, we highlight situations in which each model performs well. Second, we propose a new method to estimate the association between multiple time-varying exposures and a health outcome. The proposed approach is, to our knowledge, the first method to simultaneously account for exposure-timing, nonlinear associations, and interactions between time-varying exposures. The proposed approach is a Bayesian kernel machine regression method that accounts for exposure timing using a functional weight component within the kernel. The weight function identifies developmental periods with increased association between exposure and a future health outcome, often referred to as a window of susceptibility. We demonstrate the proposed methods in an analysis of exposure to four ambient pollutants and birth weight in a Boston-area perinatal cohort.

Motivation & Objective

• To address the gap in statistical methods that simultaneously model exposure-timing, nonlinear effects, and interactions in time-varying environmental mixtures.
• To identify critical developmental windows when exposure to environmental mixtures most strongly influences future health outcomes.
• To improve the estimation of associations between complex mixtures of pollutants and adverse birth outcomes like low birth weight.
• To develop a method that integrates functional weights into kernel machines to reflect varying susceptibility across gestational timing.

Proposed method

• The proposed method extends Bayesian kernel machine regression by incorporating a functional weight component within the kernel to model exposure-timing effects.
• The functional weight function estimates the relative importance of exposure at different time points during gestation, identifying windows of susceptibility.
• The method jointly models nonlinear associations and interactions among multiple time-varying exposures using a flexible kernel-based approach.
• A Bayesian hierarchical framework is employed to enable uncertainty quantification and shrinkage of complex interaction terms.
• The kernel function combines exposure levels across time with time-specific weights to compute a composite exposure metric.
• The model is fitted using Markov chain Monte Carlo (MCMC) sampling to estimate posterior distributions of exposure effects.

Experimental results

Research questions

• RQ1 Which periods during gestation are most critical for exposure to ambient pollutant mixtures in relation to birth weight?
• RQ2 How do nonlinear and interactive effects of multiple time-varying pollutants jointly influence birth outcomes?
• RQ3 Can a single statistical model simultaneously capture exposure-timing, nonlinearity, and interactions in environmental mixture studies?
• RQ4 What is the relative contribution of different pollutants during specific gestational windows to reduced birth weight?
• RQ5 How does the proposed method compare to traditional distributed lag and distributed lag nonlinear models in identifying windows of susceptibility?

Key findings

• The proposed Bayesian kernel machine regression with functional weights successfully identified specific gestational windows where exposure to ambient pollutants was most strongly associated with reduced birth weight.
• The method detected a window of heightened susceptibility during mid-pregnancy for certain pollutants, particularly PM2.5 and NO2.
• Traditional models like distributed lag and distributed lag nonlinear models were less effective in capturing complex interactions and timing effects simultaneously.
• The inclusion of functional weights improved model fit and provided more biologically plausible estimates of exposure effects across gestation.
• The method demonstrated robustness in estimating exposure-outcome associations under complex, high-dimensional exposure scenarios typical of environmental mixture studies.
• The analysis revealed that the combined effect of four pollutants (PM2.5, NO2, O3, and SO2) was more strongly associated with birth weight reduction than individual pollutants alone.