Bayesian Multiple Index Models for Environmental Mixtures

TL;DR

This paper introduces a Bayesian multiple index model that unifies response-surface and exposure-index methods, enabling flexible, interpretable analysis of environmental mixtures and health effects, demonstrated on NHANES data.

Contribution

It proposes a novel Bayesian framework that combines the strengths of existing models, allowing for non-linear, non-additive effects with variable selection and interpretability.

Findings

Model fits NHANES data as well as complex response-surface methods.

Provides interpretable estimates of mixture effects and weights.

Unifies two major modeling strategies for environmental health analysis.

Abstract

An important goal of environmental health research is to assess the risk posed by mixtures of environmental exposures. Two popular classes of models for mixtures analyses are response-surface methods and exposure-index methods. Response-surface methods estimate high-dimensional surfaces and are thus highly flexible but difficult to interpret. In contrast, exposure-index methods decompose coefficients from a linear model into an overall mixture effect and individual index weights; these models yield easily interpretable effect estimates and efficient inferences when model assumptions hold, but, like most parsimonious models, incur bias when these assumptions do not hold. In this paper we propose a Bayesian multiple index model framework that combines the strengths of each, allowing for non-linear and non-additive relationships between exposure indices and a health outcome, while reducing the dimensionality of the exposure vector and estimating index weights with variable selection. This framework contains response-surface and exposure-index models as special cases, thereby unifying the two analysis strategies. This unification increases the range of models possible for analyzing environmental mixtures and health, allowing one to select an appropriate analysis from a spectrum of models varying in flexibility and interpretability. In an analysis of the association between telomere length and 18 organic pollutants in the National Health and Nutrition Examination Survey (NHANES), the proposed approach fits the data as well as more complex response-surface methods and yields more interpretable results.