Bayesian multiple index models for environmental mixtures

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 analysing 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.

Powering Research through Innovative Methods for Mixtures in Epidemiology (PRIME) Program: Novel and Expanded Statistical Methods

“…The factor analysis work of Ferrari et al noted above addresses this issue by using factor analysis to reduce the dimension of the exposure space [12]. McGee et al proposed another approach, BMIM, to address this weakness [5]. BMIM combines the strengths of existing exposure-index methods, such as weighted quantile sum (WQS) regression and qGc, by reducing the dimensionality of the exposure vector and estimating index weights with variable selection and treating these indices as inputs into the kernel regression framework.…”

“…Relative potency factors-e.g., the Toxic Equivalency Factors (TEFs) of dioxin-like compounds-are one of the more familiar models of non-interaction/"additivity" in toxicology. One promising line of research connecting mixtures toxicology and epidemiology is the use of animal or in vitro data as priors for epidemiological studies using Bayesian methods such as BMIM [5].…”

Principal Component Pursuit for Pattern Identification in Environmental Mixtures

“…POP concentrations from this NHANES cycle are well characterized and have been used in prior environmental mixture analyses. 27 , 28 NHANES inclusion criteria have been reported previously. 29 For the chosen cycle, 11,039 participants were interviewed.…”

Machine learning assisted discovery of synergistic interactions between environmental pesticides, phthalates, phenols, and trace elements in child neurodevelopment

“…The concept of "interaction" has been construed in many ways through different scientific fields 21 . For example, in current epidemiological studies, interactions are usually reported through association estimates of their effect sizes or inclusion probabilities [22][23][24][25][26][27][28][29][30][31][32][33] . Though estimating associations is essential, most methods do not provide any mechanistic or biological insight, possibly because the reported interactions are of particular functional forms (for example, multiplication of exposures) rather than representing their collective activities beyond certain concentration thresholds 34 .…”