Bayesian Weighted Sums: A Flexible Approach to Estimate Summed Mixture Effects.

Ghassan B Hamra,Craig Newschaffer,Lisa Croen,Richard F Maclehose,Elizabeth M Kauffman

doi:10.3390/ijerph18041373

Abstract

Objectives: Methods exist to study exposure mixtures, but each is distinct in the research question it aims to address. We propose a new approach focused on estimating both the summed effect and individual weights of one or multiple exposure mixtures: Bayesian Weighted Sums (BWS). Methods: We applied BWS to simulated and real datasets with correlated exposures. The analytic context in our real-world example is an estimation of the association between polybrominated diphenyl ether (PBDE) congeners (28, 47, 99, 100, and 153) and Autism Spectrum Disorder (ASD) diagnosis and Social Responsiveness Scores (SRS). Results: Simulations demonstrate that BWS performs reliably. In adjusted models using Early Autism Risk Longitudinal Investigation (EARLI) data, the odds of ASD for a 1-unit increase in the weighted sum of PBDEs were 1.41 (95% highest posterior density 0.82, 2.50) times the odds of ASD for the unexposed and the change in z-score standardized SRS per 1 unit increase in the weighted sum of PBDEs is 0.15 (95% highest posterior density −0.08, 0.38). Conclusions: BWS provides a means of estimating the summed effect and weights for individual components of a mixture. This approach is distinct from other exposure mixture tools. BWS may be more flexible than existing approaches and can be specified to allow multiple exposure groups based on a priori knowledge from epidemiology or toxicology.

Highlights

Published: 3 February 2021Environmental health research is increasingly oriented towards consideration of the health effects of multiple exposures, often referred to as complex mixtures [1,2]
We propose a flexible Bayesian approach for studying complex exposure mixtures, which we will refer to as Bayesian Weighted Sums (BWS)
These quantities are distinct from those provided by Bayesian Kernel Machine Regression (BKMR) and Weighted Quantile Sums (WQS), but are of substantial interest in exposure mixtures research. We implement this approach with a widely available Gibbs sampling software package. We demonstrate this approach with simulated data and apply it to a study of the effect of summed polybrominated diphenyl ethers (PBDEs) on neurodevelopment in the Early

Summary

Introduction

Environmental health research is increasingly oriented towards consideration of the health effects of multiple exposures, often referred to as complex mixtures [1,2]. This is natural, as humans are typically exposed to multiple chemicals simultaneously and those chemicals may act on similar biological pathways or may have similar effects on health. Approaches that estimate the combined effect of a complex mixture and provide an understanding of the relative importance of each exposure to an outcome of interest are desirable.

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