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

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Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21205, USA
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Division of Epidemiology and Community Health, University of Minnesota, Minneapolis, MN 55455, USA
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Division of Research, Kaiser Permanente, Oakland, CA 94612, USA
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AJ Drexel Autism Institute, Drexel University, Philadelphia, PA 19104, USA
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College of Health and Human Development, Penn State University, State College, PA 16801, USA
*
Author to whom correspondence should be addressed.
Int. J. Environ. Res. Public Health 2021, 18(4), 1373; https://doi.org/10.3390/ijerph18041373
Received: 10 December 2020 / Revised: 25 January 2021 / Accepted: 27 January 2021 / Published: 3 February 2021
(This article belongs to the Section Environmental Health)
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. View Full-Text
Keywords: Bayesian methods; mixtures; PBDEs; neurodevelopment Bayesian methods; mixtures; PBDEs; neurodevelopment
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MDPI and ACS Style

Hamra, G.B.; Maclehose, R.F.; Croen, L.; Kauffman, E.M.; Newschaffer, C. Bayesian Weighted Sums: A Flexible Approach to Estimate Summed Mixture Effects. Int. J. Environ. Res. Public Health 2021, 18, 1373. https://doi.org/10.3390/ijerph18041373

AMA Style

Hamra GB, Maclehose RF, Croen L, Kauffman EM, Newschaffer C. Bayesian Weighted Sums: A Flexible Approach to Estimate Summed Mixture Effects. International Journal of Environmental Research and Public Health. 2021; 18(4):1373. https://doi.org/10.3390/ijerph18041373

Chicago/Turabian Style

Hamra, Ghassan B., Richard F. Maclehose, Lisa Croen, Elizabeth M. Kauffman, and Craig Newschaffer. 2021. "Bayesian Weighted Sums: A Flexible Approach to Estimate Summed Mixture Effects" International Journal of Environmental Research and Public Health 18, no. 4: 1373. https://doi.org/10.3390/ijerph18041373

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