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

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.