Having your cake (mix) and eating it too: Independent, interaction, and group effects of mixtures using Bayesian Hierarchical Regression Modelling

Abstract

BACKGROUND AND AIM: Mixtures analysis methods are increasingly being applied in environmental epidemiology, but current methods are often limited by either only providing a group effect or independent exposure effects without a group effect. We investigate Bayesian Hierarchical Regression Modelling (BHRM) and show how it can be adapted to handle highly correlated exposures to estimate: 1) independent exposure effects; 2) interactions between exposures; and 3) combined effects for a mixture exposure. METHODS: BHRM is a flexible framework that can provide robust estimation for highly correlated exposures (via g-prior specification), yield conditional exposure-specific estimates, and include interactions effects. We demonstrate how these general regression models can provide additional inference on the combined effect for a multi-pollutant exposure. To demonstrate potential advantages of certain specifications, we applied BHRM to an analysis of liver injury and exposure to perfluoroalkyl substances (PFAS), including PFOS, PFOA, PFHxS, PFNA, and PFUnDA, in 1105 children from the Human Early Life Exposome (HELIX) project. Liver injury was defined as 90th percentile for any serum liver injury biomarker (ALT, AST, GGT). We used BHRM to estimate the mixture effect and pollutant-specific effects. For comparison, we also applied Bayesian Weighted Quantile Sum regression (BWQS)—an alternative specification within Bayesian Hierarchical Modeling. RESULTS:PFAS mixture was associated with childhood liver injury: OR=1.64 (95%CI:1.34-2.00) per increased exposure equivalent to one standard deviation for all PFAS. Within this mixture effect, PFNA was the predominant exposure driving the association with OR=1.62 (95%CI:1.11-1.97) and a posterior inclusion probability of 0.969 (Bayes factor, BF=125). No strong evidence of interactions. Although BWQS estimated a mixture effect of OR=1.85 (95%CI:1.50-2.25) and indicated PFNA had the most substantial estimated weight of 0.513 (BF=4.21), the approach lacks pollutant-specific effects. CONCLUSIONS:BHRM is an efficient method for mixtures analysis. Estimation of pollutant-specific effects with group effects provide critical data for identifying causal agents in mixtures of environmental contaminants. KEYWORDS: mixtures, methods, Bayesian Hierarchical Regression Modelling, multi-pollutant