Estimation and false discovery control for the analysis of environmental mixtures

The analysis of environmental mixtures is of growing importance in environmental epidemiology, and one of the key goals in such analyses is to identify exposures and their interactions that are associated with adverse health outcomes. Typical approaches utilize flexible regression models combined with variable selection to identify important exposures and estimate a potentially nonlinear relationship with the outcome of interest. Despite this surge in interest, no approaches to date can identify exposures and interactions while controlling any form of error rates with respect to exposure selection. We propose two novel approaches to estimating the health effects of environmental mixtures that simultaneously (i) estimate and provide valid inference for the overall mixture effect and (ii) identify important exposures and interactions while controlling the false discovery rate (FDR). We show that this can lead to substantial power gains to detect weak effects of environmental exposures. We apply our approaches to a study of persistent organic pollutants and find that controlling the FDR leads to substantially different conclusions.