  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 1) Estimate and provide valid
inference for the overall mixture effect, and 2) identify important exposures
and interactions while controlling the false discovery rate. 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 our approach is able to identify more interactions than existing
approaches.
