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Humans are routinely exposed to mixtures of chemical and other environmentalfactors, making the quantification of health effects associated withenvironmental mixtures a critical goal for establishing environmental policysufficiently protective of human health. The quantification of the effects ofexposure to an environmental mixture poses several statistical challenges. Itis often the case that exposure to multiple pollutants interact with each otherto affect an outcome. Further, the exposure-response relationship between anoutcome and some exposures, such as some metals, can exhibit complex, nonlinearforms, since some exposures can be beneficial and detrimental at differentranges of exposure. To estimate the health effects of complex mixtures wepropose a flexible Bayesian approach that allows exposures to interact witheach other and have nonlinear relationships with the outcome. We inducesparsity using multivariate spike and slab priors to determine which exposuresare associated with the outcome, and which exposures interact with each other.The proposed approach is interpretable, as we can use the posteriorprobabilities of inclusion into the model to identify pollutants that interactwith each other. We illustrate our approach's ability to estimate complexfunctions using simulated data, and apply our method to two studies todetermine which environmental pollutants adversely affect health.

Estimating the health effects of environmental mixtures using Bayesian semiparametric regression and sparsity inducing priors