Nonparametric bayes shrinkage for assessing exposures to mixtures subject to limits of detection

Assessing potential associations between exposures to complex mixtures and health outcomes may be complicated by a lack of knowledge of causal components of the mixture, highly correlated mixture components, potential synergistic effects of mixture components, and difficulties in measurement. We extend recently proposed nonparametric Bayes shrinkage priors for model selection to investigations of complex mixtures by developing a formal hierarchical modeling framework to allow different degrees of shrinkage for main effects and interactions and to handle truncation of exposures at a limit of detection. The methods are used to shed light on data from a study of endometriosis and exposure to environmental polychlorinated biphenyl congeners.