Incorporating biological knowledge in analyses of environmental mixtures and health.

A key goal of environmental health research is to assess the risk posed by mixtures of pollutants. As epidemiologic studies of mixtures can be expensive to conduct, it behooves researchers to incorporate prior knowledge about mixtures into their analyses. This work extends the Bayesian multiple index model (BMIM), which assumes the exposure-response function is a nonparametric function of a set of linear combinations of pollutants formed with a set of exposure-specific weights. The framework is attractive because it combines the flexibility of response-surface methods with the interpretability of linear index models. We propose three strategies to incorporate prior toxicological knowledge into construction of indices in a BMIM: (a) imposing directional homogeneity constraints on the weights, (b) structuring index weights by exposure transformations, and (c) placing informative priors on the index weights. We propose a novel prior specification that combines spike-and-slab variable selection with an informative Dirichlet distribution based on relative potency factors often derived from previous toxicological studies. In simulations we show that the proposed priors improve inferences when prior information is correct and can protect against misspecification suffered by naïve toxicological models when prior information is incorrect. Moreover, different strategies may be mixed-and-matched for different indices to suit available information (or lack thereof). We demonstrate the proposed methods on an analysis of data from the National Health and Nutrition Examination Survey and incorporate prior information on relative chemical potencies obtained from toxic equivalency factors available in the literature.