An important goal of environmental epidemiology is to quantify the complex health effects posed by a wide array of environmental exposures. In studies of a small number of exposures, flexible models like Bayesian kernel machine regression (BKMR) are appealing because they allow for non-linear and non-additive associations among exposures. However, this flexibility comes at the cost of low power and difficult interpretation, particularly in exposomic analyses when the number of exposures is large. We propose a flexible framework that allows for the separate selection of additive and non-additive effects, unifying additive models and kernel machine regression. The proposed approach yields increased power and simpler interpretation when there is little evidence of interaction. Further, it allows users to specify separate priors for additive and non-additive effect s, and allows for statistical inference on non-additive interactions. We extend the approach to a class of multiple index models, in which the special case of kernel machine-distributed lag models is nested. We apply the method to motivating data from a subcohort of the Human Early Life Exposome (HELIX) study containing 65 mixture components grouped into 13 distinct exposure classes.
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