Model-averaged confounder adjustment for estimating multivariate exposure effects with linear regression

In environmental and nutritional epidemiology and in many other fields, there is increasing interest in estimating the effect of simultaneous exposure to several agents (e.g., multiple nutrients, pesticides, or air pollutants) on a health outcome. We consider estimating the effect of a multivariate exposure that includes several continuous agents and their interactionson an outcome, when the true confounding variables are an unknown subset of a potentially large (relative to sample size) set of measured covariates. Our approach is rooted in the ideas of Bayesian model averaging: the exposure effect is estimated as a weighted average of the estimated exposure effects obtained under several linear regression models that include different sets of the potential confounders. We introduce a data-driven prior that assigns to the likely confounders a higher probability of being included into the regression model. We show that our approach can also be formulated as a penalized likelihood formulation with an interpretable tuning parameter. Through a simulation study, we demonstrate that the proposed approach identifies parsimonious models that are fully adjusted for observed confounding and estimates the multivariate exposure effect with smaller mean squared error compared to several alternatives. We apply the method to an Environmental Wide Association Study using National Heath and Nutrition Examination Survey to estimate the effect of mixtures of nutrients and pesticides on lipid levels.