Bayesian distributed lag interaction models using spike and slab priors

Abstract

BACKGROUND AND AIM: Distributed lag models are useful in environmental epidemiology as they allow us to investigate the time periods at which exposure to a pollutant adversely affects health outcomes. Recent studies have focused on estimating the health effects of a large number of environmental exposures on health outcomes. It is important to understand which of these environmental exposures affect a particular outcome, while simultaneously understanding the time periods that are most associated with changes in an outcome. METHODS: We propose a Bayesian model to estimate the temporal effects of a large number of exposures on an outcome. We utilize spike and slab priors to identify which exposures affect the outcome, and semiparametric functions to estimate the distributed lag curves for exposures that affect the outcome. Further, we allow for interactions between all of the exposures, again using spike and slab priors to identify important interactions. RESULTS:We find that the proposed methodology is able to flexibly estimate distributed lag surfaces while simultaneously selecting which exposures are associated with an outcome. A modification to the prior distribution is able to increase the power to detect important exposures while ensuring that false discovery rates are not overly inflated. CONCLUSIONS:We apply our proposed methodology to a study of the effects of a mixture of air pollutants on birth weight and find that a subset of the exposures, which includes temperature and PM2.5, have a negative association with birth weight. KEYWORDS: Distributed lag models, Bayesian inference, exposure selection, air pollution