Modeling the health effects of time-varying complex environmental mixtures: Mean field variational Bayes for lagged kernel machine regression.

There is substantial interest in assessing how exposure to environmental mixtures, such as chemical mixtures, affect child health. Researchers are also interested in identifying critical time windows of susceptibility to these complex mixtures. A recently developed method, called lagged kernel machine regression (LKMR), simultaneously accounts for these research questions by estimating effects of time-varying mixture exposures, and identifying their critical exposure windows. However, LKMR inference using Markov chain Monte Carlo methods (MCMC-LKMR) is computationally burdensome and time intensive for large datasets, limiting its applicability. Therefore, we develop a mean field variational Bayesian inference procedure for lagged kernel machine regression (MFVB-LKMR). The procedure achieves computational efficiency and reasonable accuracy as compared with the corresponding MCMC estimation method. Updating parameters using MFVB may only take minutes, while the equivalent MCMC method may take many hours or several days. We apply MFVB-LKMR to PROGRESS, a prospective cohort study in Mexico. Results from a subset of PROGRESS using MFVB-LKMR provide evidence of significant positive association between second trimester cobalt levels and z-scored birthweight. This positive association is heightened by cesium exposure. MFVB-LKMR is a promising approach for computationally efficient analysis of environmental health datasets, to identify critical windows of exposure to complex mixtures.