Lagged Kernel Machine Regression For Identifying Time Windows Of Susceptibility To Exposures Of Complex Metal Mixtures

Abstract

Background: Exposures to metal mixtures during early life may impact cognitive function, and there may exist time windows during which vulnerability is increased. However, there is a lack of statistical methods to assess how the impact of toxicant mixture exposures depends on the timing of exposure. Aims: To develop a flexible statistical method to identify time windows of susceptibility in the context of time-varying toxicant mixture exposures, and account for complex non-linear and non-additive time-varying mixture effects. Methods: We introduce Lagged Kernel Machine Regression (LKMR), a Bayesian hierarchical model that estimates how the effects of mixture exposures change with the exposure window, using a novel grouped, fused Lasso for Bayesian shrinkage. LKMR can assess joint exposure-response surfaces through contour plots to provide information about interactions and effect modification. Simulation studies demonstrate the performance of LKMR under realistic exposure-response scenarios. LKMR was applied to tooth-metal biomarkers in PROGRESS, a prospective cohort study on metal mixture exposures and neurodevelopment. Results: Our simulation study considered a three-toxicant scenario: a gradual non-additive and non-linear effect of two toxicants over four time windows representative of early life. A regression comparing the true exposure-response terms and the LKMR estimates yielded R2 values of 0.91 – 0.98. Root mean squared error (RMSE) was reduced by 38 - 81% compared to that from kernel machine regression applied using exposure from each time window separately. LKMR provides greater reduction in RMSE with larger auto-correlation in metal exposures over time. Results from PROGRESS provide evidence of a negative association between IQ and postnatal manganese exposure that is larger in the presence of lead exposure. Conclusions: LKMR is a promising statistical approach for flexibly identifying sensitive time windows of exposure to multi-toxicant mixtures.