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However, there is a lack of statistical methods that can accommodate the complex exposure\u2010response relationship between mixtures and neurodevelopment while simultaneously estimating neurodevelopmental trajectories. We introduce Bayesian varying coefficient kernel machine regression (BVCKMR), a hierarchical model that estimates how mixture exposures at a given time point are associated with health outcome trajectories. The BVCKMR flexibly captures the exposure\u2010response relationship, incorporates prior knowledge, and accounts for potentially nonlinear and nonadditive effects of individual exposures. This model assesses the directionality and relative importance of a mixture component on health outcome trajectories and predicts health effects for unobserved exposure profiles. Using contour plots and cross\u2010sectional plots, BVCKMR also provides information about interactions between complex mixture components. The BVCKMR is applied to a subset of data from PROGRESS, a prospective birth cohort study in Mexico city on exposure to metal mixtures and temporal changes in neurodevelopment. The mixture include metals such as manganese, arsenic, cobalt, chromium, cesium, copper, lead, cadmium, and antimony. Results from a subset of Programming Research in Obesity, Growth, Environment and Social Stressors data provide evidence of significant positive associations between second trimester exposure to copper and Bayley Scales of Infant and Toddler Development cognition score at 24 months, and cognitive trajectories across 6\u201024 months. We also detect an interaction effect between second trimester copper and lead exposures for cognition at 24 months. 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