The article is motivated by an application to the EarlyBird cohort study aiming to explore how anthropometrics and clinical and metabolic processes are associated with obesity and glucose control during childhood. There is interest in inferring the relationship between dynamically changing and high-dimensional metabolites and a longitudinal response. Important aspects of the analysis include the selection of the important set of metabolites and the accommodation of missing data in both response and covariate values. With this motivation, we propose a flexible but parsimonious Bayesian semiparametric joint model for the outcome and the covariate generating processes, making novel use of nonparametric mean processes, latent factor models, and different classes of continuous shrinkage priors. The proposed approach efficiently addresses daunting dimensionality challenges, simplifies imputation tasks, and automates the selection of important predictors. Implementation via an efficient Markov chain Monte Carlo algorithm appropriately accounts for uncertainty in various aspects of the analysis. Simulation experiments illustrate the efficacy of the proposed methodology. The application to the EarlyBird cohort study illustrates its practical utility in enabling statistical integration of different molecular processes involved in glucose production and metabolism. From this study, we were able to show that glucose levels from 5 to 16 years of age are associated with different circulating levels of metabolites in the blood serum and can be fitted over time for a wide range of shapes of trajectories. The metabolites contributing the most to explaining glucose trajectories tend to be involved in different central energy metabolomic pathways. The methodology provides a tool to generate new hypotheses related to obesity and glucose control during childhood and adolescence.
