A nutritionally informed model for Bayesian variable selection with metabolite response variables

Abstract: Understanding the pathways through which diet affects human metabolism is a central task in nutritional epidemiology. This article proposes novel methodology to identify food items associated with blood metabolites in two cohorts of healthcare professionals. We analyze 30 food intake variables that exhibit relationship structure through their correlations and nutritional attributes. The metabolic responses include 244 compounds measured by mass spectrometry, presenting substantial challenges that include missingness, left-censoring, and skewness. While existing methods can address such factors in low-dimensional settings, they are not designed for high-dimensional regression involving strongly correlated predictors and non-normal outcomes. To address these challenges, we propose a novel Bayesian variable selection framework for metabolite response variables based on a skew-normal censored mixture model. To exploit substantive information on the nutritional similarities among dietary factors, we employ a Markov random field prior that encourages joint selection of related predictors, while introducing a new, efficient strategy for its hyperparameter specification. Applying this methodology to the cohort data identifies multiple metabolite-diet associations that are consistent with previous research as well as several potentially novel associations that were not detected using standard methods. The proposed approach is implemented in the R package multimetab, facilitating its use in high-dimensional metabolomic analyses.