BLOG: Bayesian longitudinal omics with group constraints

Clinical investigators are increasingly interested in discovering computational biomarkers from short-term longitudinal omics datasets. This work focuses on Bayesian regression and variable selection for longitudinal omics datasets, which can estimate posterior evidence for each candidate biomarker and control false discovery using evidence thresholds. In our univariate approach, Zellner's g-prior is used with two different options of the tuning parameter g: $g=\sqrt{n}$ and a g that minimizes Stein's unbiased risk estimate (SURE). Bayes factors are used to rank metabolites by evidence, and their mapping to posterior model probabilities under prior odds can provide local posterior null probabilities whose average over the rejection set defines a Bayesian analogue of the global FDR. In the multivariate approach, we use Bayesian group lasso with a spike and slab prior for group variable selection. In both approaches, we use the first difference (Δ) scale of longitudinal predictor and the response. These methods work together to enhance our understanding of biomarker identification, improving inference and prediction. We compare our method against commonly used linear mixed effect models on simulated data and real data from a Tuberculosis (TB) study on metabolite biomarker selection. With an automated selection of hyperparameters, the Zellner's g-prior approach correctly identifies target metabolites with high specificity and sensitivity across various simulation and real data scenarios. The multivariate Bayesian group lasso spike and slab approach also correctly selects target metabolites across various simulation scenarios.