How to model temporal changes in nontargeted metabolomics study? A Bayesian multilevel perspective.

Analysis of time series data addresses the question on mechanisms underlying normal physiology and its alteration under pathological conditions. However, adding time variable to high-dimension, collinear, noisy data is a challenge in terms of mining and analysis. Here, we used Bayesian multilevel modeling for time series metabolomics in vivo study to model different levels of random effects occurring as a consequence of hierarchical data structure. A multilevel linear model assuming different treatment effects with double exponential prior, considering major sources of variability and robustness to outliers was proposed and tested in terms of performance. The treatment effect for each metabolite was close to zero suggesting small if any effect of cancer on metabolomics profile change. The average difference in 964 signals for all metabolites varied by a factor ranging from 0.8 to 1.25. The inter-rat variability (expressed as a coefficient of variation) ranged from 3-30% across all metabolites with median around 10%, whereas the inter-occasion variability ranged from 0-30% with a median around 5%. Approximately 36% of metabolites contained outlying data points. The complex correlation structure between metabolite signals was revealed. We conclude that kinetics of metabolites can be modeled using tools accepted in pharmacokinetics type of studies.