Clinical metabolomics aims at finding statistically significant differences in metabolic statuses of patient and control groups with the intention of understanding pathobiochemical processes and identification of clinically useful biomarkers of particular diseases. After the raw measurements are integrated and pre-processed as intensities of chromatographic peaks, the differences between controls and patients are evaluated by both univariate and multivariate statistical methods. The traditional univariate approach relies on t-tests (or their nonparametric alternatives) and the results from multiple testing are misleadingly compared merely by p-values using the so-called volcano plot. This paper proposes a Bayesian counterpart to the widespread univariate analysis, taking into account the compositional character of a metabolome. Since each metabolome is a collection of some small-molecule metabolites in a biological material, the relative structure of metabolomic data, which is inherently contained in ratios between metabolites, is of the main interest. Therefore, a proper choice of logratio coordinates is an essential step for any statistical analysis of such data. In addition, a concept of b-values is introduced together with a Bayesian version of the volcano plot incorporating distance levels of the posterior highest density intervals from zero. The theoretical background of the contribution is illustrated using two data sets containing samples of patients suffering from 3-hydroxy-3-methylglutaryl-CoA lyase deficiency and medium-chain acyl-CoA dehydrogenase deficiency. To evaluate the stability of the proposed method as well as the benefits of the compositional approach, two simulations designed to mimic a loss of samples and a systematical measurement error, respectively, are added.

Department of Clinical Biochemistry University Hospital Olomouc 1 P Pavlova 185 6 779 00 Olomouc Czech Republic; Laboratory of Metabolomics Institute of Molecular and Translational Medicine Faculty of Medicine and Dentistry Palacký University Hněvotínská 5 779 00 Olomouc Czech Republic

Department of Mathematical Analysis and Applications of Mathematics Palacký University 17 Listopadu 1192 12 771 46 Olomouc Czech Republic

Department of Mathematical Analysis and Applications of Mathematics Palacký University 17 Listopadu 1192 12 771 46 Olomouc Czech Republic; Department of Clinical Biochemistry University Hospital Olomouc 1 P Pavlova 185 6 779 00 Olomouc Czech Republic; Laboratory of Metabolomics Institute of Molecular and Translational Medicine Faculty of Medicine and Dentistry Palacký University Hněvotínská 5 779 00 Olomouc Czech Republic

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