Bayesian Statistics Improves Biological Interpretability of Metabolomics Data from Human Cohorts

Univariate analyses of metabolomics data currently follow a frequentist approach, using p-values to reject a null hypothesis. We here propose the use of Bayesian statistics to quantify evidence supporting different hypotheses and discriminate between the null hypothesis versus the lack of statistical power. We used metabolomics data from three independent human cohorts that studied the plasma signatures of subjects with myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS). The data are publicly available, covering 84-197 subjects in each study with 562-888 identified metabolites of which 777 were common between the two studies and 93 were compounds reported in all three studies. We show how Bayesian statistics incorporates results from one study as "prior information" into the next study, thereby improving the overall assessment of the likelihood of finding specific differences between plasma metabolite levels. Using classic statistics and Benjamini-Hochberg FDR-corrections, Study 1 detected 18 metabolic differences and Study 2 detected no differences. Using Bayesian statistics on the same data, we found a high likelihood that 97 compounds were altered in concentration in Study 2, after using the results of Study 1 as the prior distributions. These findings included lower levels of peroxisome-produced ether-lipids, higher levels of long-chain unsaturated triacylglycerides, and the presence of exposome compounds that are explained by the difference in diet and medication between healthy subjects and ME/CFS patients. Although Study 3 reported only 92 compounds in common with the other two studies, these major differences were confirmed. We also found that prostaglandin F2alpha, a lipid mediator of physiological relevance, was reduced in ME/CFS patients across all three studies. The use of Bayesian statistics led to biological conclusions from metabolomic data that were not found through frequentist approaches. We propose that Bayesian statistics is highly useful for studies with similar research designs if similar metabolomic assays are used.