Permutational multivariate analysis of variance using distance matrices
To determine whether circulating serum inflammatory markers, untargeted serum metabolomics profiles, or ASV profiles were significantly different between the probiotic vs. placebo treatment arms or probiotic responders vs. probiotic non-responders and placebo treatment arms, analysis of variance using distance matrices was used. Input for both serum derived data types (inflammatory markers and metabolomics) was the difference from baseline (week −3) to end of intervention (week 10) into a Euclidean distance matrix. Input for the ASV profiles was the relative abundance of ASVs found in >25% of samples at the end of intervention (week 10) into a Bray–Curtis distance matrix. The adonis function (vegan package, R, permutations = 99) was used to test if there was a significant difference between probiotic vs. placebo treatment arms or probiotic responders vs. non-responders and placebo participants.