Fig. 4

Analysis of mouse cecal microbiome data. a Phylogenetic tree with the size of the circle at each internal node proportional to \(-\log 10\) (PhyloMed local mediation test p-value). The identified internal node with the minimum subcomposition mediation test p-value and the subtree under the node are highlighted in a blue rectangle. b Quantile-quantile plots of different subcomposition mediation test p-values across internal nodes. PhyloMed: proposed mixture-distribution-based test; JS: joint significance test; Sobel: Sobel’s test. c Associations of the subcomposition (in log-ratio) at the highlighted node in a with the treatment and the body fat percentage after adjusting for the treatment effect. d The highlighted subtree in a. Pair the OTU under the left child node to each of the five OTUs under the right child node. For the subcomposition of each pair, examine the treatment-subcomposition and subcomposition-outcome associations and report the maximum p-value of the two associations