Schematic explanation of the miMic approach. miMic is a three-step method: (1) Data processing (in light green). Microbiome data preprocessing involves using the MIPMLP method (see the “ Methods ” section) and converting it into a cladogram of means using the iMic algorithm (see Methods ). (2) A priori nested ANOVA (in light blue). An a priori nested ANOVA (nested GLM for continuous labels) is applied to microbiome cladograms and labels to assess the global relationship between labels and the entire microbiome. If no significant relationship is found at any taxonomy level, the label is defined “not microbially explainable,” and no further analysis is performed. (3) Post hoc Mann-Whitney test. A post hoc Mann-Whitney test, leveraging phylogenetic information, is conducted for the difference analysis (1). Starting at the first taxonomy level, a Mann-Whitney (or Spearman correlation) test is applied to each taxon’s values, with a predetermined significance level (currently (p < 0.05) ). Multiple measurement correction is applied only for the number of taxa at this level. If significant taxa are identified, the analysis iteratively proceeds along the cladogram towards the leaf nodes. To address inner sister relations, FDR control is used when multiple significant sisters are present. An additional Mann-Whitney test (utilizing Spearman correlation for continuous labels) is specifically conducted over the leaves, incorporating FDR correction for multiple measurements (2). miMic consolidates the significant taxa identified in steps 1 and 2. The schematic cladogram in the bottom right corner illustrates the inner taxa of the cladogram utilized in step 1 of the post hoc test (gray), while its white leaves are employed in both steps. “+/−” denotes samples with/without the phenotype, respectively. A white circle marked “p” represents a p -value. An orange circle labeled “Sis” signifies FDR correction applied over the sisters, as explained in the manuscript. A green square or circle labeled “s” indicates a significant taxon, while a red square or circle marked “n.s” indicates an insignificant taxon
