Fig. 2: Performance of the multivariate methods for global associations or data summarization.

A QQ-Plot of the Mantel test and the Procrustes Analysis across microbiome normalizations and distance kernels. For the Mantel test, we considered Spearman’s method for computing the global association between the two datasets. P values for both the Mantel test and Procrustes Analysis were obtained empirically based on 1000 replicates. B Power of the Mantel test and the Procrustes Analysis across microbiome normalizations and distance kernels. For the Mantel test, we considered Spearman’s method for computing the global association between the two datasets. P values for both the Mantel test and Procrustes Analysis were obtained empirically based on 1000 replicates. P values ≤ 0.05 were considered significant. C QQ-Plot of MMiRKAT, the Mantel test, and the Procrustes Analysis across microbiome normalizations and distance kernels. Points below the straight line refer to conservative behavior in the result section. To accommodate MMiRKAT (fewer number of features than sample size), we considered scenarios with a smaller number of features in both omics layers than the number of individuals (See supplementary methods). D Power of MMiRKAT, the Mantel test, and the Procrustes Analysis across microbiome normalizations and distance kernels. To accommodate MMiRKAT (fewer number of features than sample size), we considered scenarios with a smaller number of features in both omics layers than the number of individuals (See supplementary methods). P values for both the Mantel test and Procrustes Analysis were obtained empirically based on 1000 replicates. P values ≤ 0.05 were considered significant. E Proportion of explained variance for the data summarization methods across different data structures and normalizations considering the log metabolome. Data summarization methods were compared considering scenarios with a number of features half the number of individuals (See supplementary methods).