Fig. 2
Type I error and power comparison for scenario 1 with a binary outcome. A selected phylogenetic cluster (6.7 %) of the OTUs was associated with the outcome. a X and Z are independent and b X and Z are correlated. K u, K w, and K 5 represent MiRKAT results from the unweighted UniFrac kernel, weighted UniFrac kernel, and generalized UniFrac kernel with α=0.5, respectively. K opt represents the simulation results for optimal MiRKAT considering the Bray–Curtis kernel, unweighted UniFrac kernel, weighted UniFrac kernel, and generalized UniFrac kernel. MiSPUw(2), MiSPUw(∞), and aMiSPUw represent the MiSPUw test with γ=2,∞ and aMiSPUw summarizing γ=2,3,…,8,∞, respectively. aMiSPUu and aMiSPU represent the test summarizing γ=2,3,…,8,∞ with unweighted generalized taxon proportion and combining aMiSPUu and aMiSPUw, respectively. KW represents Kruskal-Wallis test. Results were presented at n=100. KW Kruskal–Wallis test