Figure 3.

Estimated statistical powers for the item-by-item cSKAT tests and aGLMM-MiRKAT based on the random intercept model with Gaussian responses (n = 50) (Unit: %). L: low within-cluster correlation (${\rho }_{j{\ne j}^{\prime }}$ = $\frac{1}{3}$); M: medium within-cluster correlation (${\rho }_{j{\ne j}^{\prime }}$ = $\frac{1}{2}$); H: high within-cluster correlation (${\rho }_{j{\ne j}^{\prime }}=$ $\frac{3}{5}$).K_J:cSKAT for Jaccard dissimilarity; K_BC:cSKAT for Bray-Curtis dissimilarity; K_U:cSKAT for Unweighted UniFrac distance; K_0.5: cSKAT for Generalized UniFrac distance (θ = 0.5); K_W: cSKAT for Weighted UniFrac distance; adaptive: adaptive GLMM-MiRKAT (aGLMM-MiRKAT). P1, P2, P3, and P4 represent the four different association scenarios: P1. $\mathcal{A}$ = {50 random OTUs in lower half of abundance}; P2. $\mathcal{A}$ = {50 random OTUs}; P3. $\mathcal{A}$ = {50 random OTUs in upper half of abundance}; P4. $\mathcal{A}$ = {A random cluster among 10 clusters partitioned by PAM}. (A) n = 20 (L); (B) n = 20 (M); (C) n = 20 (H); (D) n = 50 (L); (E) n = 50 (M); (F) n = 50 (H).