Figure 1.

Estimated statistical powers for GLMM-MiRKAT/aGLMM-MiRKAT based on the random intercept model with Gaussian, Binomial or Poisson 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: Jaccard dissimilarity; K_BC: Bray-Curtis dissimilarity; K_U: Unweighted UniFrac distance; K_0.5: Generalized UniFrac distance (θ = 0.5); K_W: 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) Gaussian (L); (B) Gaussian (M); (C) Gaussian (H); (D) Binomial (L); (E) Binomial (M); (F) Binomial (H); (G). Poisson (L); (H) Poisson (M); (I). Poisson (H).