Table 1.

Empirical type I error of different global mediation tests (significance level = 0.05). The$|{\mathcal{S}}_{\alpha }|$and$|{\mathcal{S}}_{\beta }|$denote the number of treatment-associated OTUs and outcome-associated OTUs, respectively. Different combinations of ($|{\mathcal{S}}_{\alpha }|$,$|{\mathcal{S}}_{\beta }|$) represent different mixtures of mediation nulls$H_{00}$,$H_{10}$and$H_{01}$

n	$|{\mathcal{S}}_{\alpha }|$	$|{\mathcal{S}}_{\beta }|$	PhyloMed.A	PhyloMed.P	MedTest	MODIMA	LDM-med	CMM
Continuous outcome
50	0	0	0.020	0.028	0.002	0.002	0.005	-
50	3	0	0.021	0.028	0.013	0.007	0.006	-
50	6	0	0.036	0.042	0.025	0.009	0.009	-
50	0	3	0.021	0.025	0.003	0.002	0.009	-
50	0	6	0.024	0.028	0.011	0.003	0.016	-
200	0	0	0.022	0.024	0.001	0.000	0.002	0.308
200	3	0	0.030	0.032	0.022	0.008	0.013	0.495
200	6	0	0.035	0.036	0.032	0.023	0.015	0.532
200	0	3	0.032	0.034	0.015	0.006	0.017	0.210
200	0	6	0.040	0.043	0.028	0.015	0.021	0.154
Binary outcome
50	0	0	0.017	0.020	0.000	0.000	0.004	-
50	3	0	0.028	0.033	0.011	0.002	0.010	-
50	6	0	0.029	0.037	0.023	0.011	0.012	-
50	0	3	0.021	0.031	0.002	0.000	0.006	-
50	0	6	0.018	0.029	0.004	0.002	0.007	-
200	0	0	0.018	0.021	0.002	0.000	0.003	-
200	3	0	0.043	0.044	0.025	0.011	0.009	-
200	6	0	0.040	0.040	0.030	0.016	0.018	-
200	0	3	0.024	0.028	0.008	0.002	0.005	-
200	0	6	0.038	0.045	0.018	0.007	0.011	-