Table 3.

Component-wise point and CI estimates of ME_j for the causal genera at day 28 on body weight gain for female mice

				95% $\widehat{\mathit{CI}}$a
Genus	Term1b	Term2c	${\widehat{\mathit{ME}}}_j$ d	Lower	Upper
Akkermansia	0.118	1.466	0.173	0.126	0.220
Lactobacillus	−0.301	−1.289	0.388	0.324	0.452
Eubacterium	0.117	1.462	0.171	0.147	0.199
Rikenellaceae_Other	0.065	−1.508	−0.098	−0.119	−0.077

^a95% $\widehat{\mathit{CI}}$ was calculated by bootstrapping procedure, and the number of bootstrapping is 100.

^bTerm1 represents $(\widehat{{\alpha }_{\mathit{Mj}}}+\widehat{{\alpha }_{\mathit{Cj}}})$.

^cTerm2 represents $\{\widehat{E}[\text{log}(M_j)|T=1]-\widehat{E}[\text{log}(M_j)|T=0]\}$.

^d ${\widehat{\mathit{ME}}}_j=(\widehat{{\alpha }_{\mathit{Mj}}}+\widehat{{\alpha }_{\mathit{Cj}}})\{\widehat{E}[\text{log}(M_j)|T=1]-\widehat{E}[\text{log}(M_j)|T=0]\}$ .