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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\(H_{01}\)

From: PhyloMed: a phylogeny-based test of mediation effect in microbiome

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

-