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Table 4 Table of example for the transformation of Beta-Values to M-values and the differences, respectively. The Beta-value difference between the Placebo group and the Treatments group is constant at 10%. Due to the transformation, the M-values differ and the differences in M-values can not be mapped to the differences in Beta-values

From: Estimands in epigenome-wide association studies

Grp\(_{Placebo}\)

Grp\(_{Treatment}\)

\(\Delta _{Beta}\)

\(\Delta _{M}\)

Regression formula

Beta-value

M-value

Beta-value

M-value

  

on M-values

0.001

\(-\)9.96

0.101

\(-\)3.15

0.10

6.81

\(-\)9.96 + 6.81 \(\cdot\) Grp\(_{Treatment}\)

0.101

\(-\)3.15

0.201

\(-\)1.99

0.10

1.16

\(-\)3.15 + 1.16 \(\cdot\) Grp\(_{Treatment}\)

0.201

\(-\)1.99

0.301

\(-\)1.22

0.10

0.77

\(-\)1.99 + 0.77 \(\cdot\) Grp\(_{Treatment}\)

0.301

\(-\)1.22

0.401

\(-\)0.58

0.10

0.64

\(-\)1.22 + 0.64 \(\cdot\) Grp\(_{Treatment}\)

0.401

\(-\)0.58

0.501

0.01

0.10

0.59

\(-\)0.58 + 0.59 \(\cdot\) Grp\(_{Treatment}\)

0.501

0.01

0.601

0.59

0.10

0.58

0.01 + 0.58 \(\cdot\) Grp\(_{Treatment}\)

0.601

0.59

0.701

1.23

0.10

0.64

0.59 + 0.64 \(\cdot\) Grp\(_{Treatment}\)

0.701

1.23

0.801

2.01

0.10

0.78

1.23 + 0.78 \(\cdot\) Grp\(_{Treatment}\)

0.801

2.01

0.901

3.19

0.10

1.18

2.01 + 1.18 \(\cdot\) Grp\(_{Treatment}\)

0.901

3.19

0.999

9.96

0.10

6.77

3.19 + 6.77 \(\cdot\) Grp\(_{Treatment}\)