Skip to main content

Table 2 Variable screening and selection for models considered in simulation studies for a binary confounder \(L_i \in \{0,1\}\)

From: Feature selection and causal analysis for microbiome studies in the presence of confounding using standardization

Model

Variables screened

Maximum model size

Conditional Std

\(\{\beta _1^l, \dots , \beta _p^l\}\) (independently \(\forall l\))

\(d_l = \lfloor n_l / \log (n_l)\rfloor\) \(\forall l\)

Select L

\(\{\beta _1, \dots , \beta _p, L\}\)

\(d = \lfloor n / \log (n) \rfloor\)

Select L EffMod

\(\{\beta _1^{l=0}, \dots , \beta _p^{l=0}, \beta _1^{l=1}, \dots , \beta _p^{l=1}, L\}\)

\(d = \lfloor n / \log (n) \rfloor\)

Require L

\(\{\beta _1, \dots , \beta _p \}\) (given L)

\(d = \lfloor n / \log (n) \rfloor\)

Require L EffMod

\(\{\beta _1^{l=0}, \dots , \beta _p^{l=0}, \beta _1^{l=1}, \dots , \beta _p^{l=1}\}\) (given L)

\(d = \lfloor n / \log (n) \rfloor\)

Ignore L

\(\{\beta _1, \dots , \beta _p\}\)

\(d = \lfloor n / \log (n) \rfloor\)

Ignore L EffMod

\(\{\beta _1^{l=0}, \dots , \beta _p^{l=0}, \beta _1^{l=1}, \dots , \beta _p^{l=1}\}\)

\(d = \lfloor n / \log (n) \rfloor\)