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Table 8 Confounding scenarios for indirect ICS effect on BW simulated with nonlinear GA effect on BW

From: On the use of the outcome variable “small for gestational age” when gestational age is a potential mediator: a maternal asthma perspective

Scenario
(model, interpretation of effect)
mean se null ICS effect?
Confounding 1 (M1, total) −560.30 0.2198 no
Confounding 1 (M1,V, total) −400.33 0.2377 no
Confounding 1 (M2, direct) 16.904 0.1866 no
Confounding 1 (M2,V, direct) 15.329 0.1869 no
Confounding 1 (\( {M}_2^{\ast } \), direct) −0.1993 0.1916 yes
Confounding 1 (\( {M}_{2,V}^{\ast } \), direct) −0.1992 0.1917 yes
Confounding 1 (M3, total) 1.9051 0.0017 no
Confounding 1 (M3,V, total) 1.4397 0.0017 no
Confounding 1 (M4, direct) −0.0011 0.0015 yes
Confounding 1 (M4,V, direct) −0.0001 0.0016 yes
Confounding 2 (M1, total) −400.02 0.2474 no
Confounding 2 (M1,V, total) −400.15 0.2139 no
Confounding 2 (M2, direct) 39.335 0.1709 no
Confounding 2 (M2,V, direct) 19.839 0.1745 no
Confounding 2 (\( {M}_2^{\ast } \), direct) 31.644 0.1712 no
Confounding 2 (\( {M}_{2,V}^{\ast } \), direct) −0.1679 0.1774 yes
Confounding 2 (M3, total) 1.3528 0.0013 no
Confounding 2 (M3,V, total) 1.4636 0.0014 no
Confounding 2 (M4, direct) 0.0008 0.0013 yes
Confounding 2 (M4,V, direct) 0.0010 0.0013 yes
Confounding 3 (M1, total) −399.77 0.2051 no
Confounding 3 (M1,V, total) −359.81 0.2317 no
Confounding 3 (M2, direct) −0.0345 0.1714 no
Confounding 3 (M2,V, direct) 39.950 0.1846 no
Confounding 3 (\( {M}_2^{\ast } \), direct) −40.216 0.1852 no
Confounding 3 (\( {M}_{2,V}^{\ast } \), direct) −0.2350 0.1955 yes
Confounding 3 (M3, total) 1.4528 0.0021 no
Confounding 3 (M3,V, total) 1.3339 0.0023 no
Confounding 3 (M4, direct) 0.2212 0.0013 no
Confounding 3 (M4,V, direct) 0.0006 0.0014 yes
Confounding 4 (M1, total) −600.29 0.2267 no
Confounding 4 (M1,V, total) −400.33 0.2377 no
Confounding 4 (M2, direct) 6.6866 0.1907 no
Confounding 4 (M2,V, direct) 15.329 0.1869 no
Confounding 4 (\( {M}_2^{\ast } \), direct) −1.6285 0.1930 no
Confounding 4 (\( {M}_{2,V}^{\ast } \), direct) −0.1992 0.1917 yes
Confounding 4 (M3, total) 1.9757 0.0015 no
Confounding 4 (M3,V, total) 1.4531 0.0016 no
Confounding 4 (M4, direct) 0.2212 0.0013 no
Confounding 4 (M4,V, direct) 0.0006 0.0014 yes
  1. Legend. Mean of the estimated exposure (ICS) effect (mean difference or log odds ratio) on the outcome (BW, LBW or SGA) based on 1000 samples of size 20,000, with Monte Carlo standard error (se)
  2. Confounding Scenario 1: confounder between ICS and GA; Confounding Scenario 2: confounder between GA and BW; Confounding Scenario 3: confounder between ICS and BW; Confounding Scenario 4: confounder between ICS, GA and BW
  3. M1: BW ~ ICS; M2: BW ~ ICS + GA; \( {M}_2^{\ast } \): BW ~ ICS + GA + GA2 + GA3; M3: LBW ~ ICS; M4: SGA ~ ICS;
  4. null ICS effect = yes if 0 mean ± 1.96se
  5. Models subscripted by V additionally include the V variable in the regression model.
  6. Abbreviations: BW birth weight, GA gestational age, ICS inhaled corticosteroids, LBW low birth weight, SGA small for gestational age