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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