Skip to main content

Table 2 Average absolute bias \(\left|{\widehat{\beta }}_{TM}-{\beta }_{TM}\right|\) for the different confounding adjustment methods for confounding adjustment models (b)-(d)

From: The impact of moderator by confounder interactions in the assessment of treatment effect modification: a simulation study

  

Adjustment model

Adjustment method

(a)

(b)

(c)

(d)

\({{\varvec{\beta}}}_{{\varvec{T}}{\varvec{M}}}=0.3\)

Prev.\({\varvec{M}}=0.5\)

(1)

0.066664

0.000773

0.000791

0.000791

(2)

0.082535

0.059600

0.058446

0.000765

(3)

0.063750

0.005581

0.001400

0.001400

(4)

0.055594

0.008806

0.004108

0.004226

\({{\varvec{\beta}}}_{{\varvec{T}}{\varvec{M}}}=0.3\)

Prev.\({\varvec{M}}=0.1\)

(1)

0.075085

0.001873

0.001715

0.001715

(2)

0.093259

0.062743

0.322948

0.001586

(3)

0.083261

0.017981

0.011239

0.011239

(4)

0.096792

0.038555

0.043617

0.038939

\({{\varvec{\beta}}}_{{\varvec{T}}{\varvec{M}}}=0.6\)

Prev.\({\varvec{M}}=0.5\)

(1)

0.066454

0.000816

0.000749

0.000749

(2)

0.081596

0.059213

0.056933

0.000941

(3)

0.060059

0.003119

0.002269

0.002269

(4)

0.052857

0.006547

0.007896

0.005279

\({{\varvec{\beta}}}_{{\varvec{T}}{\varvec{M}}}=0.6\)

Prev.\({\varvec{M}}=0.1\)

(1)

0.073871

0.000848

0.000925

0.000925

(2)

0.092722

0.056906

0.319295

0.00106

(3)

0.074819

0.013062

0.012955

0.012955

(4)

0.079721

0.036695

0.046072

0.041207

  1. Confounding models: (a) adjusting for no moderator-confounder interactions, (b) adjusting for the one moderator-confounder interaction, (c) adjusting for all possible moderator-confounder interactions, (d) subgroup-specific confounding adjustment
  2. Confounding methods: (1) Regression adjustment, (2) Propensity score covariate adjustment, (3) IPTW, (4) Propensity score matching