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Table 4 Model performance across all simulated scenarios, n = 500

From: Misspecification of confounder-exposure and confounder-outcome associations leads to bias in effect estimates

 

Parameter values for the confounder-exposure and confounder-outcome associations

0.14

0.39

0.59

\(\hat{\beta}\)

AB

RB

\(\hat{\beta}\)

AB

RB

\(\hat{\beta}\)

AB

RB

Scenario 1: correct specification of cx-association & correct specification of cy-association

Multivariable regression analysis

0.5900

0.0000

0.0000

0.5900

0.0000

0.0000

0.5900

0.0000

0.0000

Covariate adjustment using the PS

0.5901

0.0001

0.0001

0.5907

0.0007

0.0012

0.5909

0.0009

0.0015

Stabilized IPW

0.5903

0.0003

0.0005

0.6030

0.0130

0.0220

0.6417

0.0517

0.0876

DR estimation

0.5900

0.0000

0.0000

0.5900

0.0000

0.0000

0.5900

0.0000

0.0000

Scenario 2: correct specification of cx-association & misspecification of cy-association

Multivariable regression analysis

0.6263

0.0363

0.0615

0.8051

0.2151

0.3646

0.9859

0.3959

0.6711

Covariate adjustment using the PS

0.5901

0.0001

0.0001

0.5907

0.0007

0.0012

0.5909

0.0009

0.0015

Stabilized IPW

0.5903

0.0003

0.0005

0.6030

0.0130

0.0220

0.6417

0.0517

0.0876

DR estimation

0.5905

0.0005

0.0008

0.6064

0.0164

0.0278

0.6465

0.0565

0.0957

Scenario 3: misspecification of cx-association & correct specification of cy-association

Multivariable regression analysis

0.5900

0.0000

0.0000

0.5900

0.0000

0.0000

0.5900

0.0000

0.0000

Covariate adjustment using the PS

0.6267

0.0367

0.0622

0.8147

0.2247

0.3808

1.0155

0.4255

0.7212

Stabilized IPW

0.6276

0.0376

0.0638

0.8339

0.2439

0.4134

1.0676

0.4776

0.8096

DR estimation

0.5900

0.0000

0.0000

0.5900

0.0000

0.0000

0.5900

0.0000

0.0000

Scenario 4: misspecification of cx-association & misspecification of cy-association

Multivariable regression analysis

0.6263

0.0363

0.0615

0.8051

0.2151

0.3646

0.9859

0.3959

0.6711

Covariate adjustment using the PS

0.6267

0.0367

0.062

0.8147

0.2247

0.3808

1.0155

0.4255

0.7212

Stabilized IPW

0.6276

0.0376

0.0638

0.8339

0.2439

0.4134

1.0676

0.4776

0.8096

DR estimation

0.6273

0.0373

0.0533

0.8261

0.2361

0.4002

1.0456

0.4556

0.7723

  1. Abbreviations: n: sample size, cx-association: confounder-exposure association, cy-association: confounder-outcome association, \(\hat{\beta}\): mean estimated exposure effect, AB: absolute bias, RB: relative bias, PS: propensity score, IPW: inverse probability weighting, DR: double robustÂ