Table 5 Comparison of approaches for the estimation of natural effects on the odds ratio scale for Scenario 5 with a continuous mediator (based on 1000 data sets of size \(n=1000\))

NDE

Approx_Naive

1.415

1.609

0.194

13.708

0.274

0.336

91.3

90.2

Approx_C

1.415

1.578

0.163

11.508

0.279

0.323

93.2

91.6

Approx_IPW

1.415

1.599

0.184

12.967

0.276

0.332

91.7

90.8

Exact_Naive

1.415

1.366

-0.049

-3.494

0.270

0.274

94.3

93.7

Exact_IPW

1.415

1.445

0.030

2.127

0.271

0.273

95.7

95.1

Unified

1.415

1.623

0.207

14.661

0.283

0.351

90.4

-

NIE

Approx_Naive

2.521

2.997

0.476

18.879

0.601

0.767

89.0

86.1

Approx_C

2.521

2.363

-0.157

-6.237

0.294

0.334

98.2

92.7

Approx_IPW

2.521

2.788

0.267

10.611

0.495

0.562

94.5

90.8

Exact_Naive

2.521

2.707

0.186

7.379

0.409

0.450

92.3

92.4

Exact_IPW

2.521

2.553

0.032

1.274

0.350

0.351

96.9

95.2

Unified

2.521

2.259

-0.261

-10.369

0.246

0.359

85.3

-

TE

Approx_Naive

3.568

4.731

1.164

32.616

0.809

1.417

66.3

61.5

Approx_C

3.568

3.678

0.111

3.100

0.496

0.509

97.3

94.5

Approx_IPW

3.568

4.380

0.813

22.778

0.692

1.068

81.5

74.7

Exact_Naive

3.568

3.618

0.050

1.405

0.479

0.482

95.8

95.1

Exact_IPW

3.568

3.625

0.057

1.599

0.481

0.485

96.0

95.4

Unified

3.568

3.622

0.055

1.529

0.480

0.483

95.7

-