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Table 6 Scenarios 13 & 14: 30% 'good' prognosis, ×3 'good' prognosis survival, 50% and 75% switching probabilities, 100% treatment effect for switchers, uniform distribution for switching times

From: Assessing methods for dealing with treatment switching in randomised controlled trials: a simulation study

True HR and eψ

Method

Mean estimate

Mean SE

SE of mean

95% Confidence interval

Bias

MSE

Coverage (%)

Successful estimation (%)

     

Lower

Upper

    
 

Hazard ratio methods

         
 

ITT

0.9406

0.0940

0.0965

0.7733

1.1442

0.0406

0.0110

92.2

100.0

 

PP - Exclude switchers

1.0018

0.1448

0.1472

0.7547

1.3300

0.1018

0.0320

89.6

100.0

 

PP - Censor at switch

2.2865

0.3323

0.3282

1.7198

3.0403

1.3865

2.0301

0.0

100.0

 

Time-dependent covariate

3.2815

0.4544

0.4520

2.5017

4.3050

2.3815

5.8757

0.0

100.0

 

Law and Kaldor

0.9508

0.1230

0.1263

0.7379

1.2251

0.0508

0.0185

93.7

100.0

 

Loeys and Goethebeur

0.8548

-

0.2874

0.4414

1.7657

-0.0452

0.0847

93.6

99.9

0.9 & 1.23

AFT methods

         
 

ITT

1.1696

0.2386

0.2446

0.7843

1.7447

-0.0650

0.0640

92.6

100.0

 

PP - Exclude switchers

1.0631

0.1448

0.3143

0.5983

1.8922

-0.1715

0.1282

90.0

100.0

 

PP - Censor at switch

0.2100

0.0626

0.0640

0.1172

0.3769

-1.0246

1.0539

0.0

100.0

 

Robins and Tsiatis - Logrank

1.2876

-

0.4161

0.6611

2.3440

0.0530

0.1759

94.4

100.0

 

Robins and Tsiatis - Cox

1.2835

-

0.4156

0.6581

2.3451

0.0489

0.1751

94.4

95.9

 

Robins and Tsiatis - Exponential

1.3120

-

0.3923

0.9033

2.0554

0.0774

0.1599

84.0

99.7

 

Robins and Tsiatis - Weibull

1.2898

-

0.4125

0.6781

2.3512

0.0553

0.1732

94.5

99.8

 

Branson and Whitehead

1.2789

0.2613

0.3755

0.8571

1.9090

0.0443

0.1429

82.6

100.0

 

Walker et al

2.6653

0.9576

0.9545

1.3297

5.5524

1.4307

2.9579

46.7

99.9

 

Hazard ratio methods

         
 

ITT

0.8109

0.0842

0.0843

0.6616

0.9939

0.1109

0.0194

71.4

100.0

 

PP - Exclude switchers

0.7834

0.1147

0.1158

0.5880

1.0437

0.0834

0.0204

89.7

100.0

 

PP - Censor at switch

1.7695

0.2612

0.2559

1.3250

2.3634

1.0695

1.2092

0.0

100.0

 

Time-dependent covariate

2.5841

0.3613

0.3598

1.9647

3.3991

1.8841

3.6791

0.0

100.0

 

Law and Kaldor

0.8147

0.1113

0.1125

0.6233

1.0649

0.1147

0.0258

81.4

100.0

 

Loeys and Goethebeur

0.5287

-

0.1897

0.2352

1.0444

-0.1713

0.0653

86.9

96.9

0.7 & 2.04

AFT methods

         
 

ITT

1.5826

0.3351

0.3379

1.0452

2.3973

-0.4582

0.3242

72.8

100.0

 

PP - Exclude switchers

1.7560

0.1147

0.5427

0.9817

3.1462

-0.2849

0.3757

90.5

100.0

 

PP - Censor at switch

0.3494

0.1032

0.1020

0.1961

0.6240

-1.6914

2.8712

0.0

100.0

 

Robins and Tsiatis - Logrank

2.1469

-

0.7376

1.0853

4.0598

0.1061

0.5552

95.7

100.0

 

Robins and Tsiatis - Cox

2.1363

-

0.7256

1.0640

4.0757

0.0955

0.5356

95.9

92.4

 

Robins and Tsiatis - Exponential

2.1549

-

0.7419

1.3002

3.6453

0.1140

0.5635

88.4

100.0

 

Robins and Tsiatis - Weibull

2.1472

-

0.7359

1.0961

4.0901

0.1064

0.5528

95.6

100.0

 

Branson and Whitehead

2.0328

0.4340

0.6210

1.3380

3.0899

-0.0080

0.3857

82.6

100.0

 

Walker et al

4.2491

1.5202

1.2616

2.1208

8.6357

2.2083

6.4681

45.3

88.3