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Table 2 Bias, mean square error, empirical type I error and power in cluster randomized trials according to several types of imbalance in cluster size – Effect size = 0.50

From: Planning a cluster randomized trial with unequal cluster sizes: practical issues involving continuous outcomes

Simulation parameters1

Type of imbalance

Bias

Mean Square Error

Empirical type I error2

Empirical power2

Intraclass correlation coefficient (ρ)

Number of clusters in each arm (g)

Total number of subjects in each arm (N)

Type of imbalance

    

0.005

5

89

None

0.0025

0.0238

0.0190

0.7648

   

Moderate

0.0010

0.0243

0.0204

0.7622

   

Poisson

0.0014

0.0243

0.0214

0.7596

   

Pareto

-0.0064

0.0393

0.0256

0.6250

0.005

10

73

None

-0.0011

0.0288

0.0328

0.7660

   

Moderate

-0.0015

0.0290

0.0322

0.7718

   

Poisson

-0.0007

0.0298

0.0318

0.7662

   

Pareto

-0.0005

0.0344

0.0352

0.7090

0.005

20

67

None

-0.0011

0.0303

0.0384

0.7764

   

Moderate

-0.0038

0.0296

0.0318

0.7700

   

Poisson

-0.0012

0.0301

0.0382

0.7664

   

Pareto

-0.0004

0.0323

0.0334

0.7322

0.005

40

65

None

0.0005

0.0310

0.0446

0.7986

   

Moderate

0.0021

0.0322

0.0478

0.7896

   

Poisson

0.0028

0.0305

0.0396

0.7860

   

Pareto

-0.0007

0.0320

0.0382

0.7518

0.020

5

119

None

0.0025

0.0238

0.0190

0.7648

   

Moderate

-0.0011

0.0248

0.0310

0.7856

   

Poisson

-0.0021

0.0250

0.0306

0.7786

   

Pareto

0.0009

0.0413

0.0674

0.6262

0.020

10

81

None

-0.0031

0.0273

0.0320

0.7798

   

Moderate

0.0006

0.0282

0.0364

0.7772

   

Poisson

-0.0003

0.0288

0.0378

0.7778

   

Pareto

0.0078

0.0394

0.0550

0.6910

0.020

20

70

None

0.0026

0.0312

0.0476

0.7838

   

Moderate

0.0026

0.0312

0.0476

0.7838

   

Poisson

0.0032

0.0306

0.0436

0.7894

   

Pareto

0.0003

0.0362

0.0460

0.7056

0.020

40

66

None

-0.0026

0.0314

0.0498

0.7878

   

Moderate

0.0026

0.0312

0.0476

0.7838

   

Poisson

0.0049

0.0326

0.0476

0.7828

   

Pareto

-0.0007

0.0337

0.0422

0.7328

0.050

5

423

None

0.0015

0.0246

0.0482

0.7980

   

Moderate

-0.0001

0.0240

0.0460

0.8004

   

Poisson

-0.0005

0.0237

0.0478

0.7988

   

Pareto

0.0026

0.0337

0.0768

0.6808

0.050

10

103

None

-0.0006

0.0280

0.0426

0.7964

   

Moderate

0.0012

0.0286

0.0446

0.7952

   

Poisson

-0.0017

0.0293

0.0440

0.7754

   

Pareto

-0.0022

0.0466

0.0770

0.6342

0.050

20

76

None

0.0027

0.0298

0.0436

0.8020

   

Moderate

-0.0018

0.0308

0.0452

0.7784

   

Poisson

-0.0016

0.0323

0.0526

0.7672

   

Pareto

-0.0056

0.0396

0.0528

0.6620

0.050

40

67

None

-0.0019

0.0313

0.0468

0.7880

   

Moderate

-0.0012

0.0294

0.0516

0.7740

   

Poisson

0.0000

0.0335

0.0504

0.7712

   

Pareto

0.0022

0.0376

0.0516

0.7026

0.100

10

213

None

0.0006

0.0263

0.0426

0.8056

   

Moderate

0.0015

0.0289

0.0530

0.7940

   

Poisson

-0.0007

0.0287

0.0538

0.8004

   

Pareto

-0.0027

0.0438

0.0730

0.6394

0.100

20

89

None

-0.0029

0.0303

0.0470

0.7888

   

Moderate

-0.0020

0.0324

0.0530

0.7760

   

Poisson

-0.0004

0.0316

0.0488

0.7744

   

Pareto

0.0064

0.0492

0.0674

0.6276

0.100

40

70

None

0.0038

0.0331

0.0510

0.7890

   

Moderate

0.0031

0.0337

0.0506

0.7738

   

Poisson

0.0020

0.0332

0.0456

0.7658

   

Pareto

0.0019

0.0433

0.0536

0.6641

  1. 1N is the number of subjects per intervention arm, calculated under the assumption of constant cluster size
  2. 2 The nominal values for type I and type II error rates were fixed at 0.05 and 0.20, respectively.