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Table 1 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 = 0.25

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)

     

0.005

5

485

None

-0.0020

0.0062

0.0328

0.7756

   

Moderate

-0.0015

0.0062

0.0300

0.7800

   

Poisson

0.0003

0.0061

0.0368

0.7814

   

Pareto

0.0002

0.0100

0.0664

0.6432

0.005

10

326

None

0.0005

0.0070

0.0326

0.7868

   

Moderate

0.0009

0.0073

0.0402

0.7838

   

Poisson

-0.0010

0.0070

0.0356

0.7884

   

Pareto

0.0043

0.0100

0.0566

0.6968

0.005

20

282

None

-0.0010

0.0072

0.0320

0.7942

   

Moderate

0.0014

0.0075

0.0398

0.7878

   

Poisson

-0.0010

0.0076

0.0408

0.7802

   

Pareto

0.0000

0.0090

0.0486

0.7258

0.005

40

265

None

0.0006

0.0078

0.0444

0.7848

   

Moderate

0.0011

0.0082

0.0458

0.7936

   

Poisson

-0.0017

0.0082

0.0484

0.7772

   

Pareto

0.0000

0.0086

0.0466

0.7572

0.020

10

629

None

-0.0017

0.0070

0.0448

0.8012

   

Moderate

0.0017

0.0073

0.0544

0.7974

   

Poisson

0.0009

0.0074

0.0510

0.7992

   

Pareto

-0.0022

0.0118

0.0904

0.6236

0.020

20

353

None

-0.0004

0.0073

0.0452

0.8000

   

Moderate

0.0006

0.0074

0.0408

0.7980

   

Poisson

-0.0007

0.0075

0.0458

0.7968

   

Pareto

0.0009

0.0115

0.0660

0.6546

0.020

40

290

None

0.0017

0.0080

0.0518

0.7932

   

Moderate

0.0001

0.0077

0.0466

0.7944

   

Poisson

-0.0003

0.0077

0.0466

0.7912

   

Pareto

0.0003

0.0101

0.0556

0.7008

0.050

20

743

None

-0.0007

0.0075

0.0436

0.7916

   

Moderate

-0.0018

0.0077

0.0540

0.8026

   

Poisson

-0.0003

0.0078

0.0536

0.7950

   

Pareto

-0.0022

0.0115

0.0562

0.6256

0.050

40

361

None

-0.0012

0.0080

0.0528

0.7944

   

Moderate

0.0031

0.0080

0.0510

0.7926

   

Poisson

-0.0001

0.0080

0.0502

0.7904

   

Pareto

-0.0023

0.0121

0.0604

0.6242

0.100

40

652

None

0.0021

0.0076

0.0504

0.7966

   

Moderate

0.0013

0.0078

0.0458

0.8118

   

Poisson

-0.0022

0.0078

0.0506

0.7946

   

Pareto

-0.0031

0.0121

0.0546

0.6006

  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.