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Table 2 Validation of the approximate design effect formula.

From: Design effect in multicenter studies: gain or loss of power?

ICC = 0.01

N subjects

100

200

500

N centers

5

10

20

5

10

20

50

5

10

20

50

100

S1 Deff

0.9969

0.9938

0.9921

0.9966

0.9936

0.9922

0.9911

0.9965

0.9933

0.9919

0.9913

0.9908

rdiff

0.0065

0.0032

0.0016

0.0065

0.0032

0.0016

0.0006

0.0065

0.0032

0.0016

0.0006

0.0003

S2 Deff

0.9972

0.9949

0.9928

0.9972

0.9956

0.9938

0.9917

0.9980

0.9989

0.9956

0.9931

0.9918

rdiff

0.0065

0.0032

0.0014

0.0065

0.0032

0.0016

0.0005

0.0065

0.0033

0.0016

0.0006

0.0003

S3 Deff

1.0102

1.0306

1.0147

1.0217

1.0622

1.0431

1.0132

1.0575

1.1788

1.1143

1.0487

1.0204

rdiff

0.0066

0.0035

0.0016

0.0066

0.0036

0.0018

0.0006

0.0066

0.0036

0.0019

0.0007

0.0003

S4 Deff

1.1038

1.0323

1.0285

1.2026

1.0538

1.0604

1.0184

1.4788

1.1290

1.1588

1.0559

1.0186

rdiff

0.0077

0.0051

0.0027

0.0077

0.0052

0.0030

0.0011

0.0077

0.0053

0.0030

0.0013

0.0006

ICC = 0.10

N subjects

100

200

500

N centers

5

10

20

5

10

20

50

5

10

20

50

100

S1 Deff

0.9655

0.9356

0.9197

0.9642

0.9337

0.9209

0.9105

0.9631

0.9313

0.9177

0.9124

0.9076

rdiff

0.0643

0.0318

0.0155

0.0649

0.0320

0.0160

0.0061

0.0649

0.0324

0.0161

0.0063

0.0031

S2 Deff

0.9709

0.9469

0.9269

0.9696

0.9547

0.9359

0.9171

0.9793

0.9827

0.9549

0.9300

0.9174

rdiff

0.0656

0.0318

0.0142

0.0648

0.0323

0.0157

0.0053

0.0651

0.0325

0.0161

0.0063

0.0028

S3 Deff

1.1101

1.3018

1.1721

1.2095

1.6471

1.4256

1.1337

1.6662

2.7175

2.1685

1.4965

1.2049

rdiff

0.0654

0.0349

0.0166

0.0659

0.0354

0.0182

0.0063

0.0662

0.0358

0.0185

0.0074

0.0034

S4 Deff

2.0718

1.3360

1.2725

3.1669

1.5750

1.6252

1.1934

6.2708

2.5759

2.5886

1.5687

1.2017

rdiff

0.0768

0.0507

0.0272

0.0770

0.0517

0.0299

0.0110

0.0771

0.0513

0.0299

0.0126

0.0059

  1. ICC: Intraclass Correlation Coefficient
  2. Simulations are conducted with varying center sizes: 20% of centers recruit 80% of subjects. Average exact design effect estimate (Deff) and average relative difference (rdiff) between exact and approximate design effect formula are given for 4 situations (Si, i = 1,2,3,4), two ICC values, and obtained for 1000 simulations.
  3. S1: Equal group sizes. In each center, the probability, for a subject, to be in group 1 is 1/2
  4. S2: Slight variations in group 1 proportions among centers. The ratio between the sizes of group 1 and group 2 varies uniformly between 0.8 and 1.25 among centers
  5. S3: Important variations in group 1 proportions among centers. The ratio between the sizes of group 1 and group 2 varies uniformly between 0.1 and 10 among centers
  6. S4: "Cluster design". The center is nested within the group and the probability, for each center, to be in group 1 is 1/2
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BMC Medical Research Methodology

ISSN: 1471-2288

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