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Table 4 Under non-normal distribution, the empirical powers of testing non-inferiority with non-inferiority limit = 0.8 in \(\tau_{R} { = 1}\),\(\tau_{P} = 2\)

From: Conducting the non-inferiority test for the means with unknown coefficient of variation in a three-arm trial

\(n\)

Distribution

Method

Empirical Power

\(\mu_{R} - \mu_{P} = 9\)

\(\mu_{R} - \mu_{P} = 15\)

\(\mu_{R} - \mu_{P} = 20\)

\(\xi = 1.0\)

\(\xi = 1.2\)

\(\xi = 1.4\)

\(\xi = 1.0\)

\(\xi = 1.2\)

\(\xi = 1.4\)

\(\xi = 1.0\)

\(\xi = 1.2\)

\(\xi = 1.4\)

60

Log-Normal

GP

0.3079

0.7160

0.8848

0.6654

0.9851

0.9989

0.8611

1.0000

1.0000

DM

0.0152

0.0909

0.2677

0.0865

0.4726

0.8104

0.2192

0.7912

0.9597

EB

0.1191

0.3382

0.5064

0.5418

0.9236

0.9418

0.8355

0.9945

0.9982

Gamma

GP

0.3094

0.7365

0.9272

0.6693

0.9923

1.0000

0.8633

1.0000

1.0000

DM

0.0028

0.0293

0.1402

0.0381

0.4006

0.8595

0.1407

0.8306

0.9954

EB

0.0709

0.2855

0.5027

0.5600

0.9609

0.9891

0.8473

1.0000

1.0000

90

Log-Normal

GP

0.4379

0.8865

0.9702

0.8122

0.9998

0.9999

0.9557

1.0000

1.0000

DM

0.0193

0.1580

0.4436

0.1358

0.6888

0.9431

0.3426

0.9290

0.9933

EB

0.2055

0.5691

0.7400

0.7500

0.9873

0.9891

0.9527

1.0000

1.0000

Gamma

GP

0.399

0.9124

0.9938

0.8187

1.0000

1.0000

0.9570

1.0000

1.0000

DM

0.0049

0.0692

0.3275

0.0683

0.6989

0.9909

0.2578

0.9823

1.0000

EB

0.1836

0.5627

0.7852

0.7491

1.0000

1.0000

0.9536

1.0000

1.0000

120

Log-Normal

GP

0.5436

0.9553

0.9905

0.9015

1.0000

1.0000

0.9871

1.0000

1.0000

DM

0.0227

0.2394

0.5978

0.1973

0.8442

0.9850

0.4811

0.9832

0.9997

EB

0.3073

0.7709

0.8609

0.8891

0.9982

1.0000

0.9836

1.0000

1.0000

Gamma

GP

0.5501

0.9717

0.9912

0.9030

1.0000

1.0000

0.9880

1.0000

1.0000

DM

0.0069

0.1382

0.5777

0.1279

0.9057

1.0000

0.4276

0.9990

1.0000

EB

0.3082

0.8109

0.9173

0.8818

1.0000

1.0000

0.9818

1.0000

1.0000

480

Log-Normal

GP

0.9716

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

DM

0.2765

0.9837

1.0000

0.9365

1.0000

1.0000

0.9993

1.0000

1.0000

EB

0.9709

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

Gamma

GP

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

DM

0.2349

0.9957

1.0000

0.9607

1.0000

1.0000

0.9999

1.0000

1.0000

EB

0.9709

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

900

Log-Normal

GP

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

DM

0.7449

1.0000

1.0000

0.9999

1.0000

1.0000

1.0000

1.0000

1.0000

EB

0.9991

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

Gamma

GP

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

DM

0.7498

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

EB

0.9982

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

  1. \(n\) The total sample sizes, GP The GPV-based method, DM The Delta method and EB The empirical bootstrap method
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BMC Medical Research Methodology

ISSN: 1471-2288

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