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Table 6 Empirical type I error and the percentage of trials stopping for futility and efficacy for sample size re-estimation using conditional power

From: Impact of misspecifying the distribution of a prognostic factor on power and sample size for testing treatment interactions in clinical trials

θ

Planned distribution of the prognostic factor

Planned n t

Empirical type I error

Percent stopping for futility

Percent stopping for efficacy

Misspecification of the prognostic factor: -5%

0

10%

1,418

0.0278

43.48%

0.24%

20%

798

0.0264

44.54%

0.26%

30%

608

0.0262

42.66%

0.20%

40%

532

0.0280

44.16%

0.24%

50%

512

0.0246

42.88%

0.30%

0

10%

178

0.0304

42.94%

0.40%

20%

100

0.0276

42.44%

0.28%

30%

78

0.0252

43.16%

0.54%

40%

68

0.0230

43.08%

0.44%

50%

64

0.0298

42.00%

0.56%

Misspecification of the prognostic factor: -15%

0

10%

1,418

--

--

--

20%

798

0.0254

43.62%

0.24%

30%

608

0.0278

42.94%

0.30%

40%

532

0.0282

44.00%

0.36%

50%

512

0.0248

42.62%

0.32%

0

10%

178

--

--

--

20%

100

0.0326

44.24%

0.50%

30%

78

0.0282

42.52%

0.44%

40%

68

0.0286

42.62%

0.42%

50%

64

0.0296

43.26%

0.50%

Misspecification of the prognostic factor: +5%

0

10%

1,418

0.0314

41.46%

0.36%

20%

798

0.0284

42.94%

0.22%

30%

608

0.0296

44.76%

0.44%

40%

532

0.0312

43.82%

0.32%

50%

512

0.0290

44.16%

0.36%

0

10%

178

0.0284

43.64%

0.30%

20%

100

0.0274

43.30%

0.38%

30%

78

0.0296

43.66%

0.44%

40%

68

0.0280

44.24%

0.48%

50%

64

0.0290

43.82%

0.46%

Misspecification of the prognostic factor: +15%

0

10%

1,418

0.0244

43.32%

0.28%

20%

798

0.0274

44.44%

0.34%

30%

608

0.0232

43.98%

0.20%

40%

532

0.0290

43.18%

0.32%

50%

512

0.0284

44.22%

0.32%

0

10%

178

0.0282

43.36%

0.38%

20%

100

0.0282

42.50%

0.36%

30%

78

0.0266

43.92%

0.34%

40%

68

0.0266

44.30%

0.46%

50%

64

0.0248

42.48%

0.34%

  1. The margin of error based on the 99% confidence interval is 0.008.