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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.