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Table 1 Optimal, minimax and admissible design for Simon’s two-stage design

From: Optimal, minimax and admissible two-stage design for phase II oncology clinical trials

p0p1αβαT1-βTn1r1PETS1nrENSTypeq
0.050.250.050.200.0470.812900.63017212.0Optimal[0.000, 0.643]
    0.0430.8011200.54016213.8Minimax[0.643, 1.000]
0.100.300.050.200.0470.8051010.73629515.0Optimal[0.000, 0.286]
    0.0400.8061110.69727515.8Admissible[0.286, 0.500]
    0.0360.8051210.65926516.8Admissible[0.500, 0.730]
    0.0330.8021510.54925519.5Minimax[0.730, 1.000]
0.300.500.050.200.0500.8031550.722461823.6Optimal[0.000, 0.216]
    0.0440.8011860.722421724.7Admissible[0.216, 0.250]
    0.0460.8041960.666391625.7Minimax[0.250, 1.000]
0.050.250.100.100.0930.903900.63024214.6Optimal[0.000, 0.091]
    0.0830.9051000.59922214.8Admissible[0.091, 0.333]
    0.0780.9051100.56921215.3Admissible[0.333, 0.524]
    0.0740.9031300.51320216.4Minimax[0.524, 1.000]
0.100.300.100.100.0980.9011210.65935519.8Optimal[0.000, 0.032]
    0.100.9041820.73426420.1Admissible[0.032, 0.231]
    0.0950.9031610.51525420.4Minimax[0.231, 1.000]
0.300.500.100.100.0970.9052270.671461729.9Optimal[0.000, 0.111]
    0.0900.9012160.551421630.4Admissible[0.111, 0.605]
    0.0940.9002870.365391535.0Minimax[0.605, 1.000]
0.050.250.050.100.0490.902900.63030316.8Optimal[0.000, 0.167]
    0.0470.9131000.59929317.6Inadmissible
    0.0430.9061000.59928317.2Admissible[0.167, 0.375]
    0.0400.9081100.56927318.0Inadmissible
    0.0370.9051200.54026318.4Admissible[0.375, 0.667]
    0.0340.9011500.46325320.4Minimax[0.667, 1.000]
0.100.300.050.100.0470.9021820.73435622.5Optimal[0.000, 0.474]
    0.0440.9011920.70534623.4Admissible[0.474, 0.737]
    0.0410.9022220.62033626.2Minimax[0.737, 1.000]
0.300.500.050.100.0500.9032480.725632434.7Optimal[0.000, 0.114]
    0.0440.9022270.671622435.2Inadmissible
    0.0450.9022060.608592335.3Inadmissible
    0.0460.9032370.618562235.6Admissible[0.114, 0.250]
    0.0470.9022470.565532136.6Minimax[0.250, 1.000]
  1. (p1, p0) = (0.05, 0.25), (0.10, 0.30), (0.30, 0.50) are considered in Simon’s two-stage design. Each (p1, p0) gives three type I & II error constraints, (0.05, 0.20), (0.10, 0.10) and (0.05, 0.10), respectively. (αT, 1-βT) denotes the true type I error and power. n1 and n is the sample size required in the first stage and in the whole trial, respectively. (r1, r) are the critical values. PET1 denotes the probability of early termination at first stage. EN represents expected sample size