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Table 2 Optimal, minimax and admissible design for Fleming’s two-stage design

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

p0p1αβαT1-βTn1a1r1PETF1nrENFTypeq
0.050.250.050.200.0470.8129030.63917311.9Optimal[0.000, 0.655]
    0.0430.80112030.56016313.8Minimax[0.655, 1.000]
0.100.300.050.200.0470.80510150.73829615.0Optimal[0.000, 0.200]
    0.0480.81211140.71627615.5Admissible[0.200, 0.474]
    0.0490.81712140.68526616.4Admissible[0.474, 0.661]
    0.0430.80219250.74124620.3Minimax[0.661, 1.000]
0.300.500.050.200.0460.803186110.728421824.5Optimal[0.000, 0.250]
    0.0490.807196110.676391725.5Admissible[0.250, 0.634]
    0.0490.800278140.592361630.7Minimax[0.634, 1.000]
    0.0490.800210120.009361635.9Inadmissible
0.050.250.100.100.0930.9039030.63924314.4Optimal[0.000, 0.130]
    0.0830.90510030.61022314.7Admissible[0.130, 0.333]
    0.0780.90511030.58421315.2Admissible[0.333, 0.500]
    0.0740.90313030.53820316.2Minimax[0.500, 1.000]
0.100.300.100.100.0850.90013140.65631619.2Optimal[0.000, 0.123]
    0.0990.90418250.76226519.9Admissible[0.123, 0.231]
    0.0950.90316150.53225520.2Minimax[0.231, 1.000]
0.300.500.100.100.0970.901206100.656471929.3Optimal[0.000, 0.048]
    0.0910.900206110.625451829.4Admissible[0.048, 0.117]
    0.0930.900237120.640421729.8Admissible[0.117, 0.492]
    0.0970.901267130.486391632.7Minimax[0.492, 1.000]
0.050.250.050.100.0490.9029040.63130416.8Optimal[0.000, 0.091]
    0.0470.91310040.60029417.6Inadmissible
    0.0470.90710030.61028417.0Inadmissible
    0.0460.91111030.58427417.7Inadmissible
    0.0420.90111030.58426417.2Admissible[0.091, 0.565]
    0.0450.90313030.53825418.5Minimax[0.565, 1.000]
0.100.300.050.100.0480.90117250.78441822.2Optimal[0.000, 0.032]
    0.0480.90218260.74035722.4Admissible[0.032, 0.444]
    0.0470.90016150.53233724.0Minimax[0.444, 1.000]
0.300.500.050.100.0470.900258140.683562334.8Optimal[0.000, 0.250]
    0.0490.901268140.637532235.8Admissible[0.250, 0.670]
    0.0490.9003711180.579502142.5Minimax[0.670, 1.000]
    0.050.900280150.008502149.8Inadmissible
  1. (p1, p0) = (0.05, 0.25), (0.10, 0.30), (0.30, 0.50) are considered in Fleming’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. (a1, r1, r) are the critical values. PET1 denotes the probability of early termination at first stage. EN represents expected sample size