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Table 7 Sample scenarios assuming uniform priors p(π 1) and p(π 2) where \(\tau _{1}^{2}=\tau _{2}^{2}\). Hypothesized values of π 1 and π 2 set equal to μ 1 and μ 2, respectively, under the traditional design. Two-sided α=0.05 and 1−β=0.80 assumed

From: Sample size determination for a binary response in a superiority clinical trial using a hybrid classical and Bayesian procedure

   Traditional design CEP design  
(μ 1,μ 2) \(\tau _{1}^{2}=\tau _{2}^{2}\) \(\hat {N}\) Performance CEP N Performance E(π 2π 1|π 2>π 1) P(π 2>π 1) Marginal benefit
(0.1,0.9) 0.001 10 0.638 0.826 10 0.638 0.800 1 0
(0.1,0.8) or (0.2,0.9) 0.001 14 0.643 0.824 14 0.643 0.700 1 0
(0.1,0.7) or (0.3,0.9) 0.001 20 0.680 0.831 20 0.680 0.600 1 0
(0.2,0.8) 0.001 20 0.593 0.811 20 0.593 0.600 1 0
  0.01 20 0.556 0.775 22 0.615 0.600 1 0.030
(0.1,0.6)or (0.4,0.9) 0.001 28 0.633 0.822 28 0.633 0.500 1 0
(0.2,0.7)or (0.3,0.8) 0.001 30 0.599 0.812 30 0.599 0.500 1 0
  0.01 30 0.554 0.763 36 0.650 0.500 1 0.016
(0.1,0.5) or (0.5,0.9) 0.001 40 0.551 0.801 40 0.551 0.400 1 0
(0.2,0.6) or (0.4,0.8) 0.001 46 0.553 0.800 46 0.553 0.400 1 0
  0.01 46 0.535 0.735 62 0.663 0.400 1 0.008
(0.3,0.7) 0.001 48 0.555 0.800 48 0.555 0.400 1 0
  0.01 48 0.536 0.735 64 0.660 0.400 1 0.008
  0.02 48 0.549 0.711 80 0.694 0.407 0.983 0.005
  0.03 48 0.575 0.718 82 0.702 0.427 0.945 0.004
(0.1,0.4) or (0.6,0.9) 0.001 64 0.523 0.787 68 0.589 0.300 1 0.017
(0.2,0.5) or (0.5,0.8) 0.001 78 0.521 0.786 82 0.581 0.300 1 0.015
  0.01 78 0.526 0.704 130 0.689 0.303 0.991 0.003
(0.3,0.6) or (0.4,0.7) 0.001 84 0.506 0.781 90 0.591 0.300 1 0.014
  0.01 84 0.521 0.701 142 0.690 0.303 0.991 0.003
  0.02 84 0.566 0.712 150 0.704 0.330 0.925 0.002
  0.03 84 0.603 0.731 140 0.709 0.357 0.875 0.002
(0.1,0.3) or (0.7,0.9) 0.001 124 0.510 0.764 140 0.600 0.200 1 0.006
(0.2,0.4) or (0.6,0.8) 0.001 164 0.512 0.764 184 0.603 0.200 1 0.005
  0.01 164 0.566 0.713 292 0.703 0.224 0.911 0.001
(0.3,0.5) or (0.5,0.7) 0.001 186 0.504 0.761 210 0.603 0.200 1 0.004
  0.01 186 0.562 0.710 336 0.704 0.224 0.911 0.001
  0.02 186 0.626 0.745 284 0.709 0.263 0.825 0.001
  0.03 186 0.669 0.772 236 0.710 0.295 0.778 0.001
(0.4,0.6) 0.001 194 0.504 0.761 220 0.607 0.200 1 0.004
  0.01 194 0.562 0.709 350 0.704 0.224 0.911 0.001
  0.02 194 0.625 0.745 296 0.708 0.263 0.825 0.001
  0.03 194 0.668 0.771 248 0.711 0.295 0.778 0.001
  0.04 194 0.700 0.792 210 0.712 0.323 0.747 0.001
  0.05 194 0.725 0.809 194 0.725 0.349 0.725 0