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Table 2 Simulation results in terms of absolute bias based on a fixed sample size for increasing benefit of the experimental arm– all priors on pk (k=A,B,C) are non-informative Be (1,1) priors; p0=0.30; n=40 or 100 patients per arm

From: Evaluation of a multi-arm multi-stage Bayesian design for phase II drug selection trials – an example in hemato-oncology

Sample size True benefit Posterior mean estimate biases Mean square errors Decision criterion 1 Criterion 2 Criterion 3
  dB pA pB pA pB A B B B
40 0.00 0.0086 0.0090 0.0048 0.0048 0.4850 0.4835 0.5012 0.1414
  0.05 0.0082 0.0078 0.0048 0.0052 0.4854 0.2982 0.6358 0.2399
  0.10 0.0100 0.0042 0.0050 0.0054 0.4798 0.1632 0.7440 0.3518
  0.15 0.0097 0.0014 0.0049 0.0055 0.4798 0.0753 0.8352 0.4803
  0.20 0.0098 −0.0001 0.0049 0.0057 0.4795 0.0297 0.9028 0.6132
  0.25 0.0096 −0.0013 0.0049 0.0056 0.4800 0.0093 0.9477 0.7322
  0.30 0.0095 −0.0049 0.0049 0.0055 0.4804 0.0027 0.9731 0.8271
  0.35 0.0088 −0.0070 0.0048 0.0051 0.4841 0.0005 0.9886 0.8999
  0.40 0.0109 −0.0087 0.0048 0.0047 0.4749 0.0001 0.9958 0.9477
  0.45 0.0092 −0.0116 0.0049 0.0043 0.4808 0.0000 0.9984 0.9755
100 0.00 0.0042 0.0032 0.0020 0.0020 0.4863 0.4925 0.4960 0.0460
  0.05 0.0037 0.0030 0.0020 0.0022 0.4885 0.2156 0.7042 0.1363
  0.10 0.0040 0.0014 0.0020 0.0023 0.4866 0.0661 0.8503 0.2896
  0.15 0.0038 0.0012 0.0020 0.0024 0.4881 0.0128 0.9404 0.4925
  0.20 0.0040 −0.0003 0.0020 0.0024 0.4858 0.0015 0.9807 0.6875
  0.25 0.0027 −0.0009 0.0020 0.0023 0.4947 0.0001 0.9950 0.8473
  0.30 0.0046 −0.0017 0.0020 0.0023 0.4836 0.0000 0.9989 0.9362
  0.35 0.0042 −0.0032 0.0020 0.0022 0.4856 0.0000 0.9998 0.9792
  0.40 0.0032 −0.0037 0.0020 0.0021 0.4922 0.0000 1.0000 0.9952
  0.45 0.0036 −0.0047 0.0020 0.0018 0.4897 0.0000 1.0000 0.9992
  1. N is the sample size; pA, pB and pC refer to the posterior means of response probability in arms A, B and C, respectively; dB refers to the true benefit of B over A in terms of response probability. Bold data refer to the null hypothesis of absence of any treatment difference (dB=dC=0), or to the alternative hypothesis of an expected true 0.15 benefit of treatment B (dB=0.15)