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Table 3 Simulation results for dropping treatment arms based on the first rule (R1) and the absolute bias for such arms in the estimated treatment effect at the time of dropping decision– all priors on pk (k=A,B,C) are non-informative beta(1, 1) priors, when decision threshold is set at 0.95

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 Enrolled sample sizes % Early stopping
  dB dC pA pB pC nA nB nC A % early B % early C
40 −0.20 0.00 −0.0051 0.0305 −0.0063 36.3504 15.0121 36.3180 15.32 % 96.09 % 15.15 %
  −0.15 0.00 −0.0058 0.0061 −0.0057 36.2548 21.3829 36.3305 15.43 % 79.69 % 15.19 %
  −0.10 0.00 −0.0063 −0.0066 −0.0062 36.3540 27.9657 36.3594 15.20 % 53.98 % 15.36 %
  −0.05 0.00 −0.0056 −0.0076 −0.0072 36.2719 33.0725 36.2428 15.44 % 30.66 % 15.86 %
  0.00 0.00 −0.0050 −0.0057 −0.0063 36.2726 36.4040 36.4653 15.77 % 15.11 % 14.85 %
  0.05 0.00 −0.0073 −0.0034 −0.0049 36.2420 38.1107 36.3738 15.75 % 7.33 % 15.23 %
  0.10 0.00 −0.0077 −0.0011 −0.0049 36.2214 39.1845 36.3761 15.91 % 2.92 % 14.88 %
  0.15 0.00 −0.0044 −0.0008 −0.0070 36.4279 39.6107 36.2580 14.86 % 1.35 % 15.47 %
  0.20 0.00 −0.0044 −0.0016 −0.0060 36.3945 39.8325 36.3640 15.06 % 0.55 % 15.29 %
100 −0.20 0.00 −0.0206 0.0305 −0.0205 84.2873 15.4339 84.3159 22.80 % 99.99 % 22.82 %
  −0.15 0.00 −0.0188 −0.0007 −0.0203 84.7484 24.5031 84.4050 21.95 % 99.27 % 22.22 %
  −0.10 0.00 −0.0202 −0.0212 −0.0197 84.4487 43.6230 84.5338 22.31 % 85.84 % 22.44 %
  −0.05 0.00 −0.0191 −0.0276 −0.0199 84.8712 66.7741 84.3454 21.99 % 52.46 % 22.57 %
  0.00 0.00 −0.0216 −0.0207 −0.0216 84.0536 84.2135 83.8033 22.86 % 22.67 % 23.36 %
  0.05 0.00 −0.0203 −0.0115 −0.0196 84.6003 93.1786 84.7271 22.28 % 8.66 % 22.24 %
  0.10 0.00 −0.0194 −0.0050 −0.0202 84.6521 97.3946 84.1845 21.94 % 3.08 % 22.76 %
  0.15 0.00 −0.0194 −0.0023 −0.0202 84.8085 98.9283 84.6060 22.00 % 1.20 % 22.06 %
  0.20 0.00 −0.0199 −0.0024 −0.0215 84.5757 99.4983 84.1044 22.02 % 0.56 % 22.94 %
  1. pA, pB and pC refer to the posterior means of response probability in arms A, B and C, respectively; p0=0.3 (minimum required treatment response rate). 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)