Skip to main content

Table 4 Sample scenarios assuming beta 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 m 1 and m 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  
(m 1,m 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 0.797 0.518 12 0.742 0.783 1 0.1120
  0.01 10 0.622 0.242 16 0.627 0.674 1 0.0642
  0.02 10 0.508 0.164 26 0.673 0.585 0.993 0.0318
  0.03 10 0.433 0.123 40 0.687 0.519 0.965 0.0188
  0.04 10 0.381 0.099 60 0.698 0.469 0.915 0.0120
  0.05 10 0.342 0.082 86 0.705 0.429 0.846 0.0082
  0.06 10 0.311 0.070 120 0.710 0.397 0.761 0.0058
  0.07 10 0.285 0.060 160 0.713 0.369 0.662 0.0044
  0.08 10 0.262 0.052 214 0.716 0.342 0.545 0.0033
(0.1,0.8) or (0.2,0.9) 0.001 14 0.804 0.559 14 0.559 0.688 1 0
  0.01 14 0.656 0.314 22 0.623 0.602 1 0.0386
  0.02 14 0.553 0.237 34 0.674 0.529 0.989 0.0218
  0.03 14 0.486 0.195 52 0.692 0.476 0.953 0.0131
  0.04 14 0.439 0.168 76 0.702 0.438 0.896 0.0086
  0.05 14 0.405 0.149 102 0.706 0.408 0.823 0.0063
  0.06 14 0.377 0.134 134 0.711 0.383 0.740 0.0048
  0.07 14 0.353 0.121 172 0.713 0.361 0.646 0.0037
  0.08 14 0.331 0.110 218 0.716 0.340 0.540 0.0030
(0.1,0.7) or (0.3,0.9) 0.001 20 0.814 0.616 20 0.616 0.590 1 0
  0.01 20 0.670 0.364 30 0.636 0.518 0.999 0.0272
  0.02 20 0.578 0.295 48 0.677 0.463 0.979 0.0136
  0.03 20 0.523 0.260 72 0.697 0.426 0.931 0.0084
  0.04 20 0.488 0.238 98 0.705 0.401 0.866 0.0060
  0.05 20 0.462 0.223 126 0.708 0.382 0.792 0.0046
  0.06 20 0.442 0.211 154 0.712 0.367 0.712 0.0037
  0.07 20 0.424 0.200 186 0.714 0.353 0.627 0.0031
  0.08 20 0.407 0.189 222 0.716 0.338 0.534 0.0026
(0.2,0.8) 0.001 20 0.800 0.537 22 0.644 0.593 1 0.0537
  0.01 20 0.676 0.372 30 0.643 0.530 0.999 0.0271
  0.02 20 0.588 0.308 48 0.680 0.474 0.982 0.0133
  0.03 20 0.532 0.272 70 0.695 0.435 0.936 0.0085
  0.04 20 0.495 0.247 94 0.703 0.408 0.872 0.0062
  0.05 20 0.467 0.229 122 0.709 0.387 0.798 0.0047
  0.06 20 0.445 0.215 152 0.711 0.370 0.717 0.0038
  0.07 20 0.425 0.202 184 0.714 0.354 0.630 0.0031
  0.08 20 0.407 0.189 222 0.716 0.339 0.534 0.0026
(0.1,0.6) or (0.4,0.9) 0.001 28 0.804 0.572 28 0.572 0.491 1 0
  0.01 28 0.655 0.368 48 0.660 0.430 0.996 0.0146
  0.02 28 0.578 0.319 76 0.689 0.393 0.958 0.0077
  0.03 28 0.540 0.299 106 0.701 0.374 0.895 0.0052
  0.04 28 0.518 0.290 132 0.706 0.362 0.824 0.0040
  0.05 28 0.504 0.285 158 0.710 0.355 0.752 0.0033
  0.06 28 0.494 0.281 180 0.713 0.349 0.680 0.0028
  0.07 28 0.486 0.278 202 0.714 0.343 0.606 0.0025
  0.08 28 0.476 0.272 226 0.715 0.336 0.528 0.0022
(0.2,0.7) or (0.3,0.8) 0.001 30 0.803 0.558 30 0.558 0.494 1 0
  0.01 30 0.682 0.412 46 0.653 0.446 0.998 0.0151
  0.02 30 0.609 0.365 72 0.686 0.410 0.966 0.0076
  0.03 30 0.570 0.342 100 0.700 0.388 0.907 0.0051
  0.04 30 0.546 0.328 126 0.706 0.374 0.837 0.0039
  0.05 30 0.529 0.317 150 0.710 0.363 0.763 0.0033
  0.06 30 0.515 0.309 174 0.713 0.354 0.688 0.0028
  0.07 30 0.503 0.300 198 0.714 0.346 0.611 0.0025
  0.08 30 0.491 0.291 226 0.716 0.337 0.529 0.0022
(0.1,0.5) or (0.5,0.9) 0.001 40 0.781 0.488 42 0.566 0.392 1 0.0393
  0.01 40 0.627 0.358 80 0.675 0.343 0.985 0.0079
  0.02 40 0.573 0.335 124 0.697 0.326 0.918 0.0043
  0.03 40 0.553 0.334 160 0.706 0.322 0.841 0.0031
  0.04 40 0.546 0.339 182 0.709 0.324 0.769 0.0026
  0.05 40 0.545 0.346 200 0.712 0.327 0.703 0.0023
  0.06 40 0.545 0.353 210 0.713 0.331 0.642 0.0021
  0.07 40 0.546 0.359 220 0.715 0.334 0.584 0.0020
  0.08 40 0.545 0.362 230 0.716 0.334 0.522 0.0019
(0.2,0.6) or (0.4,0.8) 0.001 46 0.791 0.518 48 0.587 0.395 1 0.0345
  0.01 46 0.668 0.422 80 0.668 0.360 0.991 0.0072
  0.02 46 0.617 0.401 118 0.694 0.343 0.933 0.0041
  0.03 46 0.597 0.397 150 0.704 0.339 0.860 0.0030
  0.04 46 0.588 0.397 172 0.709 0.338 0.787 0.0025
  0.05 46 0.584 0.399 190 0.712 0.338 0.719 0.0022
  0.06 46 0.580 0.400 202 0.713 0.337 0.654 0.0020
  0.07 46 0.577 0.400 216 0.714 0.337 0.589 0.0018
  0.08 46 0.572 0.398 230 0.715 0.335 0.523 0.0017
(0.3,0.7) 0.001 48 0.793 0.524 50 0.558 0.396 1 0.0167
  0.01 48 0.678 0.438 80 0.665 0.365 0.992 0.0071
  0.02 48 0.629 0.419 118 0.695 0.349 0.938 0.0039
  0.03 48 0.610 0.415 146 0.704 0.344 0.866 0.0029
  0.04 48 0.601 0.415 168 0.709 0.342 0.794 0.0024
  0.05 48 0.595 0.415 186 0.711 0.341 0.724 0.0021
  0.06 48 0.591 0.415 200 0.714 0.340 0.658 0.0020
  0.07 48 0.586 0.413 214 0.715 0.338 0.591 0.0018
  0.08 48 0.580 0.409 230 0.715 0.335 0.523 0.0017
(0.1,0.4) or (0.6,0.9) 0.001 64 0.763 0.461 72 0.588 0.292 1 0.0159
  0.01 64 0.612 0.377 156 0.689 0.262 0.951 0.0034
  0.02 64 0.588 0.381 216 0.705 0.265 0.850 0.0021
  0.03 64 0.588 0.397 242 0.709 0.276 0.768 0.0018
  0.04 64 0.594 0.414 250 0.712 0.289 0.703 0.0016
  0.05 64 0.603 0.432 250 0.714 0.302 0.649 0.0015
  0.06 64 0.613 0.449 246 0.715 0.314 0.603 0.0015
  0.07 64 0.622 0.464 238 0.715 0.325 0.560 0.0014
  0.08 64 0.628 0.474 234 0.715 0.332 0.516 0.0014
(0.2,0.5) or (0.5,0.8) 0.001 78 0.776 0.491 84 0.584 0.296 1 0.0154
  0.01 78 0.654 0.441 158 0.686 0.277 0.964 0.0031
  0.02 78 0.635 0.450 210 0.703 0.282 0.872 0.0019
  0.03 78 0.635 0.465 232 0.709 0.292 0.791 0.0016
  0.04 78 0.640 0.480 238 0.711 0.302 0.724 0.0014
  0.05 78 0.647 0.493 240 0.713 0.312 0.666 0.0014
  0.06 78 0.653 0.504 238 0.714 0.321 0.615 0.0013
  0.07 78 0.658 0.514 234 0.715 0.328 0.566 0.0013
  0.08 78 0.661 0.520 234 0.716 0.332 0.517 0.0013
(0.3,0.6) or (0.4,0.7) 0.001 84 0.775 0.483 92 0.584 0.297 1 0.0126
  0.01 84 0.666 0.457 162 0.683 0.283 0.968 0.0029
  0.02 84 0.649 0.471 210 0.702 0.289 0.881 0.0018
  0.03 84 0.652 0.489 228 0.708 0.300 0.802 0.0015
  0.04 84 0.658 0.504 234 0.712 0.309 0.735 0.0014
  0.05 84 0.663 0.516 234 0.713 0.318 0.676 0.0013
  0.06 84 0.668 0.525 232 0.714 0.324 0.621 0.0013
  0.07 84 0.671 0.532 232 0.715 0.329 0.569 0.0012
  0.08 84 0.672 0.536 234 0.716 0.333 0.517 0.0012
(0.1,0.3) or (0.7,0.9) 0.001 124 0.736 0.453 152 0.614 0.194 1 0.0057
  0.01 124 0.625 0.434 346 0.703 0.193 0.866 0.0012
  0.02 124 0.636 0.470 374 0.710 0.216 0.750 0.0010
  0.03 124 0.654 0.501 358 0.712 0.239 0.680 0.0009
  0.04 124 0.671 0.528 334 0.714 0.261 0.631 0.0009
  0.05 124 0.687 0.553 306 0.714 0.281 0.594 0.0009
  0.06 124 0.701 0.575 280 0.715 0.300 0.565 0.0009
  0.07 124 0.714 0.594 258 0.715 0.317 0.538 0.0009
  0.08 124 0.725 0.610 240 0.716 0.330 0.510 0.0009
(0.2,0.4) or (0.6,0.8) 0.001 164 0.754 0.487 190 0.605 0.197 1 0.0045
  0.01 164 0.667 0.496 372 0.702 0.205 0.887 0.0010
  0.02 164 0.683 0.537 380 0.709 0.229 0.774 0.0008
  0.03 164 0.701 0.568 356 0.712 0.251 0.702 0.0007
  0.04 164 0.716 0.593 326 0.714 0.271 0.650 0.0007
  0.05 164 0.730 0.614 300 0.714 0.289 0.609 0.0007
  0.06 164 0.742 0.632 276 0.715 0.305 0.574 0.0007
  0.07 164 0.752 0.647 254 0.715 0.319 0.543 0.0008
  0.08 164 0.760 0.659 240 0.716 0.330 0.511 0.0008
(0.3,0.5) or (0.5,0.7) 0.001 186 0.755 0.487 214 0.605 0.198 1 0.0042
  0.01 186 0.679 0.513 394 0.700 0.210 0.896 0.0009
  0.02 186 0.699 0.560 390 0.709 0.236 0.787 0.0007
  0.03 186 0.719 0.594 356 0.712 0.259 0.715 0.0007
  0.04 186 0.735 0.620 324 0.713 0.278 0.662 0.0007
  0.05 186 0.748 0.640 294 0.714 0.294 0.619 0.0007
  0.06 186 0.759 0.656 272 0.715 0.308 0.581 0.0007
  0.07 186 0.768 0.669 252 0.715 0.321 0.546 0.0007
  0.08 186 0.774 0.679 238 0.716 0.331 0.511 0.0007
(0.4,0.6) 0.001 194 0.757 0.491 222 0.603 0.198 1 0.0040
  0.01 194 0.683 0.518 402 0.700 0.211 0.898 0.0009
  0.02 194 0.704 0.567 396 0.709 0.238 0.791 0.0007
  0.03 194 0.724 0.602 358 0.712 0.261 0.720 0.0007
  0.04 194 0.741 0.628 322 0.713 0.280 0.666 0.0007
  0.05 194 0.754 0.648 294 0.714 0.296 0.622 0.0007
  0.06 194 0.765 0.664 270 0.715 0.310 0.583 0.0007
  0.07 194 0.773 0.677 252 0.715 0.321 0.547 0.0007
  0.08 194 0.779 0.686 238 0.716 0.331 0.511 0.0007
(0.1,0.2) or (0.8,0.9) 0.001 398 0.683 0.470 676 0.675 0.098 0.981 0.0007
  0.01 398 0.712 0.584 794 0.712 0.141 0.708 0.0003
  0.02 398 0.750 0.642 618 0.714 0.179 0.626 0.0003
  0.03 398 0.775 0.679 504 0.715 0.211 0.586 0.0003
  0.04 398 0.794 0.706 424 0.715 0.239 0.562 0.0003
  0.05 398 0.809 0.728 364 0.715 0.265 0.544 0.0004
  0.06 398 0.822 0.747 316 0.716 0.288 0.530 0.0004
  0.07 398 0.833 0.763 276 0.716 0.310 0.518 0.0004
  0.08 398 0.843 0.777 244 0.716 0.328 0.505 0.0004
(0.2,0.3) or (0.7,0.8) 0.001 588 0.701 0.495 924 0.672 0.100 0.985 0.0005
  0.01 588 0.746 0.633 922 0.711 0.149 0.727 0.0002
  0.02 588 0.787 0.695 666 0.714 0.188 0.644 0.0002
  0.03 588 0.812 0.731 524 0.715 0.218 0.601 0.0003
  0.04 588 0.829 0.756 432 0.715 0.245 0.573 0.0003
  0.05 588 0.842 0.775 366 0.716 0.269 0.552 0.0003
  0.06 588 0.853 0.791 316 0.716 0.291 0.535 0.0003
  0.07 588 0.863 0.805 276 0.716 0.311 0.520 0.0003
  0.08 588 0.871 0.816 244 0.716 0.328 0.506 0.0003
(0.3,0.4) or (0.6,0.7) 0.001 712 0.704 0.500 1100 0.671 0.101 0.986 0.0004
  0.01 712 0.756 0.647 1034 0.711 0.153 0.736 0.0002
  0.02 712 0.800 0.713 714 0.714 0.193 0.654 0.0005
  0.03 712 0.825 0.751 544 0.714 0.224 0.611 0.0002
  0.04 712 0.843 0.776 440 0.715 0.250 0.581 0.0002
  0.05 712 0.856 0.795 368 0.715 0.273 0.559 0.0002
  0.06 712 0.867 0.810 314 0.716 0.294 0.540 0.0002
  0.07 712 0.875 0.823 274 0.716 0.312 0.523 0.0002
  0.08 712 0.882 0.833 244 0.716 0.329 0.506 0.0003
(0.4,0.5) or (0.5,0.6) 0.001 776 0.706 0.502 1190 0.670 0.101 0.986 0.0004
  0.01 776 0.760 0.652 1096 0.711 0.154 0.740 0.0002
  0.02 776 0.804 0.720 744 0.713 0.195 0.659 0.0002
  0.03 776 0.831 0.758 558 0.714 0.226 0.615 0.0002
  0.04 776 0.849 0.784 446 0.715 0.253 0.586 0.0002
  0.05 776 0.862 0.803 368 0.715 0.275 0.562 0.0002
  0.06 776 0.872 0.818 314 0.716 0.295 0.542 0.0002
  0.07 776 0.881 0.830 274 0.716 0.313 0.524 0.0002
  0.08 776 0.887 0.840 244 0.716 0.329 0.506 0.0002