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Table 6 Sample scenarios assuming beta priors p(π 1) and p(π 2) where \(\tau _{1}^{2}=0.08\). 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

  (\(\tau _{1}^{2}=0.08\)) Traditional design CEP design  
(m 1,m 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 0.127 0.389 70 0.703 0.459 0.913 0.0096
  0.01 10 0.097 0.356 88 0.707 0.435 0.861 0.0078
  0.02 10 0.083 0.335 102 0.709 0.417 0.815 0.0068
  0.03 10 0.075 0.319 118 0.711 0.402 0.774 0.0059
  0.04 10 0.069 0.306 132 0.712 0.389 0.734 0.0053
  0.05 10 0.064 0.294 148 0.713 0.378 0.693 0.0047
  0.06 10 0.060 0.283 166 0.713 0.366 0.650 0.0042
  0.07 10 0.056 0.273 186 0.714 0.355 0.602 0.0037
(0.1,0.8) 0.001 14 0.147 0.399 114 0.710 0.407 0.825 0.0056
  0.01 14 0.134 0.387 124 0.710 0.396 0.794 0.0052
  0.02 14 0.128 0.377 134 0.711 0.386 0.760 0.0049
  0.03 14 0.124 0.368 146 0.712 0.378 0.728 0.0045
  0.04 14 0.121 0.360 158 0.713 0.370 0.695 0.0041
  0.05 14 0.118 0.353 170 0.713 0.362 0.661 0.0038
  0.06 14 0.116 0.346 184 0.714 0.355 0.625 0.0035
  0.07 14 0.113 0.339 198 0.715 0.348 0.586 0.0033
(0.1,0.7) 0.001 20 0.174 0.415 172 0.713 0.355 0.731 0.0035
  0.01 20 0.172 0.414 176 0.713 0.353 0.712 0.0035
  0.02 20 0.174 0.413 182 0.713 0.350 0.691 0.0033
  0.03 20 0.177 0.412 188 0.714 0.348 0.669 0.0032
  0.04 20 0.180 0.411 192 0.714 0.346 0.646 0.0031
  0.05 20 0.183 0.410 200 0.715 0.344 0.622 0.0030
  0.06 20 0.185 0.409 206 0.714 0.342 0.596 0.0028
  0.07 20 0.187 0.408 214 0.715 0.340 0.567 0.0027
(0.2,0.8) 0.001 20 0.264 0.488 118 0.710 0.403 0.821 0.0046
  0.01 20 0.247 0.475 128 0.711 0.393 0.789 0.0043
  0.02 20 0.233 0.462 138 0.712 0.384 0.755 0.0041
  0.03 20 0.223 0.451 150 0.712 0.375 0.723 0.0038
  0.04 20 0.215 0.442 162 0.713 0.367 0.690 0.0035
  0.05 20 0.208 0.433 174 0.713 0.360 0.656 0.0033
  0.06 20 0.201 0.424 188 0.714 0.353 0.620 0.0031
  0.07 20 0.195 0.416 202 0.715 0.346 0.580 0.0029
(0.1,0.6) 0.001 28 0.193 0.426 252 0.715 0.303 0.632 0.0023
  0.01 28 0.199 0.431 250 0.715 0.307 0.623 0.0023
  0.02 28 0.209 0.437 246 0.715 0.311 0.613 0.0023
  0.03 28 0.220 0.443 244 0.715 0.316 0.601 0.0023
  0.04 28 0.231 0.449 240 0.715 0.320 0.589 0.0023
  0.05 28 0.241 0.456 238 0.715 0.324 0.576 0.0023
  0.06 28 0.252 0.463 234 0.715 0.328 0.562 0.0022
  0.07 28 0.262 0.469 230 0.715 0.332 0.546 0.0022
(0.2,0.7) 0.001 30 0.302 0.510 178 0.713 0.352 0.725 0.0028
  0.01 30 0.298 0.507 182 0.713 0.350 0.706 0.0027
  0.02 30 0.295 0.504 186 0.714 0.348 0.685 0.0027
  0.03 30 0.293 0.502 192 0.714 0.346 0.663 0.0026
  0.04 30 0.292 0.499 198 0.714 0.344 0.640 0.0025
  0.05 30 0.291 0.497 204 0.714 0.342 0.616 0.0024
  0.06 30 0.291 0.495 210 0.715 0.340 0.590 0.0024
  0.07 30 0.291 0.493 218 0.715 0.338 0.561 0.0023
(0.1,0.5) 0.001 40 0.213 0.437 364 0.716 0.253 0.531 0.0016
  0.01 40 0.226 0.448 350 0.716 0.262 0.530 0.0016
  0.02 40 0.244 0.461 334 0.716 0.272 0.529 0.0016
  0.03 40 0.264 0.474 318 0.716 0.282 0.528 0.0016
  0.04 40 0.283 0.488 300 0.715 0.293 0.527 0.0017
  0.05 40 0.303 0.502 284 0.716 0.303 0.526 0.0017
  0.06 40 0.323 0.516 266 0.716 0.313 0.525 0.0017
  0.07 40 0.342 0.530 248 0.716 0.324 0.523 0.0018
(0.2,0.6) 0.001 46 0.343 0.536 258 0.715 0.301 0.625 0.0018
  0.01 46 0.347 0.539 256 0.715 0.305 0.617 0.0018
  0.02 46 0.352 0.543 252 0.715 0.309 0.606 0.0018
  0.03 46 0.359 0.547 250 0.715 0.314 0.595 0.0017
  0.04 46 0.366 0.552 246 0.715 0.318 0.583 0.0017
  0.05 46 0.373 0.556 242 0.715 0.322 0.570 0.0017
  0.06 46 0.382 0.562 238 0.715 0.326 0.556 0.0017
  0.07 46 0.390 0.567 234 0.716 0.330 0.540 0.0017
(0.3,0.7) 0.001 48 0.435 0.605 182 0.713 0.349 0.718 0.0021
  0.01 48 0.431 0.602 186 0.713 0.347 0.700 0.0020
  0.02 48 0.427 0.599 192 0.714 0.345 0.679 0.0020
  0.03 48 0.423 0.596 196 0.714 0.343 0.657 0.0020
  0.04 48 0.419 0.592 202 0.714 0.342 0.634 0.0019
  0.05 48 0.416 0.589 208 0.715 0.340 0.610 0.0019
  0.06 48 0.414 0.586 214 0.715 0.338 0.584 0.0018
  0.07 48 0.411 0.583 222 0.715 0.336 0.555 0.0017
(0.1,0.4) 0.001 64 0.258 0.468 532 0.716 0.202 0.428 0.0010
  0.01 64 0.281 0.486 494 0.716 0.217 0.435 0.0010
  0.02 64 0.308 0.506 452 0.716 0.234 0.444 0.0011
  0.03 64 0.336 0.526 412 0.716 0.250 0.454 0.0011
  0.04 64 0.363 0.546 374 0.716 0.267 0.464 0.0011
  0.05 64 0.391 0.566 338 0.716 0.283 0.475 0.0012
  0.06 64 0.418 0.586 302 0.716 0.299 0.487 0.0013
  0.07 64 0.446 0.607 268 0.716 0.316 0.501 0.0013
(0.2,0.5) 0.001 78 0.404 0.577 374 0.716 0.251 0.524 0.0011
  0.01 78 0.414 0.585 358 0.716 0.260 0.523 0.0011
  0.02 78 0.427 0.594 342 0.716 0.270 0.522 0.0011
  0.03 78 0.441 0.604 326 0.716 0.281 0.521 0.0011
  0.04 78 0.455 0.615 308 0.716 0.291 0.521 0.0011
  0.05 78 0.470 0.625 290 0.716 0.301 0.520 0.0012
  0.06 78 0.486 0.637 272 0.716 0.312 0.519 0.0012
  0.07 78 0.503 0.649 254 0.716 0.322 0.518 0.0012
(0.3,0.6) 0.001 84 0.497 0.647 266 0.715 0.299 0.618 0.0012
  0.01 84 0.501 0.649 264 0.715 0.303 0.609 0.0012
  0.02 84 0.505 0.652 260 0.715 0.307 0.599 0.0012
  0.03 84 0.509 0.655 256 0.715 0.311 0.588 0.0012
  0.04 84 0.514 0.658 252 0.715 0.316 0.576 0.0012
  0.05 84 0.519 0.661 248 0.715 0.320 0.564 0.0012
  0.06 84 0.524 0.665 244 0.715 0.324 0.550 0.0012
  0.07 84 0.530 0.668 240 0.716 0.328 0.534 0.0012
(0.1,0.3) 0.001 124 0.339 0.526 808 0.717 0.153 0.323 0.0006
  0.01 124 0.376 0.554 708 0.717 0.176 0.341 0.0006
  0.02 124 0.414 0.582 612 0.717 0.200 0.361 0.0006
  0.03 124 0.450 0.608 530 0.717 0.223 0.382 0.0007
  0.04 124 0.483 0.632 458 0.717 0.245 0.404 0.0007
  0.05 124 0.515 0.656 394 0.717 0.266 0.428 0.0007
  0.06 124 0.546 0.679 338 0.717 0.287 0.452 0.0008
  0.07 124 0.578 0.702 286 0.716 0.308 0.480 0.0009
(0.2,0.4) 0.001 164 0.502 0.647 546 0.717 0.201 0.420 0.0006
  0.01 164 0.519 0.659 506 0.716 0.216 0.428 0.0006
  0.02 164 0.537 0.672 464 0.717 0.233 0.437 0.0006
  0.03 164 0.557 0.686 422 0.717 0.249 0.447 0.0006
  0.04 164 0.576 0.700 382 0.716 0.265 0.457 0.0006
  0.05 164 0.596 0.715 344 0.716 0.282 0.469 0.0007
  0.06 164 0.617 0.730 308 0.716 0.298 0.482 0.0007
  0.07 164 0.638 0.745 272 0.716 0.314 0.495 0.0007
(0.3,0.5) 0.001 186 0.597 0.716 384 0.716 0.249 0.516 0.0006
  0.01 186 0.605 0.721 368 0.716 0.258 0.515 0.0006
  0.02 186 0.614 0.728 352 0.716 0.269 0.515 0.0006
  0.03 186 0.623 0.735 334 0.716 0.279 0.514 0.0006
  0.04 186 0.633 0.742 314 0.716 0.289 0.514 0.0006
  0.05 186 0.644 0.749 296 0.716 0.299 0.513 0.0007
  0.06 186 0.655 0.757 278 0.716 0.310 0.513 0.0007
  0.07 186 0.667 0.766 258 0.716 0.320 0.512 0.0007
(0.4,0.6) 0.001 194 0.662 0.763 274 0.715 0.296 0.610 0.0007
  0.01 194 0.664 0.764 270 0.715 0.301 0.602 0.0007
  0.02 194 0.667 0.766 266 0.715 0.305 0.592 0.0007
  0.03 194 0.669 0.768 262 0.715 0.309 0.581 0.0007
  0.04 194 0.672 0.770 258 0.715 0.314 0.569 0.0007
  0.05 194 0.675 0.772 254 0.715 0.318 0.557 0.0007
  0.06 194 0.679 0.774 250 0.716 0.322 0.543 0.0007
  0.07 194 0.682 0.777 244 0.716 0.326 0.528 0.0007
(0.1,0.2) 0.001 398 0.506 0.648 1346 0.717 0.104 0.218 0.0002
  0.01 398 0.563 0.691 978 0.714 0.139 0.247 0.0003
  0.02 398 0.606 0.720 814 0.717 0.172 0.286 0.0003
  0.03 398 0.642 0.746 660 0.717 0.201 0.319 0.0003
  0.04 398 0.673 0.768 542 0.717 0.227 0.352 0.0003
  0.05 398 0.700 0.788 450 0.717 0.253 0.386 0.0003
  0.06 398 0.726 0.807 372 0.717 0.277 0.422 0.0004
  0.07 398 0.751 0.825 304 0.716 0.302 0.460 0.0004
(0.2,0.3) 0.001 588 0.667 0.765 828 0.717 0.152 0.316 0.0002
  0.01 588 0.691 0.783 694 0.714 0.175 0.330 0.0002
  0.02 588 0.709 0.794 624 0.717 0.199 0.355 0.0002
  0.03 588 0.728 0.808 540 0.717 0.222 0.376 0.0002
  0.04 588 0.747 0.821 466 0.717 0.243 0.398 0.0002
  0.05 588 0.764 0.834 402 0.717 0.265 0.422 0.0003
  0.06 588 0.781 0.846 344 0.717 0.286 0.447 0.0003
  0.07 588 0.799 0.858 292 0.716 0.307 0.474 0.0003
(0.3,0.4) 0.001 712 0.748 0.822 560 0.717 0.200 0.413 0.0002
  0.01 712 0.761 0.832 502 0.715 0.215 0.416 0.0002
  0.02 712 0.767 0.836 474 0.717 0.231 0.430 0.0002
  0.03 712 0.778 0.843 432 0.716 0.248 0.440 0.0002
  0.04 712 0.788 0.851 390 0.716 0.264 0.451 0.0002
  0.05 712 0.799 0.859 352 0.716 0.280 0.462 0.0002
  0.06 712 0.810 0.866 314 0.716 0.296 0.475 0.0002
  0.07 712 0.821 0.874 278 0.716 0.312 0.490 0.0002
(0.4,0.5) 0.001 776 0.797 0.857 394 0.716 0.247 0.508 0.0002
  0.01 776 0.803 0.863 368 0.714 0.257 0.503 0.0002
  0.02 776 0.806 0.863 360 0.716 0.267 0.507 0.0002
  0.03 776 0.811 0.867 342 0.716 0.277 0.507 0.0002
  0.04 776 0.816 0.871 322 0.716 0.287 0.507 0.0002
  0.05 776 0.822 0.875 302 0.716 0.298 0.506 0.0002
  0.06 776 0.827 0.879 284 0.716 0.308 0.506 0.0002
  0.07 776 0.834 0.883 264 0.716 0.318 0.506 0.0002