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Table 3 Optimal design parameters for additively adjusted program set-ups

From: Optimal designs for phase II/III drug development programs including methods for discounting of phase II results

Additively adjusted
Program set-up \( S\left({\hat{\theta}}_2^u,{\hat{\theta}}_2^{\alpha_{CI}}\right) \) Program set-up \( S\left({\hat{\theta}}_2^{\alpha_{CI}},{\hat{\theta}}_2^{\alpha_{CI}}\right) \)
bs αCI \( {HR}_{go}^{\ast } \) \( {d}_2^{\ast } \) \( {\varepsilon}_2^{\ast } \) \( {d}_3^{\ast } \) d \( {p}_{go}^{\ast } \) sP u αCI \( {HR}_{go}^{\ast } \) \( {d}_2^{\ast } \) \( {\varepsilon}_2^{\ast } \) \( {d}_3^{\ast } \) d \( {p}_{go}^{\ast } \) sP u
w = .3, i.e., \( \mathbf{\exp}\left(-\mathbf{E}\left[{\hat{\boldsymbol{\theta}}}_{\mathbf{2}}\right]\right)=.\mathbf{82} \)
1 .450 .78 88 .66 140 228 .42 .24 78 .450 .80 84 .65 138 222 .42 .23 78
2 .400 .79 113 .68 188 301 .43 .27 194 .400 .83 116 .69 192 308 .43 .28 194
3 .425 .81 140 .69 220 360 .47 .31 302 .425 .84 133 .69 229 362 .47 .31 302
4 .375 .81 155 .71 261 416 .46 .32 442 .400 .85 161 .71 261 422 .48 .33 442
5 .350 .81 189 .72 278 467 .46 .34 593 .350 .86 182 .72 289 471 .47 .34 593
6 .400 .83 190 .72 310 500 .50 .36 573 .425 .86 186 .71 311 497 .52 .36 573
7 .375 .83 204 .72 336 540 .50 .37 729 .375 .87 203 .73 346 549 .51 .37 729
w = .6, i.e., \( \mathbf{\exp}\left(-\mathbf{E}\left[{\hat{\boldsymbol{\theta}}}_{\mathbf{2}}\right]\right)=.\mathbf{76} \)
1 .450 .81 140 .66 226 366 .60 .43 372 .425 .83 130 .67 226 356 .58 .43 372
2 .350 .80 168 .69 278 446 .58 .46 614 .350 .85 172 .69 282 454 .58 .46 614
3 .425 .83 175 .68 304 479 .64 .49 772 .425 .85 193 .68 296 489 .64 .49 772
4 .350 .82 224 .70 341 565 .62 .51 1045 .325 .87 228 .71 366 594 .62 .52 1045
5 .250 .81 273 .72 406 679 .60 .53 1338 .275 .88 249 .72 411 660 .62 .53 1338
6 .375 .84 252 .70 395 647 .67 .54 1221 .375 .87 252 .70 376 628 .66 .54 1222
7 .300 .83 287 .72 437 724 .65 .56 1515 .300 .88 273 .72 419 692 .64 .55 1515
w = .9, i.e., \( \mathbf{\exp}\left(-\mathbf{E}\left[{\hat{\boldsymbol{\theta}}}_{\mathbf{2}}\right]\right)=.\mathbf{71} \)
1 .425 .82 168 .66 296 464 .75 .61 695 .450 .84 168 .66 284 452 .76 .61 695
2 .350 .82 203 .69 371 574 .76 .65 1068 .350 .86 210 .68 355 565 .76 .65 1068
3 .400 .84 224 .68 381 605 .80 .68 1272 .400 .87 228 .68 385 613 .80 .68 1272
4 .325 .83 252 .70 433 685 .79 .69 1681 .300 .88 280 .70 446 726 .79 .70 1682
5 .250 .82 308 .71 482 790 .78 .71 2122 .225 .89 315 .72 510 825 .78 .71 2122
6 .350 .84 287 .69 434 721 .81 .71 1898 .350 .88 294 .69 438 732 .82 .71 1898
7 .275 .83 315 .71 489 804 .80 .72 2333 .275 .89 326 .71 500 826 .81 .73 2334
  1. Optimal design parameters αCI, \( {d}_2^{\ast } \) and \( {HR}_{go}^{\ast } \), corresponding value of expected utility u, expected estimate used for sample size calculation \( {\varepsilon}_2^{\ast } \), expected number of events in phase III when going to phase III \( {d}_3^{\ast } \), expected total number of events of program d, expected probability to go to phase III \( {p}_{go}^{\ast } \), and expected probability of a successful program sP for the optimal design, for c2 = 0.75,c3 = 1, c02 = 100,c03 = 150 in $ 105, ξ2= ξ3 = 0.7, 1 − β = 0.9, α = 0.025 (one sided), benefit scenarios bs 1–7, weights for the prior distribution w = 0.3, 0.6, 0.9 for the additively adjusted program set-ups \( S\left({\hat{\theta}}_2^{s_1},{\hat{\theta}}_2^{\alpha_{CI}}\right) \)