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Table 2 Optimal design parameters for unadjusted and multiplicatively adjusted program set-ups

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

  Unadjusted Multiplicatively adjusted
Program set-up \( S\left({\hat{\theta}}_2^u,{\hat{\theta}}_2^u\right) \) Program set-up \( S\left({\hat{\theta}}_2^u,{\hat{\theta}}_2^{\lambda}\right) \) Program set-up \( S\left({\hat{\theta}}_2^{\lambda },{\hat{\theta}}_2^{\lambda}\right) \)
bs \( {HR}_{go}^{\ast } \) \( {d}_2^{\ast } \) \( {\varepsilon}_2^{\ast } \) \( {d}_3^{\ast } \) d \( {p}_{go}^{\ast } \) sP u λ \( {HR}_{go}^{\ast } \) \( {d}_2^{\ast } \) \( {\varepsilon}_2^{\ast } \) \( {d}_3^{\ast } \) d \( {p}_{go}^{\ast } \) sP u λ \( {HR}_{go}^{\ast } \) \( {d}_2^{\ast } \) \( {\varepsilon}_2^{\ast } \) \( {d}_3^{\ast } \) 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 .80 82 .65 146 228 .46 .24 76 .750 .76 81 .70 170 251 .38 .25 99 .750 .81 84 .70 161 245 .37 .25 100
2 .82 109 .67 189 298 .49 .28 188 .700 .77 116 .73 222 338 .39 .29 235 .725 .83 112 .73 214 326 .40 .29 235
3 .83 133 .68 218 351 .51 .31 299 .750 .80 133 .74 275 408 .45 .33 343 .750 .84 133 .73 252 385 .43 .32 343
4 .84 144 .69 248 392 .53 .33 432 .700 .80 158 .75 320 478 .44 .35 509 .725 .85 161 .75 296 457 .44 .34 508
5 .85 161 .70 284 445 .55 .35 569 .700 .81 196 .76 366 562 .46 .38 690 .700 .86 182 .76 348 530 .45 .37 690
6 .85 172 .70 287 459 .55 .35 567 .750 .82 179 .75 357 536 .48 .38 640 .750 .86 175 .75 347 522 .48 .37 640
7 .86 193 .71 331 524 .57 .38 712 .700 .82 196 .77 413 609 .48 .40 828 .700 .87 200 .77 412 612 .48 .40 828
w = .6, i.e., \( \mathbf{\exp}\left(-\mathbf{E}\left[{\hat{\boldsymbol{\theta}}}_{\mathbf{2}}\right]\right)=.\mathbf{76} \)
1 .82 133 .65 213 346 .61 .43 370 .775 .79 126 .71 265 391 .55 .45 412 .775 .83 140 .71 259 399 .55 .45 411
2 .84 147 .66 262 409 .65 .46 598 .725 .80 175 .73 348 523 .58 .50 696 .725 .85 168 .73 343 511 .58 .50 696
3 .85 182 .67 299 481 .68 .50 764 .775 .82 196 .73 374 570 .62 .53 849 .750 .86 189 .73 390 579 .62 .53 849
4 .86 196 .68 333 529 .70 .52 1012 .700 .82 210 .75 462 672 .62 .56 1172 .700 .87 217 .75 462 679 .62 .56 1172
5 .86 210 .68 336 546 .70 .52 1267 .675 .82 245 .76 505 750 .62 .57 1523 .675 .88 238 .76 542 780 .64 .58 1521
6 .86 217 .68 338 555 .70 .53 1200 .750 .83 235 .74 450 685 .64 .57 1342 .750 .87 238 .74 453 691 .65 .57 1343
7 .87 217 .69 374 591 .72 .54 1460 .700 .83 259 .76 521 780 .65 .59 1693 .700 .88 249 .76 535 784 .65 .59 1693
w = .9, i.e., \( \mathbf{\exp}\left(-\mathbf{E}\left[{\hat{\boldsymbol{\theta}}}_{\mathbf{2}}\right]\right)=.\mathbf{71} \)
1 .84 154 .65 278 432 .78 .60 693 .800 .81 161 .70 346 507 .73 .64 753 .775 .85 158 .71 370 528 .73 .65 753
2 .86 182 .66 332 514 .82 .65 1039 .725 .82 203 .73 472 675 .76 .70 1193 .725 .86 210 .73 447 657 .75 .69 1193
3 .86 207 .66 338 545 .83 .66 1255 .750 .83 217 .73 480 697 .78 .72 1384 .750 .87 231 .73 486 717 .79 .73 1384
4 .87 221 .67 367 588 .84 .68 1623 .700 .83 252 .75 562 814 .79 .75 1871 .700 .88 245 .75 573 818 .79 .75 1871
5 .88 235 .67 399 634 .86 .70 1996 .650 .83 287 .76 661 948 .80 .77 2394 .675 .89 280 .76 665 945 .81 .78 2394
6 .88 245 .67 401 646 .86 .70 1855 .725 .84 277 .74 570 847 .81 .76 2072 .750 .88 266 .73 544 810 .81 .76 2072
7 .88 256 .67 402 658 .86 .70 2233 .700 .85 301 .75 664 965 .83 .79 2589 .700 .89 298 .75 647 945 .82 .78 2590
  1. Optimal design parameters λ, \( {d}_2^{\ast } \) and \( {HR}_{go}^{\ast } \), corresponding value of maximal 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 unadjusted program set-up \( S\left({\hat{\theta}}_2^u,{\hat{\theta}}_2^u\right) \) and multiplicatively adjusted program set-ups \( S\left({\hat{\theta}}_2^{s_1},{\hat{\theta}}_2^{\lambda}\right) \), respectively