Background
Methods
Simon’s two-stage designs with binary endpoint
Survival endpoint | Simon’s design, interim accrual | ||||||||||||
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The proposed method | Belin | No | Yes | ||||||||||
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Minimax | 44 | 73 | 0.240 | -1.281 | 61.3 | 3.1 | 59.3 | 4.0 | 72 | 69.8 | 3.5 | ||
Optimal | 41 | 79 | -0.085 | -1.279 | 58.7 | 2.9 | 59.1 | 69 | 53.2 | 3.6 | 81 | 67.4 | 3.2 |
Two-stage optimal designs with survival endpoint when the follow-up time is limited
Optimal design search
Results
Minimax design | Optimal design | Belin | |||||||||||
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Power |
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90% | 15 | 28 | 52 | -0.10 | -1.64 | 39.1 | 26 | 56 | -0.30 | -1.64 | 37.5 | 53 | 42.3 |
95% | 15 | 36 | 65 | -0.09 | -1.64 | 49.5 | 33 | 70 | -0.29 | -1.64 | 47.3 | 65 | 52.6 |
90% | 30 | 30 | 52 | 0.30 | -1.64 | 43.6 | 30 | 55 | -0.04 | -1.64 | 42.2 | 53 | 44.6 |
95% | 30 | 40 | 65 | 0.19 | -1.64 | 54.3 | 40 | 69 | -0.20 | -1.64 | 52.2 | 65 | 54.8 |
90% | 50 | 34 | 52 | 0.51 | -1.64 | 46.5 | 32 | 54 | 0.32 | -1.63 | 45.7 | 52 | 47.0 |
95% | 50 | 44 | 65 | 0.46 | -1.64 | 58.2 | 42 | 68 | 0.17 | -1.64 | 56.7 | 64 | 57.5 |
Minimax design | Optimal design | ||||
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Power |
θ
| TIE | Power | TIE | Power |
90% | 15 | 0.040 (0.036,0.044) | 0.907 (0.901,0.913) | 0.037 (0.033,0.041) | 0.903 (0.898,0.909) |
95% | 15 | 0.041 (0.037,0.045) | 0.957 (0.953,0.961) | 0.038 (0.035,0.042) | 0.955 (0.951,0.959) |
90% | 30 | 0.040 (0.037,0.044) | 0.911 (0.905,0.916) | 0.039 (0.035,0.043) | 0.910 (0.904,0.916) |
95% | 30 | 0.042 (0.038,0.046) | 0.959 (0.955,0.963) | 0.040 (0.036,0.044) | 0.958 (0.954,0.962) |
90% | 50 | 0.041 (0.037,0.045) | 0.911 (0.905,0.916) | 0.040 (0.037,0.044) | 0.909 (0.903,0.914) |
95% | 50 | 0.042 (0.038,0.046) | 0.960 (0.956,0.963) | 0.041 (0.037,0.045) | 0.959 (0.955,0.963) |
Simon’s two-stage minimax designs | |||||||||||
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Survival endpoint | No interim accrual | Interim accrual | |||||||||
S0(tc) | S1(tc) |
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| ESS0(%) | ETSL0(%) | ESS0(%) | ETSL0(%) |
0.1 | 0.2 | 37 | 63 | 50.5 | 2.5 | 45 | 78 | 60.6 (17%) | 3.8 (35%) | 74.3 (32%) | 3.3 (26%) |
0.1 | 0.25 | 19 | 33 | 26.2 | 2.5 | 22 | 40 | 28.8 (9%) | 3.5 (30%) | 37.5 (30%) | 3.1 (21%) |
0.1 | 0.3 | 11 | 21 | 15.6 | 2.3 | 15 | 25 | 19.5 (20%) | 3.8 (39%) | 24.5 (36%) | 3.3 (30%) |
0.6 | 0.7 | 87 | 162 | 126.6 | 3.2 | 139 | 142 | 139.2 (9%) | 4.0 (20%) | 184.5 (31%) | 3.9 (19%) |
0.6 | 0.75 | 33 | 70 | 49.4 | 2.8 | 30 | 62 | 43.8 (-13%) | 3.6 (20%) | 55.7 (11%) | 3.1 (9%) |
0.6 | 0.8 | 17 | 39 | 26.0 | 2.6 | 13 | 35 | 20.8 (-25%) | 3.1 (16%) | 28.5 (9%) | 2.8 (5%) |
Simon’s two-stage optimal designs | |||||||||||
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Survival endpoint | No interim accrual | Interim accrual | |||||||||
S0(tc) | S1(tc) |
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| ESS0(%) | ETSL0(%) | ESS0(%) | ETSL0(%) |
0.1 | 0.2 | 26 | 72 | 45.1 | 2.2 | 30 | 89 | 50.8 (11%) | 3.3 (35%) | 67.6 (33%) | 3.0 (27%) |
0.1 | 0.25 | 15 | 37 | 24.0 | 2.2 | 18 | 43 | 24.7 (3%) | 3.1 (29%) | 34.9 (31%) | 2.8 (22%) |
0.1 | 0.3 | 10 | 23 | 15.0 | 2.2 | 10 | 29 | 15.0 (0%) | 3.1 (29%) | 21.6 (30%) | 2.8 (21%) |
0.6 | 0.7 | 66 | 179 | 109.2 | 2.7 | 53 | 173 | 91.4 (-20%) | 3.3 (18%) | 124.0 (12%) | 2.9 (9%) |
0.6 | 0.75 | 27 | 76 | 46.1 | 2.6 | 27 | 67 | 39.4 (-17%) | 3.2 (18%) | 53.9 (14%) | 2.9 (10%) |
0.6 | 0.8 | 15 | 41 | 25.1 | 2.5 | 11 | 43 | 20.5 (-23%) | 3.1 (17%) | 28.9 (13%) | 2.8 (7%) |