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Table 4 Comparison between the proposed two-stage minimax design with survival endpoint and Simon’s two-stage minimax design with binary endpoint with or without interim accrual, when α=5%, β=20%, and the shape parameter k=0.5 in the Weibull distribution

From: Two-stage optimal designs with survival endpoint when the follow-up time is restricted

       Simon’s two-stage minimax designs
   Survival endpoint No interim accrual Interim accrual
S0(tc) S1(tc) n 1 n E S S 0 E T S L 0 n 1 n 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%)
  1. % is for the ESS0 or the ETSL0 percentage saving of the new proposed two-stage design as compared to Simon’s two-stage design, which is computed as (Simon-New)/Simon. When the percentage saving is positive, the new design requires a smaller ESS0 or a shorter ETSL0 as compared to the existing Simon’s design
  2. The patient accrual rate θ is determined by the sample size from Simon’s minimax design with no interim accrual as θ=nminimax/3