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Table 5 Comparison between the proposed two-stage optimal design with survival endpoint and Simon’s two-stage optimal 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 optimal 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 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%)
  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