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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