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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