Table 1 Boundary values and type I error rate spent for Bayesian and frequentist five-look group sequential tests

Bayesian tests

I₀

θ₀

p₁=⋯=p₅

\(u^{B}_{1}, \ldots, u^{B}_{5}\)

\(\alpha ^{B}_{1}, \ldots, \alpha ^{B}_{5}\)

20.0

-0.25

0.6063

4.43, 3.16, 2.60, 2.27, 2.05

0.0000, 0.0008, 0.0049, 0.0133, 0.0250

1.0

-0.25

0.9818

2.74, 2.46, 2.36, 2.31, 2.27

0.0031, 0.0089, 0.0148, 0.0202, 0.0250

1.0

0.00

0.9856

2.68, 2.45, 2.36, 2.32, 2.29

0.0037, 0.0097, 0.0155, 0.0205, 0.0250

1.0

0.25

0.9889

2.62, 2.43, 2.37, 2.34, 2.32

0.0044, 0.0105, 0.0161, 0.0209, 0.0250

1.0

0.50

0.9914

2.57, 2.42, 2.37, 2.35, 2.34

0.0051, 0.0114, 0.0168, 0.0213, 0.0251

0.5

-0.25

0.9872

2.58, 2.43, 2.37, 2.35, 2.33

0.0049, 0.0110, 0.0163, 0.0210, 0.0250

0.5

0.00

0.9888

2.55, 2.42, 2.38, 2.36, 2.34

0.0053, 0.0114, 0.0167, 0.0212, 0.0250

0.5

0.25

0.9903

2.53, 2.42, 2.38, 2.37, 2.36

0.0058, 0.0119, 0.0171, 0.0213, 0.0250

0.5

0.50

0.9916

2.50, 2.41, 2.39, 2.38, 2.37

0.0063, 0.0124, 0.0174, 0.0215, 0.0250

0.0

0.00

0.9921

2.41, 2.41, 2.41, 2.41, 2.41

0.0079, 0.0138, 0.0183, 0.0220, 0.0250

Frequentist tests

u₁,…,u₅

α₁,…,α₅

O’Brien & Fleming

4.56, 3.23, 2.63, 2.28, 2.04

0.0000, 0.0006, 0.0045, 0.0128, 0.0250

Pocock

2.41, 2.41, 2.41, 2.41, 2.41

0.0079, 0.0138, 0.0183, 0.0219, 0.0250

α^∗(t)=αt

2.58, 2.49, 2.41, 2.34, 2.28

0.0050, 0.0100, 0.0150, 0.0200, 0.0250