Type 1 error
Power
Design
κ
Test
At
k
th
interim look
k
= 1
k
= 2
total
k
= 1
k
= 2
total
δ=1.5
0.5
Z
(
t
)
Empirical
0.0067
0.0457
0.0524
0.3659
0.4293
0.7952
S
(
t
)
Empirical
0.0082
0.0435
0.0517
0.4104
0.3887
0.7992
L
(
t
)
Empirical
0.0066
0.046
0.0526
0.3545
0.4402
0.7947
Nominal
0.0068
0.0435
0.0503
0.3686
0.4311
0.7997
1
Z
(
t
)
Empirical
0.0052
0.0484
0.0535
0.2874
0.5062
0.7936
S
(
t
)
Empirical
0.0066
0.0454
0.0521
0.3397
0.4594
0.799
L
(
t
)
Empirical
0.0058
0.0483
0.0541
0.2674
0.5245
0.7918
Nominal
0.0055
0.045
0.0505
0.2912
0.5083
0.7995
2.0
Z
(
t
)
Empirical
0.0037
0.0503
0.054
0.185
0.6096
0.7946
S
(
t
)
Empirical
0.0054
0.0448
0.0502
0.2541
0.547
0.801
L
(
t
)
Empirical
0.0043
0.0498
0.0541
0.1655
0.6257
0.7912
Nominal
0.0045
0.0463
0.0508
0.1997
0.5994
0.7991
δ =1.7
0.5
Z
(
t
)
Empirical
0.0037
0.0457
0.0494
0.2611
0.556
0.8171
S
(
t
)
Empirical
0.0059
0.0455
0.0514
0.3054
0.4989
0.8043
L
(
t
)
Empirical
0.0041
0.0457
0.0497
0.2708
0.5467
0.8176
Nominal
0.0054
0.0451
0.0505
0.2851
5144
0.7995
1
Z
(
t
)
Empirical
0.0023
0.047
0.0493
0.1612
0.6522
0.8134
S
(
t
)
Empirical
0.0052
0.0479
0.0531
0.2259
0.5806
0.8065
L
(
t
)
Empirical
0.0029
0.0466
0.0495
0.1753
0.5245
0.7918
Nominal
0.0045
0.0462
0.0508
0.2049
0.5943
0.7992
2
Z
(
t
)
Empirical
0.0014
0.0486
0.0499
0.0607
0.7496
0.8104
S
(
t
)
Empirical
0.0046
0.0477
0.0523
0.1366
0.704
0.8031
L
(
t
)
Empirical
0.0024
0.0486
0.051
0.0858
0.7227
0.8085
Nominal
0.0043
0.0471
0.0514
0.1259
0.6726
0.7985
δ= 1.9
0.5
Z
(
t
)
Empirical
0.0022
0.0452
0.0474
0.2041
0.629
0.833
S
(
t
)
Empirical
0.0051
0.0465
0.0516
0.2732
0.5402
0.8135
L
(
t
)
Empirical
0.003
0.0449
0.0479
0.2326
0.6015
0.8341
Nominal
0.005
0.0455
0.0505
0.2574
0.542
0.7994
1
Z
(
t
)
Empirical
0.0011
0.0453
0.0464
0.0947
0.733
0.8276
S
(
t
)
Empirical
0.0046
0.0472
0.0518
0.1883
0.6239
0.8122
L
(
t
)
Empirical
0.003
0.0449
0.0479
0.2326
0.6015
0.8341
Nominal
0.004
0.0465
0.0509
0.1803
0.6187
0.799
2
Z
(
t
)
Empirical
0.0002
0.047
0.0472
0.0067
0.8168
0.8235
S
(
t
)
Empirical
0.005
0.0484
0.0533
0.1005
0.704
0.8045
L
(
t
)
Empirical
0.0017
0.0468
0.0485
0.0513
0.771
0.8224
Nominal
0.0044
0.0473
0.0516
0.1084
0.6899
0.7983
Table 2:
Simulated empirical type I error and power of the two-stage SCPRT designs based on 100,000 simulation runs for sequential Z(t), log-rank L(t) and S(t) tests with a nominal type I error of 0.05 and power 80% (one-sided test).
