|
Scenario
|
Undesirable rate, p0
|
Desirable rates
|
n
|
Nominal alpha (exact alpha)
|
Nominal beta (exact beta)
|
First segment (Simon’s 2 stage)
|
Overall probability of correctly selecting a superior arm
|
|---|
| | |
pA*
|
pB
| | | |
r1/n1
|
r/n
| |
|---|
|
1
|
1%
|
20%
|
35%
|
29
|
0.05 (0.026)
|
0.05 (0.049)
|
0/14
|
1/29
|
0.900
|
|
2
|
5%
|
20%
|
35%
|
29
|
0.2 (0.169)
|
0.06 (0.059)
|
0/18
|
2/29
|
0.901
|
|
3
|
10%
|
30%
|
45%
|
35
|
0.2 (0.187)
|
0.05 (0.049)
|
2/19
|
4/35
|
0.903
|
|
4
|
15%
|
30%
|
45%
|
35
|
0.2 (0.197)
|
0.15 (0.122)
|
5/28
|
6/35
|
0.903
|
|
5
|
20%
|
40%
|
55%
|
37
|
0.18 (0.177)
|
0.05 (0.048)
|
3/19
|
9/37
|
0.902
|
|
6
|
25%
|
40%
|
55%
|
37
|
0.2 (0.191)
|
0.14 (0.138)
|
4/22
|
11/37
|
0.902
|
|
7
|
30%
|
50%
|
65%
|
36
|
0.2 (0.160)
|
0.07 (0.070)
|
5/21
|
13/36
|
0.901
|
|
8
|
35%
|
50%
|
65%
|
36
|
0.2 (0.198)
|
0.2 (0.191)
|
9/24
|
14/36
|
0.900
|
|
9
|
40%
|
60%
|
75%
|
32
|
0.2 (0.159)
|
0.1 (0.100)
|
8/21
|
15/32
|
0.900
|
|
10
|
45%
|
60%
|
75%
|
32
|
0.2 (0.198)
|
0.21 (0.204)
|
12/25
|
16/32
|
0.900
|
|
11
|
50%
|
70%
|
85%
|
26
|
0.2 (0.161)
|
0.13 (0.128)
|
7/16
|
15/26
|
0.904
|
|
12
|
55%
|
70%
|
85%
|
26
|
0.2 (0.194)
|
0.23 (0.230)
|
10/20
|
16/26
|
0.903
|
|
13
|
60%
|
80%
|
95%
|
16
|
0.2 (0.163)
|
0.21 (0.209)
|
4/8
|
11/16
|
0.904
|
|
14
|
65%
|
80%
|
95%
|
16
|
0.2 (0.191)
|
0.36 (0.357)
|
7/10
|
11/16
|
0.901
|
- p0 : response proportion of a poor drug.
- pA : response proportion of Arm A.
- pB : response proportion of Arm B.
- alpha : probability of rejecting p ≤ p0 when this is true (exact alpha provided in parenthesis).
- beta : probability of rejecting p ≥ pA* when this is true (exact beta provided in parenthesis).
- pA is taken as the minimum response rate of a good drug.
- n1 : no. of subjects required for Stage 1 in Simon’s 2 stage.
- r1 : maximum number of successes in which will terminate trial.
- r : maximum number of successes at the end of Stage 2 not to warrant further investigation.
