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. 2013 Jul 3;13:87. doi: 10.1186/1471-2288-13-87

Table 3.

Sample size and overall probability of correctly selecting a superior arm in SSD for different response rates based on 1 million replications

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.