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.