# 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
1. p0 : response proportion of a poor drug.
2. pA : response proportion of Arm A.
3. pB : response proportion of Arm B.
4. alpha : probability of rejecting p ≤ p0 when this is true (exact alpha provided in parenthesis).
5. beta : probability of rejecting p ≥ pA* when this is true (exact beta provided in parenthesis).
6. pA is taken as the minimum response rate of a good drug.
7. n1 : no. of subjects required for Stage 1 in Simon’s 2 stage.
8. r1 : maximum number of successes in which will terminate trial.
9. r : maximum number of successes at the end of Stage 2 not to warrant further investigation.