From: Minimax and admissible adaptive two-stage designs in phase II clinical trials
Power=80 % | Power=90 % | ||||||
---|---|---|---|---|---|---|---|
S | n2(S) | n(S) | r(S) | S | n2(S) | n(S) | r(S) |
π u =0.1 | |||||||
Simon: (2/22,7/40) | Simon: (3/31,9/55) | ||||||
Minimax-EF: ((4,6)/33,7/38) | Minimax-EF: ((6,8)/47,9/53) | ||||||
New: n1=18 | New: n1=33 | ||||||
≤1 | 0 | 18 | 0 | ≤3 | 0 | 33 | 0 |
2 | 20 | 38 | 7 | 4 | 20 | 53 | 8 |
3 | 20 | 38 | 7 | 5 | 20 | 53 | 9 |
4 | 19 | 37 | 6 | 6 | 20 | 53 | 9 |
5 | 19 | 37 | 6 | 7 | 18 | 51 | 8 |
6 | 18 | 36 | 6 | 8 | 17 | 50 | 8 |
≥7 | 0 | 18 | 0 | ≥9 | 0 | 33 | 0 |
π u =0.2 | |||||||
Simon: (6/31,15/53) | Simon: (8/42,21/77) | ||||||
Minimax-EF: ((6,13)/31,15/53) | Minimax-EF: ((13,18)/62,21/76) | ||||||
New: n1=31 | New: n1=47 | ||||||
≤6 | 0 | 31 | 0 | ≤9 | 0 | 47 | 0 |
7 | 22 | 53 | 15 | 10 | 27 | 74 | 20 |
8 | 22 | 53 | 15 | 11 | 27 | 74 | 20 |
9 | 22 | 53 | 15 | 12 | 27 | 74 | 20 |
10 | 22 | 53 | 15 | 13 | 27 | 74 | 20 |
11 | 22 | 53 | 15 | 14 | 26 | 73 | 20 |
12 | 21 | 52 | 15 | 15 | 26 | 73 | 20 |
≥13 | 0 | 31 | 0 | 16 | 26 | 73 | 20 |
17 | 25 | 72 | 20 | ||||
18 | 14 | 61 | 18 | ||||
≥19 | 0 | 47 | 0 | ||||
π u =0.3 | |||||||
Simon: (16/46,25/65) | Simon: (27/77,33/88) | ||||||
Minimax-EF: ((13,19)/43,25/64) | Minimax-EF: ((27,33)/77,33/88) | ||||||
New: n1=32 | New: n1=51 | ||||||
≤9 | 0 | 32 | 0 | ≤15 | 0 | 51 | 0 |
10 | 32 | 64 | 24 | 16 | 37 | 88 | 33 |
11 | 32 | 64 | 25 | 17 | 37 | 88 | 33 |
12 | 32 | 64 | 25 | 18 | 37 | 88 | 33 |
13 | 32 | 64 | 25 | 19 | 37 | 88 | 33 |
14 | 32 | 64 | 25 | 20 | 37 | 88 | 33 |
15 | 31 | 63 | 24 | 21 | 37 | 88 | 33 |
16 | 30 | 62 | 24 | 22 | 37 | 88 | 33 |
17 | 29 | 61 | 24 | 23 | 37 | 88 | 33 |
18 | 24 | 56 | 22 | 24 | 37 | 88 | 34 |
≥19 | 0 | 32 | 0 | 25 | 36 | 87 | 33 |
26 | 34 | 85 | 33 | ||||
27 | 34 | 85 | 33 | ||||
≥28 | 0 | 51 | 0 | ||||
π u =0.4 | |||||||
Simon: (28/59,34/70) | Simon: (24/62,45/94) | ||||||
Minimax-EF: ((16,23)/41,34/69) | Minimax-EF: ((21,31)/55,45/94) | ||||||
New: n1=37 | New: n1=52 | ||||||
≤15 | 0 | 37 | 0 | ≤20 | 0 | 52 | 0 |
16 | 32 | 69 | 33 | 21 | 42 | 94 | 44 |
17 | 32 | 69 | 34 | 22 | 42 | 94 | 45 |
18 | 32 | 69 | 34 | 23 | 42 | 94 | 45 |
19 | 32 | 69 | 34 | 24 | 42 | 94 | 45 |
20 | 32 | 69 | 34 | 25 | 42 | 94 | 45 |
21 | 31 | 68 | 33 | 26 | 42 | 94 | 45 |
22 | 31 | 68 | 33 | 27 | 42 | 94 | 45 |
23 | 31 | 68 | 33 | 28 | 42 | 94 | 45 |
24 | 21 | 58 | 29 | 29 | 42 | 94 | 45 |
≥25 | 0 | 37 | 0 | 30 | 42 | 94 | 45 |
31 | 39 | 91 | 43 | ||||
≥32 | 0 | 52 | 0 | ||||
π u =0.5 | |||||||
Simon: (39/66,40/68) | Simon: (28/57,54/93) | ||||||
Minimax-EF: ((39,40)/66,40/68) | Minimax-EF: ((30,38)/59,54/93) | ||||||
New: n1=54 | New: n1=55 | ||||||
≤28 | 0 | 54 | 0 | ≤28 | 0 | 55 | 0 |
29 | 13 | 67 | 39 | 29 | 38 | 93 | 54 |
30 | 13 | 67 | 40 | 30 | 38 | 93 | 54 |
31 | 13 | 67 | 40 | 31 | 38 | 93 | 54 |
32 | 13 | 67 | 40 | 32 | 38 | 93 | 54 |
33 | 13 | 67 | 40 | 33 | 38 | 93 | 54 |
34 | 13 | 67 | 39 | 34 | 38 | 93 | 54 |
35 | 13 | 67 | 39 | 35 | 38 | 93 | 53 |
36 | 13 | 67 | 39 | 36 | 38 | 93 | 54 |
37 | 9 | 63 | 38 | 37 | 38 | 93 | 53 |
≥38 | 0 | 54 | 0 | ≥38 | 0 | 55 | 0 |
π u =0.6 | |||||||
Simon: (18/30,43/62) | Simon: (48/72,57/84) | ||||||
Minimax-EF: ((16,22)/27,43/62) | Minimax-EF: ((48,53)/72,57/84) | ||||||
New: n1=32 | New: n1=58 | ||||||
≤19 | 0 | 32 | 0 | ≤37 | 0 | 58 | 0 |
20 | 29 | 61 | 42 | 38 | 26 | 84 | 57 |
21 | 29 | 61 | 42 | 39 | 26 | 84 | 57 |
22 | 29 | 61 | 42 | 40 | 26 | 84 | 57 |
23 | 28 | 60 | 42 | 41 | 26 | 84 | 57 |
24 | 28 | 60 | 42 | 42 | 25 | 83 | 57 |
25 | 28 | 60 | 42 | 43 | 25 | 83 | 57 |
26 | 27 | 59 | 41 | 44 | 23 | 81 | 56 |
27 | 27 | 59 | 41 | ≥45 | 0 | 58 | 0 |
28 | 15 | 47 | 34 | ||||
≥29 | 0 | 32 | 0 | ||||
π u =0.7 | |||||||
Simon: (16/23,39/49) | Simon: (33/44,53/68) | ||||||
Minimax-EF: ((16,21)/23,39/49) | Minimax-EF: ((29,35)/41,51/65) | ||||||
New: n1=25 | New: n1=37 | ||||||
≤18 | 0 | 25 | 0 | ≤26 | 0 | 37 | 0 |
19 | 24 | 49 | 39 | 27 | 28 | 65 | 51 |
20 | 24 | 49 | 39 | 28 | 28 | 65 | 51 |
21 | 24 | 49 | 39 | 29 | 28 | 65 | 51 |
22 | 23 | 48 | 38 | 30 | 28 | 65 | 51 |
23 | 8 | 33 | 26 | 31 | 27 | 64 | 50 |
≥24 | 0 | 25 | 0 | 32 | 27 | 64 | 50 |
33 | 24 | 61 | 48 | ||||
≥34 | 0 | 37 | 0 |