Table II.
Probabilities in percent: π to reject at least one null hypothesis, πi to reject a particular hypothesis Hi, and ηi to drop treatment arm i at interim. Numbers in brackets give rejection probabilities if no sample size reallocation is performed. 106 trials were simulated assuming mean difference δi for treatment i (equal across endpoints) and mean toxicity response κ in treatment arm 2. In each scenario, the fixed sample gMCP was applied to the preplanned design. Adaptive trials were simulated applying the rules SB, 50:50 (FF), or SF. These were simulated with and without sample size reallocation of dropped treatment arms and evaluated using the agMTP and the gPA.
| (δ1, δ2) | Rule(κ) | Procedure | π | π 1 | π 2 | π 3 | π 4 | η 1 | η 2 |
|---|---|---|---|---|---|---|---|---|---|
| (0, 0) | PP | gMCP | 2.3 | 1.3 | 1.3 | 0.1 | 0.1 | 0 | 0 |
| SB | agMTP | 2.2 (2.2) | 1.1 (1.1) | 1.1 (1.1) | 0.1 (0.1) | 0.1 (0.1) | 50 | 50 | |
| gPA | 2.1 (2.1) | 1.0 (1.0) | 1.0 (1.0) | 0.1 (0.1) | 0.1 (0.1) | 50 | 50 | ||
| FF | agMTP | 1.4 (1.4) | 0.7 (0.7) | 0.7 (0.7) | 0.1 (0.1) | 0.1 (0.1) | 50 | 50 | |
| gPA | 1.2 (1.2) | 0.6 (0.6) | 0.6 (0.6) | 0.0 (0.0) | 0.0 (0.0) | 50 | 50 | ||
| SF(0.2) | agMTP | 1.4 (1.4) | 1.0 (1.0) | 0.5 (0.5) | 0.1 (0.1) | 0.0 (0.0) | 5 | 29 | |
| gPA | 1.4 (1.4) | 1.0 (1.0) | 0.4 (0.5) | 0.1 (0.1) | 0.0 (0.0) | 5 | 29 | ||
| SF(0.4) | agMTP | 1.2 (1.2) | 1.1 (1.1) | 0.1 (0.1) | 0.1 (0.1) | 0.0 (0.0) | 5 | 70 | |
| gPA | 1.1 (1.1) | 1.0 (1.0) | 0.1 (0.1) | 0.1 (0.1) | 0.0 (0.0) | 5 | 70 | ||
| (0, 0.4) | PP | gMCP | 79.0 | 2.3 | 78.9 | 0.2 | 65.1 | 0 | 0 |
| SB | agMTP | 86.7 (78.6) | 0.2 (0.2) | 86.6 (78.4) | 0.0 (0.0) | 77.5 (64.9) | 98 | 2 | |
| gPA | 86.6 (78.3) | 0.1 (0.1) | 86.4 (78.2) | 0.0 (0.0) | 77.2 (64.5) | 98 | 2 | ||
| FF | agMTP | 45.0 (40.8) | 1.2 (1.2) | 43.8 (39.6) | 0.1 (0.1) | 39.2 (32.8) | 50 | 50 | |
| gPA | 44.4 (40.1) | 0.6 (0.6) | 43.7 (39.5) | 0.0 (0.0) | 39.0 (32.6) | 50 | 50 | ||
| SF(0.2) | agMTP | 54.2 (54.0) | 1.9 (1.8) | 53.4 (53.3) | 0.2 (0.2) | 43.7 (43.5) | 5 | 28 | |
| gPA | 53.8 (53.7) | 1.5 (1.5) | 53.4 (53.3) | 0.1 (0.1) | 43.7 (43.5) | 5 | 28 | ||
| SF(0.4) | agMTP | 21.7 (21.7) | 1.9 (1.9) | 20.2 (20.2) | 0.2 (0.2) | 16.3 (16.3) | 5 | 70 | |
| gPA | 21.0 (21.0) | 1.1 (1.2) | 20.2 (20.2) | 0.1 (0.1) | 16.3 (16.3) | 5 | 70 | ||
| (0.3, 0.4) | PP | gMCP | 85.1 | 64.4 | 80.7 | 46.8 | 68.0 | 0 | 0 |
| SB | agMTP | 90.0 (83.3) | 28.1 (25.5) | 61.9 (57.8) | 22.7 (18.8) | 56.9 (49.7) | 67 | 33 | |
| gPA | 88.4 (80.9) | 27.2 (24.3) | 61.2 (56.6) | 20.5 (16.4) | 55.0 (47.1) | 67 | 33 | ||
| FF | agMTP | 82.7 (74.2) | 37.6 (32.9) | 45.1 (41.4) | 30.2 (23.9) | 41.4 (35.5) | 50 | 50 | |
| gPA | 77.8 (68.4) | 34.1 (28.9) | 43.7 (39.5) | 25.2 (19.0) | 39.0 (32.6) | 50 | 50 | ||
| SF(0.2) | agMTP | 78.7 (76.4) | 62.4 (60.2) | 54.9 (54.8) | 46.8 (43.8) | 45.9 (45.7) | 5 | 28 | |
| gPA | 76.8 (74.2) | 60.6 (58.1) | 54.8 (54.7) | 44.1 (40.9) | 45.8 (45.6) | 5 | 28 | ||
| SF(0.4) | agMTP | 73.2 (67.1) | 66.9 (60.8) | 21.0 (21.0) | 52.3 (44.3) | 17.4 (17.3) | 5 | 69 | |
| gPA | 68.4 (61.7) | 62.1 (55.4) | 21.0 (21.0) | 45.5 (37.4) | 17.4 (17.3) | 5 | 69 | ||
| (0.4, 0.4) | PP | gMCP | 90.6 | 82.6 | 82.7 | 71.2 | 71.2 | 0 | 0 |
| SB | agMTP | 94.4 (89.2) | 47.2 (44.6) | 47.2 (44.6) | 43.8 (38.9) | 43.8 (38.9) | 50 | 50 | |
| gPA | 93.2 (87.1) | 46.6 (43.5) | 46.6 (43.6) | 42.0 (36.4) | 42.0 (36.4) | 50 | 50 | ||
| FF | agMTP | 91.0 (84.0) | 45.5 (42.0) | 45.5 (42.0) | 42.0 (36.5) | 42.0 (36.4) | 50 | 50 | |
| gPA | 87.4 (78.9) | 43.7 (39.5) | 43.7 (39.4) | 39.0 (32.5) | 39.0 (32.5) | 50 | 50 | ||
| SF(0.2) | agMTP | 86.7 (85.2) | 79.5 (78.1) | 56.5 (56.4) | 69.8 (67.3) | 48.3 (48.2) | 5 | 29 | |
| gPA | 85.8 (83.9) | 78.7 (76.9) | 56.4 (56.3) | 68.3 (65.2) | 48.2 (48.0) | 5 | 29 | ||
| SF(0.4) | agMTP | 85.6 (81.4) | 82.9 (78.8) | 21.9 (21.9) | 75.0 (68.1) | 18.5 (18.5) | 5 | 69 | |
| gPA | 83.2 (78.0) | 80.6 (75.4) | 21.9 (21.9) | 70.9 (62.8) | 18.5 (18.5) | 5 | 69 |
gMCP, graphical multiple comparison procedure; SB, select better; SF, safety; agMTP, adaptive graph-based multiple testing procedure; gPA, graph-based partitioning algorithm.