Table II.
Selection percentage and number of patients treated (in parentheses) at each dose combination under the proposed designs assuming partial stochastic ordering (PSO I and PSO II), the design using Bayesian isotonic regression transformation (BIT), and a design based on parametric change-point models (Cai). The combinations in bold are the OBDCs.
| Dose | 1 |
2 |
3 |
1 |
2 |
3 |
||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Selection percent (number patients) | Tox | Eff | Selection percent (number patients) | Tox | Eff | |||||||
| Scenario 1 | Scenario 2 | |||||||||||
| 1 | 0.5 (5.3) | 52.4 (16.9) | 24.5 (7.7) | 0.3 (4.9) | 0.9 (4.8) | 2.7 (3.5) | ||||||
| PSO I | 2 | 6.6 (5.5) | 18.8 (6.8) | 8.9 (2.5) | 15.1 | 32.9 | 46.2 (16.5) | 25.4 (8.3) | 15.4 (3) | 15.1 | 25.1 | |
| 3 | 3 (3.9) | 1.5 (3.9) | 0.5 (1.1) | 8.2 (5.6) | 2.1 (5.7) | 0.2 (1) | ||||||
| 1 | 0.1 (5.1) | 52.5 (16.8) | 23.9 (7.3) | 0.5 (4.9) | 1.6 (4.8) | 2 (3.7) | ||||||
| PSO II | 2 | 8 (5.9) | 21.7 (6.9) | 8.2 (2.7) | 14.7 | 33.0 | 47.0 (16.5) | 26.2 (8.3) | 15.5 (3.4) | 14.7 | 25.2 | |
| 3 | 4 (3.9) | 1.7 (3.8) | 0.5 (1.2) | 7 (5.3) | 1.5 (5.2) | 0.2 (1.1) | ||||||
| 1 | 0.1 (3.8) | 46.4 (15.7) | 30 (9.2) | 0 (3.1) | 0.5 (3.6) | 2.5 (4.2) | ||||||
| BIT | 2 | 5.9 (5.2) | 29.4 (9) | 6.1 (2.7) | 14.9 | 34.1 | 35.6 (14.8) | 35 (10.9) | 18.5 (3.4) | 15.3 | 26.4 | |
| 3 | 4.8 (3.9) | 1.4 (3.7) | 0.1 (0.6) | 12.4 (7) | 1.5 (5.8) | 0.1 (0.5) | ||||||
| 1 | 22 (16.5) | 55.2 (10.4) | 16.1 (5.3) | 4.8 (8.8) | 8.5 (4.4) | 5.2 (3.6) | ||||||
| Cai | 2 | 22.5 (5.1) | 9.8 (3.9) | 3.2 (3.3) | 14.7 | 27.1 | 47.4 (12.7) | 20 (5.7) | 9.9 (4.1) | 18.7 | 25.4 | |
| 3 | 4.7 (3.5) | 0.6 (3.1) | 0.4 (2.7) | 16.9 (7.7) | 3.6 (3.8) | 1.2 (2.7) | ||||||
| Scenario 3 | Scenario 4 | |||||||||||
| 1 | 55.0 (23.2) | 4.9 (5.5) | 3.3 (2.4) | 52.8 (23.7) | 27 (8.6) | 1.9 (3.5) | ||||||
| PSO I | 2 | 22.4 (10.6) | 4.5 (2.7) | 0.1 (0.7) | 15.4 | 35.7 | 26.6 (8.8) | 1.9 (3.7) | 0.1 (0.4) | 16.6 | 30.2 | |
| 3 | 15.5 (7.3) | 0.7 (1.4) | 0.4 (0.2) | 1.4 (3.7) | 0.2 (1.2) | 0 (0.1) | ||||||
| 1 | 53.1 (23.0) | 6.6 (5.6) | 1.6 (2.2) | 50.5 (23.0) | 28.1 (8.9) | 1.5 (3.8) | ||||||
| PSO II | 2 | 24 (10.8) | 3.2 (2.5) | 0.2 (0.6) | 15.4 | 35.5 | 28.7 (8.9) | 1.4 (3.7) | 0.1 (0.4) | 16.9 | 29.5 | |
| 3 | 16.7 (7.8) | 0.3 (1.2) | 0 (0.2) | 1.8 (3.7) | 0.2 (1.2) | 0 (0.1) | ||||||
| 1 | 35.1 (16.3) | 11.5 (7.5) | 1.1 (2.4) | 23.8 (12.1) | 39.8 (12.9) | 2.9 (4.3) | ||||||
| BIT | 2 | 40.9 (15.6) | 4.1 (3.1) | 0.2 (0.7) | 17.4 | 35.9 | 38.7 (12.7) | 3.2 (4.4) | 0.1 (0.4) | 19.4 | 29.7 | |
| 3 | 14.6 (6.9) | 0.5 (1.3) | 0 (0.1) | 2.1 (4.4) | 0.1 (1.2) | 0 (0) | ||||||
| 1 | 93.5 (31.0) | 2 (3.5) | 0.2 (3.1) | 90.7 (30.9) | 4.1 (3.7) | 1.5 (3.3) | ||||||
| Cai | 2 | 3.8 (3.6) | 0.6 (3.2) | 0 (2.3) | 17.6 | 36.7 | 3.8 (3.7) | 0.9 (3.1) | 0.1 (2.3) | 18.4 | 29.5 | |
| 3 | 1.3 (3.3) | 0.3 (2.6) | 0 (1.5) | 0.8 (3.3) | 0.2 (2.5) | 0 (1.1) | ||||||
| Scenario 5 | Scenario 6 | |||||||||||
| 1 | 0.1 (4.1) | 2.5 (5.3) | 8 (5.6) | 0.7 (5.3) | 2 (5.1) | 7.9 (4.8) | ||||||
| PSO I | 2 | 2.4 (5.1) | 34.6 (11.3) | 3 (2.4) | 13.2 | 28.5 | 2.4 (5.1) | 12.4 (5.8) | 49.6 (11.1) | 7.7 | 21.0 | |
| 3 | 5.4 (4.7) | 52.0 (14.2) | 0.4 (1) | 8 (4.8) | 11.9 (4.9) | 18.9 (6.8) | ||||||
| 1 | 0.4 (4) | 1.2 (5.3) | 8.7 (5.5) | 0.8 (5.5) | 3.2 (5.1) | 5.8 (4.7) | ||||||
| PSO II | 2 | 1.5 (4.7) | 35.9 (11.6) | 2.1 (2.3) | 13.1 | 28.9 | 3.2 (5.3) | 9.9 (5.6) | 49.8 (11.2) | 7.6 | 21.0 | |
| 3 | 4.7 (4.8) | 52.4 (14.7) | 0.6 (1) | 6.8 (4.7) | 12 (5) | 19.3 (6.7) | ||||||
| 1 | 0 (3.1) | 1 (5) | 13.5 (6.4) | 0 (3) | 0.3 (3.5) | 5 (5.7) | ||||||
| BIT | 2 | 0.6 (4.1) | 47.7 (14.6) | 2.3 (2.2) | 13.3 | 28.4 | 0.4 (3.5) | 8 (5.8) | 67.8 (15.1) | 8.0 | 22.9 | |
| 3 | 8.1 (5.8) | 43.1 (12.1) | 0 (0.6) | 3.7 (4.9) | 17.2 (6.4) | 13.6 (5.6) | ||||||
| 1 | 3 (8) | 15.9 (7.3) | 26.1 (7.9) | 4.6 (8.3) | 5.6 (4.8) | 24.6 (7.5) | ||||||
| Cai | 2 | 9.3 (5.2) | 30.3 (6.8) | 4.9 (4.1) | 16.8 | 23.9 | 7.6 (4.7) | 9.6 (4.2) | 20.7 (6.6) | 6.9 | 17.4 | |
| 3 | 18.6 (5.4) | 28.5 (6.2) | 2.8 (2.9) | 17.9 (6) | 14.7 (4.6) | 23.8 (5.9) | ||||||
| Scenario 7 | Scenario 8 | |||||||||||
| 1 | 0.5 (5.1) | 10.2 (8.7) | 2.4 (2.3) | 0.2 (4.3) | 2.2 (5.6) | 51.8 (9.0) | ||||||
| PSO I | 2 | 62.7 (22.3) | 2.9 (2.7) | 0.3 (0.5) | 20.4 | 34.1 | 2.1 (5.7) | 48.0 (8.9) | 8.1 (3.6) | 11.7 | 25.0 | |
| 3 | 25.1 (10.3) | 0.5 (1) | 0 (0.1) | 52.0 (9.7) | 8.4 (4.2) | 0.7 (2.7) | ||||||
| 1 | 0.3 (5.1) | 10.1 (8.7) | 1.7 (2.3) | 0.3 (4.3) | 2.1 (5.4) | 53.6 (9.4) | ||||||
| PSO II | 2 | 61.3 (22.6) | 1.3 (2.5) | 0.1 (0.4) | 20.2 | 34.0 | 1.5 (5.6) | 47.1 (9.3) | 8 (3.7) | 11.9 | 25.1 | |
| 3 | 26.4 (10.5) | 0.4 (1) | 0 (0.1) | 51.1 (9.2) | 7.2 (3.9) | 1.2 (2.9) | ||||||
| 1 | 0 (4.5) | 19.4 (10.9) | 2.1 (2.8) | 0 (3.1) | 1.2 (4.5) | 49.1 (10.0) | ||||||
| BIT | 2 | 69.1 (23.1) | 2.5 (3) | 0.1 (0.5) | 22.2 | 34.9 | 0.9 (4.6) | 42.8 (8.9) | 11.4 (4.6) | 11.9 | 26.7 | |
| 3 | 20.2 (7.9) | 0.2 (0.9) | 0 (0) | 48.7 (10.4) | 12.5 (5.1) | 0.7 (2.6) | ||||||
| 1 | 11.5 (15.4) | 25.2 (8.4) | 2.2 (3.6) | 3.4 (10.3) | 17.2 (6.7) | 38.6 (7.2) | ||||||
| Cai | 2 | 51.0 (11.6) | 5.7 (3.8) | 0.2 (2) | 24.0 | 30.0 | 17.3 (6.4) | 30.8 (5.2) | 6.5 (3.8) | 11.6 | 21.2 | |
| 3 | 22.6 (5.5) | 0.7 (2.4) | 0.2 (1.2) | 40.3 (7.1) | 6.6 (3.8) | 1.7 (3.2) | ||||||
| Scenario 9 | Scenario 10 | |||||||||||
| 1 | 0.1 (4.7) | 1.4 (5.6) | 5.7 (4.9) | 0 (4) | 46.7 (14.8) | 17.3 (6.4) | ||||||
| PSO I | 2 | 2 (5.5) | 9.2 (5.5) | 41.1 (8.0) | 10.4 | 19.6 | 44.4 (13.5) | 5 (4.3) | 0.7 (1.7) | 14.5 | 28.6 | |
| 3 | 6.5 (5.1) | 41.8 (9.0) | 11.3 (4.7) | 20.3 (7.2) | 0.9 (1.7) | 0 (0.3) | ||||||
| 1 | 0.1 (4.7) | 2 (5.8) | 7.9 (5.1) | 0.2 (4) | 46.3 (14.2) | 18.9 (6.5) | ||||||
| PSO II | 2 | 1.9 (5.7) | 11.1 (5.6) | 40.8 (8.0) | 10.4 | 19.4 | 47.1 (14.8) | 4.2 (4.2) | 0.4 (1.6) | 14.2 | 28.6 | |
| 3 | 7.5 (5.1) | 40.1 (8.4) | 8.9 (4.5) | 18.6 (6.6) | 0.6 (1.7) | 0.2 (0.4) | ||||||
| 1 | 0 (3) | 0.4 (3.5) | 3.5 (5.4) | 0 (3.3) | 40.7 (13.6) | 23.2 (7.5) | ||||||
| BIT | 2 | 0.5 (3.7) | 5.7 (5.6) | 52.8 (10.5) | 10.9 | 21.7 | 41.1 (14.0) | 7.1 (4.6) | 0.4 (1.6) | 14.6 | 29.1 | |
| 3 | 5.1 (5.9) | 54.2 (11.3) | 7.5 (4) | 22.7 (7.3) | 0.6 (1.8) | 0 (0.2) | ||||||
| 1 | 1.4 (7) | 5.6 (5.1) | 25.4 (7) | 9.8 (14.1) | 47.8 (9.0) | 14 (4.7) | ||||||
| Cai | 2 | 6.1 (5) | 13.2 (4.5) | 19.8 (5.7) | 10.1 | 17.1 | 48.1 (8.7) | 13.9 (4.1) | 1.1 (3.1) | 17.4 | 23.7 | |
| 3 | 25.7 (7.1) | 19.6 (5.7) | 17.4 (5.4) | 16.5 (4.6) | 1.2 (3.3) | 0.4 (2.4) | ||||||
| Scenario 11 | Scenario 12 | |||||||||||
| 1 | 0.1 (3.7) | 0.7 (4.3) | 8 (5.5) | 0.2 (4.3) | 15.6 (8.8) | 25.6 (7.3) | ||||||
| PSO I | 2 | 1.2 (4.4) | 6.2 (4.7) | 17.4 (6.2) | 6.0 | 25.7 | 15.7 (9) | 11 (5.6) | 0.7 (1.8) | 18.2 | 30.4 | |
| 3 | 6.3 (5.3) | 17.3 (6.6) | 52.6 (13.2) | 57.6 (14.1) | 1.4 (2.3) | 0.4 (0.5) | ||||||
| 1 | 0.2 (3.8) | 90.9 (4.4) | 9.1 (5.3) | 0.3 (4.4) | 13.1 (8.9) | 29.1 (7.7) | ||||||
| PSO II | 2 | 1.4 (4.6) | 9.4 (5.3) | 16.4 (6.1) | 6.0 | 24.9 | 14.4 (8.8) | 9.7 (5.2) | 0.5 (1.7) | 18.1 | 30.5 | |
| 3 | 6.6 (5) | 17 (6.7) | 51.2 (12.5) | 57.5 (14.3) | 1.5 (2.2) | 0.2 (0.5) | ||||||
| 1 | 0 (3) | 0.1 (3.6) | 10.5 (5.8) | 0 (3.5) | 15.8 (9.2) | 32.1 (8.1) | ||||||
| BIT | 2 | 0.3 (3.6) | 8 (5.1) | 30.7 (8.4) | 5.8 | 24.1 | 19.9 (10.7) | 14.8 (5.5) | 0.6 (1.7) | 18.2 | 30.0 | |
| 3 | 9.8 (5.9) | 27.7 (8.7) | 36.9 (9.5) | 57.9 (12.8) | 1.4 (2.1) | 0 (0.2) | ||||||
| 1 | 1.4 (7) | 7.6 (4.9) | 28.1 (7.5) | 7.1 (10.5) | 22.7 (6.6) | 20.9 (5.3) | ||||||
| Cai | 2 | 7.6 (4.9) | 14.3 (4.6) | 14.8 (5.3) | 5.1 | 19.7 | 25.8 (8) | 22.8 (5.2) | 2.8 (3.5) | 21.0 | 28.6 | |
| 3 | 25.1 (7.2) | 16.6 (5.7) | 24.8 (6.4) | 38.5 (8.6) | 6.4 (3.8) | 1 (2.4) | ||||||