Table III.
Illustration of a simulated trial using the PSO I design.
| Data |
Estimates |
Dose | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| combo | |||||||||||||
| assignment | |||||||||||||
| Combo | Tox | Eff |
P1 |
P2 |
qmax | Sjk | Smax | δ | Accpt | Lowest | |||
| Unc | C | Unc | C | plateau | accpt | ||||||||
| plateau | |||||||||||||
| (1,1) | 0/3 | 0/3 | 0.89 | 0.89 | (1,2), (2,1) | ||||||||
| (1,1) | 0/3 | 0/3 | 0.89 | 0.89 | (3,1), (2,2), (1,3) | ||||||||
| (2,1) | 0/3 | 0/3 | 0.89 | 0.89 | |||||||||
| (1,2) | 1/3 | 1/3 | 0.46 | 0.46 | |||||||||
| (1,1) | 0/3 | 0/3 | 0.89 | 0.89 | (3,2), (2,3) | ||||||||
| (2,1) | 0/3 | 0/3 | 0.89 | 0.89 | |||||||||
| (1,2) | 1/3 | 1/3 | 0.46 | 0.81 | |||||||||
| (3,1) | 1/3 | 1/3 | 0.46 | 0.46 | |||||||||
| (2,2) | 0/3 | 2/3 | 0.89 | 0.81 | |||||||||
| (1,3) | 0/3 | 3/3 | 0.89 | 0.81 | |||||||||
| (1,1) | 0/3 | 0/3 | 0.89 | 0.89 | 0.13 | 0.13 | 0.5 | 0.03 | 0.5 | 0.42 | (1,2) | ||
| (2,1) | 0/3 | 0/3 | 0.89 | 0.89 | 0.13 | 0.13 | 0.03 | ||||||
| (1,2) | 1/3 | 1/3 | 0.46 | 0.84 | 0.58 | 0.46 | 0.29 | X | X | ||||
| (3,1) | 1/3 | 1/3 | 0.46 | 0.46 | 0.58 | 0.46 | 0.29 | X | |||||
| (2,2) | 0/3 | 2/3 | 0.89 | 0.84 | 0.911 | 0.46 | 0.37 | X | |||||
| (1,3) | 0/3 | 3/3 | 0.89 | 0.84 | 0.995 | 0.56 | 0.5 | X | |||||
| (3,2) | 2/3 | 0/3 | 0.11 | 0.11 | 0.13 | 0.46 | 0.37 | ||||||
| (2,3) | 0/3 | 0/3 | 0.89 | 0.84 | 0.13 | 0.56 | 0.5 | X | |||||
| (1,1) | 0/3 | 0/3 | 0.89 | 0.89 | 0.13 | 0.13 | 0.5 | 0.03 | 0.5 | 0.41 | (3,1) | ||
| (2,1) | 0/3 | 0/3 | 0.89 | 0.89 | 0.13 | 0.13 | 0.03 | ||||||
| (1,2) | 1/6 | 1/6 | 0.80 | 0.87 | 0.25 | 0.25 | 0.047 | ||||||
| (3,1) | 1/3 | 1/3 | 0.46 | 0.46 | 0.58 | 0.43 | 0.29 | X | X | ||||
| (2,2) | 0/3 | 2/3 | 0.89 | 0.87 | 0.911 | 0.43 | 0.37 | X | X | ||||
| (1,3) | 0/3 | 3/3 | 0.89 | 0.87 | 0.995 | 0.56 | 0.5 | X | X | ||||
| (3,2) | 2/3 | 0/3 | 0.11 | 0.11 | 0.13 | 0.43 | 0.37 | ||||||
| (2,3) | 0/3 | 0/3 | 0.89 | 0.87 | 0.13 | 0.56 | 0.5 | X | |||||
| (1,1) | 0/3 | 0/3 | 0.89 | 0.89 | 0.13 | 0.13 | 0.5 | 0.03 | 0.5 | 0.4065 | (2,2) | ||
| (2,1) | 0/3 | 0/3 | 0.89 | 0.89 | 0.13 | 0.13 | 0.03 | ||||||
| (1,2) | 1/6 | 1/6 | 0.80 | 0.87 | 0.25 | 0.25 | 0.047 | ||||||
| (3,1) | 2/6 | 1/6 | 0.47 | 0.47 | 0.25 | 0.25 | 0.047 | ||||||
| (2,2) | 0/3 | 2/3 | 0.89 | 0.87 | 0.911 | 0.38 | 0.37 | X | X | ||||
| (1,3) | 0/3 | 3/3 | 0.89 | 0.87 | 0.995 | 0.56 | 0.5 | X | X | ||||
| (3,2) | 2/3 | 0/3 | 0.11 | 0.11 | 0.13 | 0.38 | 0.37 | ||||||
| (2,3) | 0/3 | 0/3 | 0.89 | 0.87 | 0.13 | 0.56 | 0.5 | X | |||||
Notes: (1) 
, 
, where 
, 
. (2) The dose combinations in bold are used to treat the current cohort of patients. When multiple combinations are in bold, they are used to treat cohorts of patients in an order randomly chosen, essentially on the basis of our proposed dose-combination-finding algorithm. The same statement is true when the dose-combination assignment for the next cohort of patients (last column) includes multiple combinations. (3) The underlined combinations are found to be excessively toxic. (4) Combo: combination; Tox: toxicity; Eff: efficacy; Unc: unconstrained; C: constrained; accpt: acceptable.