Table 1.
Urn model of the block urn design procedure (Two-treatment balanced allocation with block size b = 6)
| i | Prior randomization | Randomization | Post randomization | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Active urn | Pr(Ti = A) | Random number | Subject allocation | Na | Nb | |Na-Nb| | Inactive urn | Balls return to active urn | |
| 1 | AAABBB | 0.5 | 0.4026 | A | 1 | 0 | 1 | A | |
| 2 | AABBB | 0.4 | 0.5654 | B | 1 | 1 | 0 | AB | AB |
| 3 | AAABBB | 0.5 | 0.0927 | A | 2 | 1 | 1 | A | |
| 4 | AABBB | 0.4 | 0.3080 | A | 3 | 1 | 2 | AA | |
| 5 | ABBB | 0.25 | 0.7758 | B | 3 | 2 | 1 | AAB | AB |
| 6 | AABBB | 0.4 | 0.9219 | B | 3 | 3 | 0 | AB | AB |
| 7 | AAABBB | 0.5 | 0.6115 | B | 3 | 4 | 1 | B | |
| 8 | AAABB | 0.6 | 0.8604 | B | 3 | 5 | 2 | BB | |
| 9 | AAAB | 0.75 | 0.4848 | A | 4 | 5 | 1 | ABB | AB |
| 10 | AAABB | 0.6 | 0.7746 | B | 4 | 6 | 2 | BB | |
| 11 | AAAB | 0.75 | 0.2345 | A | 5 | 6 | 1 | ABB | AB |
| 12 | AAABB | 0.6 | 0.8507 | B | 5 | 7 | 2 | BB | |
| 13 | AAAB | 0.75 | 0.0661 | A | 6 | 7 | 1 | ABB | AB |
| 14 | AAABB | 0.6 | 0.2630 | A | 7 | 7 | 0 | AB | AB |
Ti: treatment allocation for subject i.
Random number: computer generated random number with a uniform distribution on (0,1).
Na: total number of subjects allocated to treatment A.
Nb: total number of subjects allocated to treatment B.