In clinical trials, the most popular randomization approach is probably the randomized block design. With a randomized block design, study participants (subjects) are to be divided into subgroups called blocks. The balance based on the randomization ratio is then achieved within blocks. In other words, within each block, subjects are randomly assigned to treatment different groups.
The block size must be the multiplier of the sum of the treatment ratio. For example, if the treatment assignment is A: B in 1:1 ratio, the block size must be 2, 4, 6, 8, …
If the treatment assignment is A:B in 2:1 ratio, the block size must be 3, 6, 9, 12,…
If the treatment assignment is A:B:C in 2:2:1 ratio, the block size must be 5, 10, 15…
If a block size of 5 is chosen, it indicates that within each block (every 5 subjects), 2 should randomly assigned to A and 2 should be randomly assigned to B, and 1 should be randomized assigned to C.
If a block size of 10 is chosen, it indicates that within each block (every 10 subjects), 4 should randomly assigned to A and 4 should be randomly assigned to B, and 2 should be randomized assigned to C.
To achieve the treatment balance, the smaller block size is usually chosen if central randomization (not by investigational site) is used. Central randomization is usually implemented through IRT (interactive response technology) such as IVRW (interactive voice response system) or IWRS (interactive web response system).
If the randomization is performed within each site or by site and if a smaller block size is chosen, there could be a risk of potential guess / unblinding if other subjects within the block are unblinded. For example, if the randomization is by site and if a block size of 2 is chosen, once the treatment assignment for one subject within the block is revealed, the treatment for the other subject in that block is automatically revealed.
To prevent the potential guessing / unblinding, the following approaches may be used:
- Choose variable block size
- Do not disclose the block size to the sites
Note that if the randomization is centralized, there is usually not necessary to have variable block size since the randomization is across all sites and the investigator at a specific site will not be able to guess the treatment assignment based on the block size.
Following two papers discussed how to program the randomization schedule with variable block size in SAS: one using ranuni() function and one using Proc Plan.
- Jimmy Efird (2011) Blocked Randomization with Randomly Selected Block Sizes
- Lei Li (2011) Permuted-block randomization with varying block sizes using SAS® Proc Plan
For generating the randomization schedule with fixed block size, my SUGI paper "Generating Randomization Schedule Using SAS" is still very relevant.