I am planning a trial in which I have two groups: A and B. The plan is to have 40 subjects in each group, a total of 80 subjects. There is also a need for stratification by site, where 4 sites are planned. Theoretically, the ideal is to have 20 subjects in each site, and with block randomization, I get a 1:1 ratio, with a perfect randomization.
The client wished to allow bigger sites to recruit more subjects than smaller sites, to speed up the trials. This means that once 20 subjects were already enrolled, the site will continue further on. This can result in a situation in which site 1 will start a block, site 2 will start a block, and non of them will finish the block due to the arrival to 80 subjects, and a 1:1 will not occur.
Is there a way of calculating the worst case scenario, what will be the worst ratio (from unequal point of view) in such case ?