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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 ?

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  • $\begingroup$ What size blocks are you planning? $\endgroup$
    – Todd D
    Commented Dec 24, 2017 at 3:13
  • $\begingroup$ I was thinking about 2 and 4, combined, so no one can guess the block size $\endgroup$
    – user3275222
    Commented Dec 24, 2017 at 14:13

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It would seem that requiring center stratification and allowing asymmetric enrollment are completely at odds with one another. If centers can enroll ahead of others, then center imbalance could be quite large. Assuming randomization is not working properly and all sites are allowed to randomize without the study leadership intervening, I imagine the worst treatment imbalance would be 34:46. That is 3 centers partially enrolling a block of 4 where each randomized to the first treatment twice (“a”,”a”) and the last two positions of each block are left unrandomized. This, while the last remaining functional center gets new blocks and completes the requisite sample size.

There are myriad other ways to create further imbalance. However, these require further degeneracy of the randomization plan.

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