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Stat Methods Med Res. 2018 Jul;27(7):2142-2153. doi: 10.1177/0962280216677107. Epub 2016 Nov 16.

The asymptotic maximal procedure for subject randomization in clinical trials.

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1 Department of Public Health Sciences, Medical University of South Carolina, Charleston, USA.
2 Biometry Research Group, National Cancer Institute, Rockville, USA.
3 University of Maryland Baltimore County, Baltimore, USA.


The maximal procedure is a restricted randomization method that maximizes the number of feasible allocation sequences under the constraints of the maximum tolerated imbalance and the allocation sequence length. It assigns an equal probability to all feasible sequences. However, its implementation is not easy due to the lack of the Markovian property of the conditional allocation probabilities. In this paper, we propose the asymptotic maximal procedure, which replaces the sequence-length-dependent conditional allocation probabilities with their asymptotic values. The new randomization procedure is compared with the original maximal procedure and few other randomization procedures with the maximum tolerated imbalance via simulations and is found to be a practical choice for future clinical trials.


Allocation predictability; asymptotic maximal procedure; randomized controlled trial; subject randomization; treatment imbalance


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