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Wei's Urn

Wei's Urn weights the assignment of a new subject by adjusting the probability of the Bernoulli random variable used to determine the next group according to which group is under represented. The adjusted probability is a dynamic value based on the imbalance in the current list.

Suppose that \(n_{r}\) is the total number of subjects already randomize and \(n_{r1}\) is the number of subjects already randomized to Group 1. The probability that the next subject will be randomized to Group 1 is:

\[ p_{1} = 1 - \frac{n_{r1}}{n_{r}} \]

This method is only approriate for 2 groups.

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  • M. Lachin, John, P. Matts, John & Wei, L.J. (1989), "Randomization in clinical trials: Conclusions and recommendations," Controlled clinical trials, 9, 365-74.
  • Suresh K. (2011), "An overview of randomization techniques: An unbiased assessment of outcome in clinical research," Journal of Human Reproductive Sciences, 4(1), 8-11.
  • Vickers AJ. (2006), "How to randomize," Journal of the Society for Integrative Oncology, 4(4), 194-198.