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Smith's Exponent

Smith's Exponent 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. Let $$\rho$$ be the exponent chosed. The probability that the $$j^{th}$$ subject is allocated to group 1 is given by:

$p_{j} = \frac{n_{j2}}{n_{j1} + n_{j2}} (j - 1)^{\rho}$

where $$n_{j1}$$ and $$n_{j2}$$ are the number of subjects that have been allocated to groups 1 and 2 respecively when the $$j^{th}$$ subject is allocated. This method is only approriate for 2 groups.

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References

• 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.