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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.