Exact optimum coin bias in Efron's randomization procedure |
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| Authors: | Alessandro Baldi Antognini William F. Rosenberger Yang Wang Maroussa Zagoraiou |
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| Affiliation: | 1. Department of Statistical Sciences, University of Bologna, Bologna, Italy;2. Department of Statistics, George Mason University, Fairfax, VA, U.S.A.;3. Department of Business Administration and Law, University of Calabria, Arcavacata di Rende (CS), Italy |
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| Abstract: | Efron's biased coin design is a restricted randomization procedure that has very favorable balancing properties, yet it is fully randomized, in that subjects are always randomized to one of two treatments with a probability less than 1. The parameter of interest is the bias p of the coin, which can range from 0.5 to 1. In this note, we propose a compound optimization strategy that selects p based on a subjected weighting of the relative importance of the two fundamental criteria of interest for restricted randomization mechanisms, namely balance between the treatment assignments and allocation randomness. We use exact and asymptotic distributional properties of Efron's coin to find the optimal p under compound criteria involving imbalance variability, expected imbalance, selection bias, and accidental bias, for both small/moderate trials and large samples. Copyright © 2015 John Wiley & Sons, Ltd. |
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| Keywords: | accidental bias biased coin design compound optimality restricted randomization selection bias |
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