Antognini Alessandro Baldi, Zagoraiou Maroussa
Department of Statistical Sciences, University of Bologna, Via Belle Arti 41, Bologna, Italy.
Pharm Stat. 2014 Mar-Apr;13(2):119-27. doi: 10.1002/pst.1607. Epub 2014 Jan 17.
Efron's biased coin design (BCD) is a well-known randomization technique that helps neutralize selection bias, while keeping the experiment fairly balanced for every sample size. Several extensions of this rule have been proposed, and their properties were analyzed from an asymptotic viewpoint and compared via simulations in a finite setup. The aim of this paper is to push forward these comparisons by taking also into account the adjustable BCD, which is never considered up to now. Firstly, we show that the adjustable BCD performs better than Efron's coin with respect to both loss of precision and randomness. Moreover, the adjustable BCD is always more balanced than the other coins and, only for some sample sizes, slightly more predictable. Therefore, we suggest the dominant BCD, namely a new and flexible class of procedures that can change the allocation rule step by step in order to ensure very good performance in terms of both balance and selection bias for any sample size. Our simulations demonstrate that the dominant BCD is more balanced and, at the same time, less or equally predictable than Atkinson's optimum BCD.
埃弗龙的偏倚硬币设计（BCD）是一种著名的随机化技术，它有助于消除选择偏倚，同时使实验在每个样本量下都保持相当的平衡。人们已经提出了该规则的几种扩展形式，并从渐近的角度分析了它们的性质，并在有限设置中通过模拟进行了比较。本文的目的是通过同时考虑可调整的BCD（到目前为止从未被考虑过）来推进这些比较。首先，我们表明，在精度损失和随机性方面，可调整的BCD比埃弗龙硬币表现更好。此外，可调整的BCD总是比其他硬币更平衡，并且仅在某些样本量下，其可预测性略高。因此，我们提出了主导BCD，即一类新的灵活程序，可以逐步改变分配规则，以便在任何样本量下都能在平衡和选择偏倚方面确保非常好的性能。我们的模拟表明，主导BCD比阿特金森的最优BCD更平衡，同时其可预测性更低或相同。
