Exact optimum coin bias in Efron's randomization procedure

• Published in: Statistics in medicine Vol. 34; no. 28; pp. 3760 - 3768
• Main Authors: Antognini, Alessandro Baldi, Rosenberger, William F., Wang, Yang, Zagoraiou, Maroussa
• Format: Journal Article
• Language: English
• Published: England Blackwell Publishing Ltd 10.12.2015; Wiley Subscription Services, Inc
• Subjects: accidental bias; Asymptotic methods; biased coin design; Clinical Trials as Topic - statistics & numerical data; compound optimality; Humans; Medical statistics; Medical treatment; Optimization techniques; Probability distribution; Random Allocation; Research Design; restricted randomization; Selection Bias; selection bias; compound optimality; biased coin design; accidental bias; restricted randomization
• ISSN: 0277-6715; 1097-0258
• DOI: 10.1002/sim.6576

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.