title: Exact optimum coin bias in Efron's randomization procedure.
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.
authors.affiliation: Department of Statistical Sciences, University of Bologna, Via Belle Arti 41, 40127, Bologna, Italy.
authors.forename: Alessandro Baldi
authors.initials: AB
authors.lastname: Antognini
authors.affiliation: Department of Statistics, George Mason University, 4400 University Drive MS 4A7, Fairfax, VA, U.S.A.
authors.forename: William F
authors.initials: WF
authors.lastname: Rosenberger
authors.affiliation: Department of Statistics, George Mason University, 4400 University Drive MS 4A7, Fairfax, VA, U.S.A.
authors.forename: Yang
authors.initials: Y
authors.lastname: Wang
authors.affiliation: Department of Business Administration and Law, University of Calabria, 87036, Arcavacata di Rende (CS), Italy.
authors.forename: Maroussa
authors.initials: M
authors.lastname: Zagoraiou
mesh_terms: D002986:Clinical Trials as Topic / Q000706:statistics & numerical data; D006801:Humans; D011897:Random Allocation; D012107:Research Design; D015983:Selection Bias
keywords: accidental bias; biased coin design; compound optimality; restricted randomization; selection bias