Journal of Probability and Statistics
Volume 2012 (2012), Article ID 842369, 13 pages
Research Article

Balancing Treatment Allocation over Continuous Covariates: A New Imbalance Measure for Minimization

1Department of Statistics, West Virginia University, Hodges Hall, Morgantown, WV 26506, USA
2Department of Statistics, University of Virginia, Halsey Hall, Charlottesville, VA 22904, USA

Received 12 January 2012; Revised 10 April 2012; Accepted 7 May 2012

Academic Editor: Peter van der Heijden

Copyright © 2012 Yanqing Hu and Feifang Hu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In many clinical trials, it is important to balance treatment allocation over covariates. Although a great many papers have been published on balancing over discrete covariates, the procedures for continuous covariates have been less well studied. Traditionally, a continuous covariate usually needs to be transformed to a discrete one by splitting its range into several categories. Such practice may lead to loss of information and is susceptible to misspecification of covariate distribution. The more recent papers seek to define an imbalance measure that preserves the nature of continuous covariates and set the allocation rule in order to minimize that measure. We propose a new design, which defines the imbalance measure by the maximum assignment difference when all possible divisions of the covariate range are considered. This measure depends only on ranks of the covariate values and is therefore free of covariate distribution. In addition, we developed an efficient algorithm to implement the new procedure. By simulation studies we show that the new procedure is able to keep good balance properties in comparison with other popular designs.