Balancing treatment allocation for influential covariates is critical in clinical trials. This has become increasingly important as more and more biomarkers are found to be associated with different diseases in translational research (genomics, proteomics and metabolomics). Stratified permuted block randomization and minimization methods [Pocock and Simon Biometrics 31 (1975) 103-115, etc.] are the two most popular approaches in practice. However, stratified permuted block randomization fails to achieve good overall balance when the number of strata is large, whereas traditional minimization methods also suffer from the potential drawback of large within-stratum imbalances. Moreover, the theoretical bases of minimization methods remain largely elusive. In this paper, we propose a new covariate-adaptive design that is able to control various types of imbalances. We show that the joint process of within-stratum imbalances is a positive recurrent Markov chain under certain conditions. Therefore, this new procedure yields more balanced allocation. The advantages of the proposed procedure are also demonstrated by extensive simulation studies. Our work provides a theoretical tool for future research in this area.Comment: Published in at http://dx.doi.org/10.1214/12-AOS983 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

In controlled clinical trials, balanced allocation over covariates is often viewed as an essential component in ensuring valid treatment comparisons. Minimization, sometimes called 'dynamic allocation', or 'covariate-adaptive randomization' has an advantage over stratified randomization, in that it is able to achieve balance over a large number of covariates when the sample size is small to medium. Despite its effectiveness, minimization has been questioned by regulatory agencies, mainly because of its increased complexity in practice and its potential impact on subsequent analysis. In recent years, however, with developments in clinical trials information technology, as well as advances in statistical theory, the attitudes toward minimization have evolved. In its 2013 draft guidelines, the European Medicines Agency (EMA) provided instructive guidelines for the implementation of minimization. In this paper we review the broad class of methods that belong to minimization, including its original forms for balancing over covariate margins and its generalization to balancing over other subgroups of interest or over continuous covariates. Moreover, we review the theoretical development in recent years, including the large-sample properties of balance under minimization, the impact of minimization on inference for different data types, and on suitable randomization tests.

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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.