Balancing the Objectives of Statistical Efficiency and Allocation Randomness in Randomized Controlled Trials

Abstract

Various restricted randomization procedures are available to achieve equal (1:1) allocation in a randomized clinical trial. However, for some procedures, there is a nonnegligible probability of imbalance in the final numbers which may result in an underpowered study. It is important to assess such probability at the study planning stage and make adjustments in the design if needed. In this article, we perform a quantitative assessment of the tradeoff between randomness, balance, and power of restricted randomization designs targeting equal allocation. First, we study the small-sample performance of biased coin designs with known asymptotic properties and identify a design with an excellent balance–randomness tradeoff. Second, we investigate the issue of randomization-induced treatment imbalance and the corresponding risk of an underpowered study. We propose two risk mitigation strategies: increasing the total sample size or fine-tuning the biased coin parameter to obtain the least restrictive randomization procedure that attains the target power with a high, user-defined probability for the given sample size. Additionally, we investigate an approach for finding the most balanced design that satisfies a constraint on the chosen measure of randomness. Our proposed methodology is simple and yet generalizable to more complex settings, such as trials with stratified randomization and multi-arm trials with possibly unequal randomization ratios.

KEYWORDS:

• Biased coin design
• Equal allocation
• Maximum tolerated imbalance
• Power
• Restricted randomization
• Variability in the allocation proportion

Supplementary Materials

The R Markdown document with Julia and R code for performing simulations and summarizing/visualizing the simulation results is available at the journal website.

Acknowledgments

The authors are grateful to the two anonymous reviewers and the journal editors whose comments helped improve this article.

Disclosure Statement

The authors have no conflict of interest with regards to the contents presented in this article.

Additional information

Funding

The author(s) reported there is no funding associated with the work featured in this article.