Journal Article

Minimization of expected balance distribution differences: optimization of the randomized allocation algorithm based on the Pocock-Simon design

Zhuang, Hui-ying, Wu, Min, Xing, Ying, Xu, Julia Ao-Chen, Zhao, Yun, Feng, Lin, Wen, Tian-cai, Zhang, Xue-qin

2026

Overview

Objectives Building upon the minimization random grouping algorithm designed by Pocock and Simon, this study proposes a randomization algorithm based on the minimization of expected balance distribution differences. This approach aims to balance key covariates and other potential confounding factors. Methods A global difference algorithm based on expected balance distribution was proposed upon analysis of the limitations of the local range algorithm used in traditional minimization randomization for imbalance calculation. The study implemented three algorithms using R 4.3.2 and conducted three experiments through Monte Carlo simulations, In Experiment One, the sample size was fixed, while the number of control factors varied. In Experiment Two, the control factors and their levels were fixed, and the sample sizes varied. Imbalance performance was compared the imbalance performance across groups and control factors. Additionally, in Experiment Three, a real-data analysis was conducted to assess the applicability of the new design in clinical trials. Results In Experiment One, the Expected Balance Distribution and Minimized Variations(EBDMV) consistently outperformed the minimum sufficient balance and the traditional minimization method in terms of the sample size difference between the groups (e.g., 0.716 vs. 15.55 vs. 0.574). Additionally, the P -values distribution was more concentrated, approaching 1. When the number of control factors was increased to 10, the minimum P -value of the traditional method was individually less than 0.05, whereas the minimum P -value of the expected balance distribution and minimized variations(EBDMV) remained greater than 0.05, indicating that the latter method exhibited stronger stability and adaptability. In Experiment Two, the EBDMV also demonstrated higher performance in terms of the sample size difference between groups (e.g., 0.708 vs. 7 vs. 0.726). Furthermore, as the sample size increased, the P -value approached 1, demonstrating greater stability. The results of Experiment Three were consistent with the simulated data. The EBDMV method generally outperformed the traditional minimization method in terms of sample size difference between groups (e.g., 1.08 vs. 9.652 vs. 0.968) and exhibited a more centralized distribution of P -values. Conclusions When the number of control factors is high and the sample size is small, the EBDMV method demonstrates significantly superior balance in both inter-group distributions and control factor balance compared to the traditional minimization method.

• Publisher: BioMed Central,BioMed Central Ltd,Springer Nature B.V,BMC
• Subject: Algorithms / Allocation randomness / Analysis / Bias / Clinical trial / Clinical trials / Computer simulation / Design / Health Sciences / Medical research / Medicine / Medicine & Public Health / Medicine, Experimental / Methods / Minimization / Monte Carlo method / Optimized algorithm / Simulation methods / Simulation study / Statistical power / Statistical Theory and Methods / Statistics for Life Sciences / Theory of Medicine/Bioethics / Type 2 diabetes