Modern randomization methods in clinical trials are invariably adaptive, meaning that the assignment of the next subject to a treatment group uses the accumulated information in the trial. Some of the recent adaptive randomization methods use mathematical programming to construct attractive clinical trials that balance the group features, such as their sizes and covariate distributions of their subjects. We review some of these methods and compare their performance with common covariate-adaptive randomization methods for small clinical trials. We introduce an energy distance measure that compares the discrepancy between the two groups using the joint distribution of the subjects' covariates. This metric is more appealing than evaluating the discrepancy between the groups using their marginal covariate distributions. Using numerical experiments, we demonstrate the advantages of the mathematical programming methods under the new measure. In the supplementary material, we provide R codes to reproduce our study results and facilitate comparisons of different randomization procedures.

翻译：现代临床试验中的随机化方法通常是自适应的，即下一位受试者的治疗分组需利用试验中累积的信息。部分近期提出的自适应随机化方法采用数学规划构建具有吸引力的临床试验，以平衡各组特征（如样本量及受试者协变量分布）。我们回顾了其中若干方法，并将其与用于小型临床试验的常见协变量自适应随机化方法进行性能比较。我们引入一种基于受试者协变量联合分布进行两组间差异比较的能量距离度量。这一指标比通过边际协变量分布评估组间差异更优。通过数值实验，我们展示了数学规划方法在新度量下的优势。在补充材料中，我们提供R代码以复现研究结果，并便于不同随机化程序的比较。