Wei L J, Lachin J M
Department of Biostatistics, School of Public Health, University of Michigan, Ann Arbor.
Control Clin Trials. 1988 Dec;9(4):345-64. doi: 10.1016/0197-2456(88)90048-7.
In this article we review the important statistical properties of the urn randomization (design) for assigning patients to treatment groups in a clinical trial. The urn design is the most widely studied member of the family of adaptive biased-coin designs. Such designs are a compromise between designs that yield perfect balance in treatment assignments and complete randomization which eliminates experimental bias. The urn design forces a small-sized trial to be balanced but approaches complete randomization as the size of the trial (n) increases. Thus, the urn design is not as vulnerable to experimental bias as are other restricted randomization procedures. In a clinical trial it may be difficult to postulate that the study subjects constitute a random sample from a well-defined homogeneous population. In this case, a randomization model provides a preferred basis for statistical inference. We describe the large-sample permutational null distributions of linear rank statistics for testing the equality of treatment groups based on the urn design. In general, these permutation tests may be different from those based on the population model, which is equivalent to assuming complete randomization. Poststratified subgroup analyses can also be performed on the basis of the urn design permutational distribution. This provides a basis for analyzing the subset of patients with observed responses when some patients' responses can be assumed to be missing-at-random. For multiple mutually exclusive strata, these tests are correlated. For this case, a combined covariate-adjusted test of treatment effect is described. Finally, we show how to generalize the urn design to a prospectively stratified trial with a fairly large number of strata.
在本文中，我们回顾了用于在临床试验中将患者分配至治疗组的瓮随机化（设计）的重要统计特性。瓮设计是自适应偏倚硬币设计家族中研究最为广泛的成员。此类设计是在能使治疗分配达到完美平衡的设计与消除实验偏倚的完全随机化设计之间的一种折衷。瓮设计迫使小规模试验达到平衡，但随着试验规模（n）的增加趋近于完全随机化。因此，瓮设计不像其他受限随机化程序那样容易受到实验偏倚的影响。在临床试验中，可能难以假定研究对象构成来自定义明确的同质总体的随机样本。在这种情况下，随机化模型为统计推断提供了一个更好的基础。我们描述了基于瓮设计用于检验治疗组相等性的线性秩统计量的大样本置换零分布。一般来说，这些置换检验可能与基于总体模型（等同于假设完全随机化）的检验不同。事后分层亚组分析也可基于瓮设计置换分布进行。这为在假定一些患者的反应可随机缺失时分析有观察到反应的患者子集提供了基础。对于多个相互排斥的分层，这些检验是相关的。针对这种情况，描述了一种综合的协变量调整治疗效果检验。最后，我们展示了如何将瓮设计推广到具有相当多分层的前瞻性分层试验。
