Lachin J M
George Washington University, Department of Statistics/Computer and Information Systems, Rockville, Maryland 20852.
Control Clin Trials. 1988 Dec;9(4):312-26. doi: 10.1016/0197-2456(88)90046-3.
This article presents the properties of complete randomization (e.g., coin toss) and of the random allocation rule (random permutation of n/2 of n elements). The latter is principally used in cases where the total sample size n is known exactly a priori. The likelihood of treatment imbalances is readily computed and is shown to be negligible for large trials (n greater than 200), regardless of whether a stratified randomization is used. It is shown that substantial treatment imbalances are extremely unlikely in large trials, and therefore there is likely to be no substantial effect on power. The large-sample permutational distribution of the family of linear rank tests is presented for complete randomization unconditionally and conditionally, and for the random allocation rule. Asymptotically the three are equivalent to the distribution of these tests under a sampling-based population model. Permutation tests are also presented for a stratified analysis within one or more subgroups of patients defined post hoc on the basis of a covariate. This provides a basis for analysis when some patients' responses are assumed to be missing-at-random. Using the Blackwell-Hodges model, it is shown that complete randomization eliminates the potential for selection bias, but that the random allocation rule yields a substantial potential for selection bias in an unmasked trial. Finally, the Efron model for accidental bias is used to assess the potential for bias in the estimate of treatment effect due to covariate imbalance. Asymptotically, this probability approaches zero for complete randomization and for the random allocation rule. However, for finite n, complete randomization minimizes the probability of accidental bias, whereas this probability is slightly higher with a random allocation rule. It is concluded that complete randomization has merit in large clinical trials.
本文介绍了完全随机化（如抛硬币）和随机分配规则（对(n)个元素中的(n/2)个进行随机排列）的性质。后者主要用于总样本量(n)在事先就确切已知的情况。治疗组不均衡的可能性很容易计算出来，并且对于大型试验（(n\gt200)），无论是否使用分层随机化，结果都表明这种可能性可忽略不计。结果表明，在大型试验中出现显著的治疗组不均衡极不可能，因此对检验效能可能不会有显著影响。给出了完全随机化无条件和有条件情况下以及随机分配规则下线性秩检验族的大样本排列分布。渐近地，这三种分布与基于抽样的总体模型下这些检验的分布等价。还给出了基于协变量事后定义的一个或多个患者亚组内分层分析的排列检验。当假定某些患者的反应为随机缺失时，这为分析提供了基础。使用布莱克韦尔 - 霍奇斯模型表明，完全随机化消除了选择偏倚的可能性，但在开放试验中随机分配规则会产生相当大的选择偏倚可能性。最后，使用埃弗龙意外偏倚模型来评估由于协变量不均衡导致治疗效果估计中出现偏倚的可能性。渐近地，完全随机化和随机分配规则下这种概率趋近于零。然而，对于有限的(n)，完全随机化使意外偏倚的概率最小化，而随机分配规则下这种概率略高。结论是完全随机化在大型临床试验中有其优点。
