Singh Bahadur, Halabi Susan, Schell Michael J
Lineberger Comprehensive Cancer Center-UNC, Chapel Hill, NC, USA.
Department of Biostatistics and Bioinformatics, Duke University Medical Center, Durham, NC, USA.
J Appl Stat. 2008;35(5):583-600. doi: 10.1080/02664760801924780. Epub 2008 Apr 23.
The statistical methodology under order restriction is very mathematical and complex. Thus, we provide a brief methodological background of order restricted likelihood ratio tests for the normal theory case for the basic understanding of its applications, and relegate more technical details to the appendices. For data analysis, algorithms for computing the order restricted estimates and computation of -values are described. A two-step procedure is presented for obtaining the sample size in clinical trials when the minimum power, say 0.80 or 0.90 is specified, and the normal means satisfy an order restriction. Using this approach will result in reduction of 14-24% in the sample size required when one-sided ordered alternatives are used, as illustrated by several examples.
序约束下的统计方法非常数学化且复杂。因此，我们提供正态理论情形下序约束似然比检验的简要方法背景，以便对其应用有基本的理解，并将更多技术细节放在附录中。对于数据分析，描述了计算序约束估计值的算法和p值的计算。当规定了最小检验功效（比如0.80或0.90）且正态均值满足序约束时，给出了一个在临床试验中获取样本量的两步程序。如几个例子所示，使用这种方法将使在使用单侧有序备择假设时所需的样本量减少14% - 24%。
