Strassburger K, Bretz F, Finner H
German Diabetes Center, Leibniz Center at Heinrich-Heine-University Düsseldorf, Institute of Biometrics and Epidemiology, Düsseldorf, Germany.
Biometrics. 2007 Dec;63(4):1143-51. doi: 10.1111/j.1541-0420.2007.00813.x. Epub 2007 May 8.
This article considers the problem of comparing several treatments (dose levels, interventions, etc.) with the best, where the best treatment is unknown and the treatments are ordered in some sense. Order relations among treatments often occur quite naturally in practice. They may be ordered according to increasing risks, such as tolerability or safety problems with increasing dose levels in a dose-response study, for example. We tackle the problem of constructing a lower confidence bound for the smallest index of all treatments being at most marginally less effective than the (best) treatment having the largest effect. Such a bound ensures at confidence level 1 -alpha that all treatments with lower indices are relevantly less effective than the best competitor. We derive a multiple testing strategy that results in sharp confidence bounds. The proposed lower confidence bound is compared with those derived from other testing strategies. We further derive closed-form expressions for power and sample size calculations. Finally, we investigate several real data sets to illustrate various applications of our methods.
本文考虑了将几种治疗方法（剂量水平、干预措施等）与最佳治疗方法进行比较的问题，其中最佳治疗方法未知且治疗方法在某种意义上是有序的。治疗方法之间的顺序关系在实际中经常自然出现。例如，在剂量反应研究中，它们可能根据风险增加的顺序排列，如随着剂量水平增加的耐受性或安全性问题。我们解决的问题是为所有治疗方法中最小的指标构建一个置信下限，该指标至多比具有最大效果的（最佳）治疗方法略差。这样一个界限确保在置信水平为1 -α时，所有指标较低的治疗方法与最佳竞争者相比效果显著较差。我们推导了一种多重检验策略，该策略能得出精确的置信界限。将所提出的置信下限与从其他检验策略得出的下限进行比较。我们还推导了用于功效和样本量计算的封闭形式表达式。最后，我们研究了几个真实数据集以说明我们方法的各种应用。
