Decision theory results for one-sided multiple comparison procedures
Decision theory results for one-sided multiple comparison procedures
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DOI：
10.1214/009053604000000968
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发表时间：
2005-02-01
影响因子：
4.5
通讯作者：
Sackrowitz, HB
中科院分区：
文献类型：
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作者：
Cohen, A;Sackrowitz, HB
在过去的十年里，对多重假设检验的兴趣重新抬头。受基因组学研究的启发。微阵列、DNA测序、药物筛选、临床试验。在生物测定、教育和心理学领域，统计学家一直在投入相当大的研究精力，努力正确分析多个终点数据。针对新的应用。在新标准和新方法的基础上，出现了许多临时程序。传统的要求是使用将强族错误率（FWE）控制在某个预定水平a的程序。也就是说，对真零假设的任何错误拒绝的概率应该小于或等于alpha。在这种要求下，找到理想的和强大的多重检验程序是困难的。最近的一个想法是关注控制错误发现率（FDR），即被拒绝的假设的预期比例，事实上，是真的。许多多重检验程序确实控制着FDR。23（1952）541 - 552和28（1957）1 - 25]。莱曼的方法是决策理论和他对待的多个端点的问题作为一个2（k）有限行动的问题时，有k个端点。这种方法是有吸引力的，因为不像FWE和FDR标准，有限行动的方法注意到错误的接受以及错误的拒绝。在本文中，我们认为多个端点的问题作为一个2（k）有限行动问题。本文从容许性、贝叶斯和贝叶斯极限的角度研究了目前流行的单步、逐步和逐步逼近方法。对于我们的模型，这是一个原型，和我们的损失函数。我们能够证明下列结果在一些相当一般的条件下，他指定：（i）单步程序是可容许的，（ii）一个序列的先验分布，其中的降压程序是一个序列的贝叶斯程序的限制。(iii)对于一个向量风险函数，其中每个分量是一个单独的测试问题的风险，各种可容许性和不可容许性的结果得到了在一个配套文件[Cohen和Sackrowit/，Ann，Statist，33（2005）145 - 158]中，我们能够给出贝叶斯，程序和它们的限制的特征。的特征产生一个完整的类和额外的有用的结果，升压过程是不可接受的。对于更严格的损失函数，证明了步升的不容许性。本文还获得了其他决策理论类型的结果。
A resurgence of interest in multiple hypothesis testing has Occurred in the last decade. Motivated by studies in genomics. microarrays, DNA sequencing, drug screening, clinical trials. bioassays, education and psychology, statisticians have been devoting considerable research energy in an effort to properly analyze multiple endpoint data. In response to new applications. new criteria and new methodology, many ad hoc procedures have emerged. The classical requirement has been to use procedures which control the strong familywise error rate (FWE) at some predetermined level a. That is, the probability of any false rejection of a true null hypothesis should be less than or equal to alpha. Finding desirable and powerful multiple test procedures is difficult under this requirement.One of the more recent ideas is concerned with controlling the false discovery rate (FDR), that is, the expected proportion of rejected hypotheses which are, in fact, true. Many multiple test procedures do control the FDR.A much earlier approach to multiple testing was formulated by Lehmann [Ann. Math. Statist. 23 (1952) 541-552 and 28 (1957) 1-25]. Lehmann's approach is decision theoretic and he treats the multiple endpoints problem as a 2(k) finite action problem when there are k endpoints. This approach is appealing since unlike the FWE and FDR criteria, the finite action approach pays attention to false acceptances as well as false rejections. In this paper we view the multiple endpoints problem as a 2(k) finite action problem. We study the popular procedures single-step, step-down and step-tip front the point of view of admissibility, Bayes and limit of Bayes properties. For our model, which is a prototypical one, and our loss function. we are able to demonstrate the following results under some fairly general conditions to he specified:(i) The single-step procedure is admissible,(ii) A sequence of prior distributions is given for which the step-down procedure is a limit of a sequence of Bayes procedures.(iii) For a vector risk function, where each component is the risk for an individual testing problem, various admissibility and inadmissibility results are obtained.In a companion paper [Cohen and Sackrowit/, Ann, Statist, 33 (2005) 145-158], we are able to give a characterization of Bayes, procedures and their limits. The characterization yields a complete class and the additional useful result that the step-up procedure is inadmissible. The inadmissibility of step-up is demonstrated there for a more stringent loss function. Additional decision theoretic type results are also obtained in this paper.