Consonance and the Closure Method in Multiple Testing

IF 1.2 4区 数学
Joseph P. Romano, A. Shaikh, Michael Wolf
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引用次数: 6

Abstract

Consider the problem of testing s null hypotheses simultaneously. In order to deal with the multiplicity problem, the classical approach is to restrict attention to multiple testing procedures that control the familywise error rate (FWE). The closure method of Marcus et al. (1976) reduces the problem of constructing such procedures to one of constructing single tests that control the usual probability of a Type 1 error. It was shown by Sonnemann (1982, 2008) that any coherent multiple testing procedure can be constructed using the closure method. Moreover, it was shown by Sonnemann and Finner (1988) that any incoherent multiple testing procedure can be replaced by a coherent multiple testing procedure which is at least as good. In this paper, we first show an analogous result for dissonant and consonant multiple testing procedures. We show further that, in many cases, the improvement of the consonant multiple testing procedure over the dissonant multiple testing procedure may in fact be strict in the sense that it has strictly greater probability of detecting a false null hypothesis while still maintaining control of the FWE. Finally, we show how consonance can be used in the construction of some optimal maximin multiple testing procedures. This last result is especially of interest because there are very few results on optimality in the multiple testing literature.
多重测试中的谐音与闭合法
考虑同时检验5个零假设的问题。为了解决多重性问题,经典的方法是将注意力限制在控制家族错误率的多个测试程序上。Marcus等人(1976)的闭包方法将构造此类过程的问题简化为构造单个测试的问题之一,这些测试可以控制类型1错误的通常概率。Sonnemann(1982, 2008)表明,任何连贯的多重测试过程都可以使用闭包方法构建。此外,Sonnemann和Finner(1988)表明,任何不连贯的多重测试程序都可以被至少同样好的连贯多重测试程序所取代。在本文中,我们首先展示了不谐音和辅音多重测试程序的类似结果。我们进一步表明,在许多情况下,辅音多重测试程序对不和谐多重测试程序的改进实际上可能是严格的,因为它在仍然保持对FWE的控制的同时,具有严格更大的检测错误零假设的概率。最后,我们展示了如何在构建一些最优最大值的多重测试程序中使用一致性。最后一个结果特别有趣,因为在多重测试文献中很少有关于最优性的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
International Journal of Biostatistics
International Journal of Biostatistics Mathematics-Statistics and Probability
CiteScore
2.30
自引率
8.30%
发文量
28
期刊介绍: The International Journal of Biostatistics (IJB) seeks to publish new biostatistical models and methods, new statistical theory, as well as original applications of statistical methods, for important practical problems arising from the biological, medical, public health, and agricultural sciences with an emphasis on semiparametric methods. Given many alternatives to publish exist within biostatistics, IJB offers a place to publish for research in biostatistics focusing on modern methods, often based on machine-learning and other data-adaptive methodologies, as well as providing a unique reading experience that compels the author to be explicit about the statistical inference problem addressed by the paper. IJB is intended that the journal cover the entire range of biostatistics, from theoretical advances to relevant and sensible translations of a practical problem into a statistical framework. Electronic publication also allows for data and software code to be appended, and opens the door for reproducible research allowing readers to easily replicate analyses described in a paper. Both original research and review articles will be warmly received, as will articles applying sound statistical methods to practical problems.
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