{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">A general consonance principle for closure tests based on <ns0:math><ns0:mi>p</ns0:mi></ns0:math>-values.","authors":"Sonja Zehetmayer, Franz Koenig, Martin Posch","doi":"10.1177/09622802241269624","DOIUrl":null,"url":null,"abstract":"<p><p>The closure principle is a powerful approach to constructing efficient testing procedures controlling the familywise error rate in the strong sense. For small numbers of hypotheses and the setting of independent elementary <math><mi>p</mi></math>-values we consider closed tests where each intersection hypothesis is tested with a <math><mi>p</mi></math>-value combination test. Examples of such combination tests are the Fisher combination test, the Stouffer test, the Omnibus test, the truncated test, or the Wilson test. Some of these tests, such as the Fisher combination, the Stouffer, or the Omnibus test, are not consonant and rejection of the global null hypothesis does not always lead to rejection of at least one elementary null hypothesis. We develop a general principle to uniformly improve closed tests based on <math><mi>p</mi></math>-value combination tests by modifying the rejection regions such that the new procedure becomes consonant. For the Fisher combination test and the Stouffer test, we show by simulations that this improvement can lead to a substantial increase in power.</p>","PeriodicalId":22038,"journal":{"name":"Statistical Methods in Medical Research","volume":"33 9","pages":"1595-1609"},"PeriodicalIF":1.6000,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistical Methods in Medical Research","FirstCategoryId":"3","ListUrlMain":"https://doi.org/10.1177/09622802241269624","RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"HEALTH CARE SCIENCES & SERVICES","Score":null,"Total":0}
引用次数: 0
Abstract
The closure principle is a powerful approach to constructing efficient testing procedures controlling the familywise error rate in the strong sense. For small numbers of hypotheses and the setting of independent elementary -values we consider closed tests where each intersection hypothesis is tested with a -value combination test. Examples of such combination tests are the Fisher combination test, the Stouffer test, the Omnibus test, the truncated test, or the Wilson test. Some of these tests, such as the Fisher combination, the Stouffer, or the Omnibus test, are not consonant and rejection of the global null hypothesis does not always lead to rejection of at least one elementary null hypothesis. We develop a general principle to uniformly improve closed tests based on -value combination tests by modifying the rejection regions such that the new procedure becomes consonant. For the Fisher combination test and the Stouffer test, we show by simulations that this improvement can lead to a substantial increase in power.
封闭原理是构建有效检验程序的有力方法,它能从强意义上控制族内误差率。对于少量假设和独立基本 p 值的设置,我们可以考虑封闭检验,即用 p 值组合检验对每个交叉假设进行检验。这类组合检验的例子有费雪组合检验、斯托弗检验、全能检验、截断检验或威尔逊检验。其中一些检验,如费雪组合检验、Stouffer 检验或 Omnibus 检验,并不一致,拒绝全局零假设并不总是导致拒绝至少一个基本零假设。我们提出了一个一般原则,通过修改拒绝区域,使新的检验过程变得协整,从而统一改进基于 p 值组合检验的封闭检验。对于费雪组合检验和斯托弗检验,我们通过模拟证明了这种改进可以大幅提高检验的有效性。
期刊介绍:
Statistical Methods in Medical Research is a peer reviewed scholarly journal and is the leading vehicle for articles in all the main areas of medical statistics and an essential reference for all medical statisticians. This unique journal is devoted solely to statistics and medicine and aims to keep professionals abreast of the many powerful statistical techniques now available to the medical profession. This journal is a member of the Committee on Publication Ethics (COPE)