Screening for Partial Conjunction Hypotheses
Screening for Partial Conjunction Hypotheses
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DOI：
10.1111/j.1541-0420.2007.00984.x
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发表时间：
2008-12-01
期刊：
影响因子：
1.9
通讯作者：
Heller, Ruth
中科院分区：
文献类型：
--
作者：
Benjamini, Yoav;Heller, Ruth
我们考虑假设的部分合取检验问题，它认为至少u出n个测试的假设是假的。它提供了一种介于两者之间的方法来测试零假设的合取对至少一个不是零的替代方案，以及测试零假设的分离对所有假设都不是零的替代方案。我们建议强大的检验统计量，用于测试这样的部分合取假设，是有效的检验统计量之间的依赖关系，以及独立。然后，我们解决的问题，同时使用错误发现率（FDR）的方法测试许多部分合取假设。我们证明，如果FDR控制过程中Benjamini和Hochberg（1995年，皇家统计学会杂志，系列B 57，289-300）是用于此目的的FDR控制下的各种依赖结构。此外，我们可以同时在所有级别进行筛选，以便在叠加图上显示结果，并仍然控制适当的FDR测量。我们应用该方法的例子，从微阵列分析和功能性磁共振成像（fMRI），两个应用领域，需要部分连接分析已被确定。
We consider the problem of testing for partial conjunction of hypothesis, which argues that at least u out of n tested hypotheses are false. It offers an in-between approach to the testing of the conjunction of null hypotheses against the alternative that at least one is not, and the testing of the disjunction of null hypotheses against the alternative that all hypotheses are not null. We suggest powerful test statistics for testing such a partial conjunction hypothesis that are valid under dependence between the test statistics as well as under independence. We then address the problem of testing many partial conjunction hypotheses simultaneously using the false discovery rate (FDR) approach. We prove that if the FDR controlling procedure in Benjamini and Hochberg (1995, Journal of the Royal Statistical Society, Series B 57, 289-300) is used for this purpose the FDR is controlled under various dependency structures. Moreover, we can screen at all levels simultaneously in order to display the findings on a superimposed map and still control an appropriate FDR measure. We apply the method to examples from microarray analysis and functional magnetic resonance imaging (fMRI), two application areas where the need for partial conjunction analysis has been identified.