Bonferroni parallel Gatekeeping -: Transparent generalizations, adjusted P-values, and short direct proofs
Bonferroni parallel Gatekeeping -: Transparent generalizations, adjusted P-values, and short direct proofs
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DOI：
10.1002/bimj.200610361
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发表时间：
2007-12-01
影响因子：
1.7
通讯作者：
Guilbaud, Olivier
中科院分区：
文献类型：
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作者：
Guilbaud, Olivier
在Bonferroni并行把关多重测试程序(MTP)的两步版本(Dmitrienko，Tamhane，Wang和Chen，2006)中：(A)零假设的族F1被用作另一族F2的把关人，因为除非在F1中至少有一个H被拒绝，否则F2中的H不能被拒绝；(B)在第一步中，在局部多级阿尔法中对F1使用Bonferroni MTP；以及(C)在F2的第二步中使用Holm(1979)的降级MTP，其局部多重水平取决于在第一步中做出的拒绝。本文指出，这种两步法可以推广，在第二步中，可以用任何具有多层控制和可用的多重数调整p值的MTP来代替Holm的MTP。还给出了与Dmitrienko，Molenberghs，Chuang-Stein和Offen(2005)所称的改进Bonferroni并行门控有关的进一步推广，其中在F2中的所有HS被拒绝的情况下，F1中的附加拒绝可以通过比初始Bonferroni MTP更强大的任何MTP，例如Holm的MTP，在本地多级阿尔法的第三步中进行。这两个广义Bonferroni并行守门MTP具有多水平α的证明是简短而直接的，没有封闭检验的论点。可以很容易地计算出这些MTP的多重性调整的p值。对几个连续的看门人系列的扩展是简单的。文中给出了一个实例。
In the two-step version (Dmitrienko, Tamhane, Wang and Chen, 2006) of the Bonferroni parallel-gatekeeping multiple-testing procedure (MTP): (a) a family F1 of null hypotheses H is used as a gatekeeper for another family F2 in that no H in F2 can be rejected unless at least one H is rejected in F1; (b) a Bonferroni MTP is used for F1 at local multiple-level alpha in the first step; and (c) Holm's (1979) step-down MTP is used in the second step for F2 at a local multiple level that depends on the rejections made in the first step. It is shown in this article that this two-step procedure can be generalized in that any MTP with multiple-level control and available multiplicity-adjusted p-values can be used instead of Holm's MTP in the second step. A further generalization related to what Dmitrienko, Molenberghs, Chuang-Stein and Offen (2005) called modified Bonferroni parallel gatekeeping is also given where in case all Hs in F2 are rejected, additional rejections in F1 can be made in a third step at local multiple-level alpha through any MTP that is more powerful than the initial Bonferroni MTP, e.g. Holm's MTP. The proofs that these two generalized Bonferroni parallel-gatekeeping MTPs have multiple-level alpha are short and direct, without closed-testing arguments. Multiplicity-adjusted p-values can easily be calculated for these MTPs. The extensions to several successive gatekeeper families are straightforward. An illustration is given.