论文标题
强大的部分结合假设通过调节测试
Powerful Partial Conjunction Hypothesis Testing via Conditioning
论文作者
论文摘要
部分结合假设（PCH）测试结合了一组基础假设的信息，以确定某些子集是否是非零子集。 PCH测试在各种各样的字段中都会出现，但是标准PCH测试方法可能是高度保守的，尤其是在应用程序中通常遇到的低信号设置中。在本文中，我们介绍了条件PCH（CPCH）测试，这是一种测试单个PCH的新方法，该方法通过根据基本P值的某些顺序统计数据来直接纠正标准方法的保守性。在PCH测试中通常遇到的分布假设下，CPCH测试是有效的，并且在零下几乎均匀分布的P值（即CPCH P值仅非常保守）。我们证明，CPCH测试匹配或胜过现有的单个PCH测试，即在低信号设置中具有特定功率增益，即使在模型错误指定下也可以维持I型错误控制，并且可以用来在某些设置中超越最先进的多个PCH测试程序，尤其是在存在附带信息的情况下。最后，我们通过跨DNA微阵列研究的可复制性分析说明了CPCH检验的应用。
A Partial Conjunction Hypothesis (PCH) test combines information across a set of base hypotheses to determine whether some subset is non-null. PCH tests arise in a diverse array of fields, but standard PCH testing methods can be highly conservative, leading to low power especially in low signal settings commonly encountered in applications. In this paper, we introduce the conditional PCH (cPCH) test, a new method for testing a single PCH that directly corrects the conservativeness of standard approaches by conditioning on certain order statistics of the base p-values. Under distributional assumptions commonly encountered in PCH testing, the cPCH test is valid and produces nearly uniformly distributed p-values under the null (i.e., cPCH p-values are only very slightly conservative). We demonstrate that the cPCH test matches or outperforms existing single PCH tests with particular power gains in low signal settings, maintains Type I error control even under model misspecification, and can be used to outperform state-of-the-art multiple PCH testing procedures in certain settings, particularly when side information is present. Finally, we illustrate an application of the cPCH test through a replicability analysis across DNA microarray studies.
