Multiple Testing When Many p-Values are Uniformly Conservative, with Application to Testing Qualitative Interaction in Educational Interventions
Multiple Testing When Many p-Values are Uniformly Conservative, with Application to Testing Qualitative Interaction in Educational Interventions
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当许多 p 值一致保守时的多重测试，应用于测试教育干预中的定性互动
DOI：
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发表时间：
2017
影响因子：
3.7
通讯作者：
Weijie J. Su
中科院分区：
文献类型：
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作者：
Qingyuan Zhao;Dylan S. Small;Weijie J. Su
在评价治疗效果时，了解治疗是否对某些人有益而对另一些人有害，这是一种被称为定性相互作用的现象，具有重大的政策意义。我们将这个问题表述为具有许多保守的空p值的多重检验问题，其中经典的多重检验方法可能会大大失去功效。我们提出了一个简单的技术-空调-以提高功率。我们需要的一个关键假设是一致保守性，这意味着对于任何保守的p值p，条件分布（p/τ）|对于任意的τ，p ∈ τ随机大于（0，1）上的均匀分布。我们证明了这个属性适用于一维指数族中的单侧检验（例如，定性交互测试）以及测试|μ|使用统计量Y N（μ，1）（例如，用阈值η测试实际重要性）。我们提出了一种自适应的方法来选择阈值τ。我们的理论和模拟结果表明，所提出的测试获得显着的权力时，许多p值是一致保守的，并失去很少的权力时，没有p值是一致保守的。我们将我们的方法应用于两个教育干预数据集。本文的补充材料可在网上查阅。
ABSTRACT In the evaluation of treatment effects, it is of major policy interest to know if the treatment is beneficial for some and harmful for others, a phenomenon known as qualitative interaction. We formulate this question as a multiple testing problem with many conservative null p-values, in which the classical multiple testing methods may lose power substantially. We propose a simple technique—conditioning—to improve the power. A crucial assumption we need is uniform conservativeness, meaning for any conservative p-value p, the conditional distribution (p/τ) | p ⩽ τ is stochastically larger than the uniform distribution on (0, 1) for any τ. We show this property holds for one-sided tests in a one-dimensional exponential family (e.g., testing for qualitative interaction) as well as testing |μ| ⩽ η using a statistic Y ∼ N(μ, 1) (e.g., testing for practical importance with threshold η). We propose an adaptive method to select the threshold τ. Our theoretical and simulation results suggest that the proposed tests gain significant power when many p-values are uniformly conservative and lose little power when no p-value is uniformly conservative. We apply our method to two educational intervention datasets. Supplementary materials for this article are available online.
影响因子：
2.7
作者：
Lei, Lihua;Ramdas, Aaditya;Fithian, William
通讯作者：
Fithian, William