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Estimating the proportion of true null hypotheses using the pattern of observed p-values

机译：使用观察到的p值模式估算真实零假设的比例

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摘要

Estimating the proportion of true null hypotheses, π_0, has attracted much attention in the recent statistical literature. Besides its apparent relevance for a set of specific scientific hypotheses, an accurate estimate of this parameter is key for many multiple testing procedures. Most existing methods for estimating π_0 in the literature are motivated from the independence assumption of test statistics, which is often not true in reality. Simulations indicate that most existing estimators in the presence of the dependence among test statistics can be poor, mainly due to the increase of variation in these estimators. In this paper, we propose several data-driven methods for estimating π_0 by incorporating the distribution pattern of the observed p-values as a practical approach to address potential dependence among test statistics. Specifically, we use a linear fit to give a data-driven estimate for the proportion of true-null p-values in (λ, 1| over the whole range |0, 1| instead of using the expected proportion at 1 -λ . We find that the proposed estimators may substantially decrease the variance of the estimated true null proportion and thus improve the overall performance.
机译：估计真实零假设π_0的比例在最近的统计文献中引起了很多关注。除了与一组特定的科学假设具有明显的相关性外，对该参数的准确估计对于许多多重测试程序也很关键。文献中大多数现有的估计π_0的方法都是基于检验统计量的独立性假设，而这在现实中通常是不正确的。模拟表明，在存在检验统计量之间的依存关系的情况下，大多数现有的估计量可能较差，这主要是由于这些估计量之间的差异增加所致。在本文中，我们提出了几种数据驱动的方法，通过结合观察到的p值的分布模式来估计π_0，以此作为解决测试统计量之间潜在依赖性的实用方法。具体来说，我们使用线性拟合为（λ，1 |在整个范围| 0，1 |中）的真空p值比例提供数据驱动的估计，而不是使用1-λ处的预期比例。我们发现，提出的估计量可能会大大减少估计的真实无效比例的方差，从而提高总体性能。

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  • 来源
    《Journal of applied statistics》 |2013年第10期|1949-1964|共16页
  • 作者

    Tiejun Tong; Zeny Feng; Julia S. Hilton; Hongyu Zhao;

  • 作者单位

    Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, People's Republic of China,Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong, People's Republic of China;

    Department of Mathematics and Statistics, University of Guelph, Guelph, Canada;

    Department of Applied Mathematics, University of Colorado, Boulder, CO 80309, USA;

    Department of Biostatistics, Yale School of Public Health, Yale University, New Haven, CT, USA;

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  • 原文格式 PDF
  • 正文语种 eng
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  • 关键词

    gene expression data; multiple testing; proportion of true null hypotheses; ρ-value;

    机译：基因表达数据;多次测试;真实零假设的比例;ρ值;

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