期刊
ANNALS OF STATISTICS
卷 50, 期 2, 页码 807-857出版社
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/21-AOS2128
关键词
EM algorithm; false discovery rate; isotonic regression; local false discovery rate; multiple testing; Pool-Adjacent-Violators algorithm
资金
- NIH [2UL1TR001427-05]
- Mayo Clinic Center for Individualized Medicine
- NSF [DMS-1830392, DMS1811747]
- National Institutes of Health [R21 HG011662]
The article introduces a method to improve the statistical power of large-scale multiple testing by utilizing auxiliary information in high-dimensional statistical inference. By using a framework based on a two-group mixture model and imposing structural relationship constraints and an optimal rejection rule to control the false discovery rate, the method's power is enhanced. The advantages of the proposed method are verified through empirical and theoretical analysis.
Large-scale multiple testing is a fundamental problem in high dimensional statistical inference. It is increasingly common that various types of auxiliary information, reflecting the structural relationship among the hypotheses, are available. Exploiting such auxiliary information can boost statistical power. To this end, we propose a framework based on a two-group mixture model with varying probabilities of being null for different hypotheses a priori, where a shape-constrained relationship is imposed between the auxiliary information and the prior probabilities of being null. An optimal rejection rule is designed to maximize the expected number of true positives when average false discovery rate is controlled. Focusing on the ordered structure, we develop a robust EM algorithm to estimate the prior probabilities of being null and the distribution of p-values under the alternative hypothesis simultaneously. We show that the proposed method has better power than state-of-the-art competitors while controlling the false discovery rate, both empirically and theoretically. Extensive simulations demonstrate the advantage of the proposed method. Datasets from genome-wide association studies are used to illustrate the new methodology.
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