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June 2014 Detection boundary and Higher Criticism approach for rare and weak genetic effects
Zheyang Wu, Yiming Sun, Shiquan He, Judy Cho, Hongyu Zhao, Jiashun Jin
Ann. Appl. Stat. 8(2): 824-851 (June 2014). DOI: 10.1214/14-AOAS724


Genome-wide association studies (GWAS) have identified many genetic factors underlying complex human traits. However, these factors have explained only a small fraction of these traits’ genetic heritability. It is argued that many more genetic factors remain undiscovered. These genetic factors likely are weakly associated at the population level and sparsely distributed across the genome. In this paper, we adapt the recent innovations on Tukey’s Higher Criticism (Tukey [The Higher Criticism (1976) Princeton Univ.]; Donoho and Jin [Ann. Statist. 32 (2004) 962–994]) to SNP-set analysis of GWAS, and develop a new theoretical framework in large-scale inference to assess the joint significance of such rare and weak effects for a quantitative trait. In the core of our theory is the so-called detection boundary, a curve in the two-dimensional phase space that quantifies the rarity and strength of genetic effects. Above the detection boundary, the overall effects of genetic factors are strong enough for reliable detection. Below the detection boundary, the genetic factors are simply too rare and too weak for reliable detection. We show that the HC-type methods are optimal in that they reliably yield detection once the parameters of the genetic effects fall above the detection boundary and that many commonly used SNP-set methods are suboptimal. The superior performance of the HC-type approach is demonstrated through simulations and the analysis of a GWAS data set of Crohn’s disease.


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Zheyang Wu. Yiming Sun. Shiquan He. Judy Cho. Hongyu Zhao. Jiashun Jin. "Detection boundary and Higher Criticism approach for rare and weak genetic effects." Ann. Appl. Stat. 8 (2) 824 - 851, June 2014.


Published: June 2014
First available in Project Euclid: 1 July 2014

zbMATH: 06333778
MathSciNet: MR3262536
Digital Object Identifier: 10.1214/14-AOAS724

Keywords: Detection boundary , Genome-wide association studies , higher criticism , large-scale inference , Multiple hypotheses testing , rare and weak effects , SNP-set methods , statistical power

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.8 • No. 2 • June 2014
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