The Cauchy Combination Test under Arbitrary Dependence Structures
Long, Mingya1; Li, Zhengbang2; Zhang, Wei1; Li, Qizhai1
AbstractAggregating multiple effects is often encountered in large-scale data analysis where the fraction of significant effects is generally small. Many existing methods cannot handle it effectively because of lack of computational accuracy for small p-values. The Cauchy combination test (abbreviated as CCT) ( J Am Statist Assoc, 2020, 115(529):393-402) is a powerful and computational effective test to aggregate individual $p$-values under arbitrary correlation structures. This work revisits CCT and shows three key contributions including that (i) the tail probability of CCT can be well approximated by a standard Cauchy distribution under much more relaxed conditions placed on individual p-values instead of the original test statistics; (ii) the relaxation conditions are shown to be satisfied for many popular copulas formulating bivariate distributions; (iii) the power of CCT is no less than that of the minimum-type test as the number of tests goes to infinity with some regular conditions. These results further broaden the theories and applications of CCT. The simulation results verify the theoretic results and the performance of CCT is further evaluated with data from a prostate cancer study.
KeywordCauchy combination test Cauchy distribution Copula p-value combination Sparse signals
Indexed BySCI
Funding ProjectBeijing Natural Science Foundation[Z180006]
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000866053200001
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Document Type期刊论文
Corresponding AuthorLi, Qizhai
Affiliation1.Chinese Acad Sci, Univ Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
2.Cent China Normal Univ, Wuhan, Peoples R China
Recommended Citation
GB/T 7714
Long, Mingya,Li, Zhengbang,Zhang, Wei,et al. The Cauchy Combination Test under Arbitrary Dependence Structures[J]. AMERICAN STATISTICIAN,2022:9.
APA Long, Mingya,Li, Zhengbang,Zhang, Wei,&Li, Qizhai.(2022).The Cauchy Combination Test under Arbitrary Dependence Structures.AMERICAN STATISTICIAN,9.
MLA Long, Mingya,et al."The Cauchy Combination Test under Arbitrary Dependence Structures".AMERICAN STATISTICIAN (2022):9.
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