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Shi Y, Shi W, Wang M, Lee JH, Kang H, Jiang H. Accurate and fast small p-value estimation for permutation tests in high-throughput genomic data analysis with the cross-entropy method. Stat Appl Genet Mol Biol 2023; 22:sagmb-2021-0067. [PMID: 37622330 DOI: 10.1515/sagmb-2021-0067] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2021] [Accepted: 06/23/2023] [Indexed: 08/26/2023]
Abstract
Permutation tests are widely used for statistical hypothesis testing when the sampling distribution of the test statistic under the null hypothesis is analytically intractable or unreliable due to finite sample sizes. One critical challenge in the application of permutation tests in genomic studies is that an enormous number of permutations are often needed to obtain reliable estimates of very small p-values, leading to intensive computational effort. To address this issue, we develop algorithms for the accurate and efficient estimation of small p-values in permutation tests for paired and independent two-group genomic data, and our approaches leverage a novel framework for parameterizing the permutation sample spaces of those two types of data respectively using the Bernoulli and conditional Bernoulli distributions, combined with the cross-entropy method. The performance of our proposed algorithms is demonstrated through the application to two simulated datasets and two real-world gene expression datasets generated by microarray and RNA-Seq technologies and comparisons to existing methods such as crude permutations and SAMC, and the results show that our approaches can achieve orders of magnitude of computational efficiency gains in estimating small p-values. Our approaches offer promising solutions for the improvement of computational efficiencies of existing permutation test procedures and the development of new testing methods using permutations in genomic data analysis.
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Affiliation(s)
- Yang Shi
- Division of Biostatistics and Data Science, Department of Population Health Sciences and Department of Neuroscience and Regenerative Medicine, Medical College of Georgia, Augusta University, Augusta, GA 30912, USA
- University of New Mexico Comprehensive Cancer Center Biostatistics Shared Resource, University of New Mexico, Albuquerque, NM 87131, USA
- Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109, USA
| | - Weiping Shi
- College of Mathematics, Jilin University, Changchun, 130012, China
| | - Mengqiao Wang
- Department of Epidemiology and Biostatistics, School of Public Health, Chengdu Medical College, Chengdu, 610500, China
| | - Ji-Hyun Lee
- Division of Quantitative Sciences, University of Florida Health Cancer Center and Department of Biostatistics, University of Florida, Gainesville, FL 32610, USA
| | - Huining Kang
- University of New Mexico Comprehensive Cancer Center Biostatistics Shared Resource, University of New Mexico, Albuquerque, NM 87131, USA
- Department of Internal Medicine, University of New Mexico, Albuquerque, NM 87131, USA
| | - Hui Jiang
- Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109, USA
- Center for Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, MI 48109, USA
- University of Michigan Rogel Cancer Center, University of Michigan, Ann Arbor, MI 48109, USA
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Wei W, Gao S, Gao B, Zhong Y, Gu C, Gao Z. Random weighting-based quantile estimation via importance resampling. COMMUN STAT-THEOR M 2019. [DOI: 10.1080/03610926.2018.1496256] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Wenhui Wei
- School of Automatics, Northwestern Polytechnical University, Xi’an, China
- School of Geological and Surveying Engineering, Chang’an University, Xi’an, China
| | - Shesheng Gao
- School of Automatics, Northwestern Polytechnical University, Xi’an, China
| | - Bingbing Gao
- School of Automatics, Northwestern Polytechnical University, Xi’an, China
| | - Yongmin Zhong
- School of Engineering, RMIT University, Bundoora, Victoria, Australia
| | - Chengfan Gu
- School of Engineering, RMIT University, Bundoora, Victoria, Australia
| | - Zhaohui Gao
- School of Automatics, Northwestern Polytechnical University, Xi’an, China
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Gao B, Gao S, Zhong Y, Gu C. Random weighting estimation of sampling distributions via importance resampling. COMMUN STAT-SIMUL C 2016. [DOI: 10.1080/03610918.2014.977915] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Bingbing Gao
- School of Automatics, Northwestern Polytechnical University, Xi'an, China
| | - Shesheng Gao
- School of Automatics, Northwestern Polytechnical University, Xi'an, China
| | - Yongmin Zhong
- School of Engineering, RMIT University, Bundoora, Australia
| | - Chengfan Gu
- School of Engineering, RMIT University, Bundoora, Australia
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Abstract
Importance sampling is an efficient strategy for reducing the variance of certain bootstrap estimates. It has found wide applications in bootstrap quantile estimation, proportional hazards regression, bootstrap confidence interval estimation, and other problems. Although estimation of the optimal sampling weights is a special case of convex programming, generic optimization methods are frustratingly slow on problems with large numbers of observations. For instance, interior point and adaptive barrier methods must cope with forming, storing, and inverting the Hessian of the objective function. In this paper, we present an efficient procedure for calculating the optimal importance weights and compare its performance to standard optimization methods on a representative data set. The procedure combines several potent ideas for large scale optimization.
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