The Cauchy Combination Test under Arbitrary Dependence Structures

References

• Barach, Y. S., Lee, J. S., and Zang, X. (2011), “T Cell Coinhibition in Prostate Cancer: New Immune Evasion Pathways and Emerging Therapeutics,” Trends in Molecular Medicine, 17, 47–55. DOI: 10.1016/j.molmed.2010.09.006.
   PubMed Web of Science ®Google Scholar
• Barnett, I., Mukherjee, R., and Lin, X. (2017), “The Generalized Higher Criticism for Testing SNP-set Effects in Genetic Association Studies,” Journal of the American Statistical Association, 112, 64–76. DOI: 10.1080/01621459.2016.1192039.
   PubMed Web of Science ®Google Scholar
• Berk, R. H., and Jones, D. H. (1979), “Goodness-of-Fit Test Statistics that Dominate the Kolmogorov Statistics,” Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 47, 47–59. DOI: 10.1007/BF00533250.
   Web of Science ®Google Scholar
• Bu, D., Yang, Q., Meng, Z., Zhang, S., and Li, Q. (2020), “Truncated Tests for Combining Evidence of Summary Statistics,” Genetic Epidemiology, 44, 687–701. DOI: 10.1002/gepi.22330.
   PubMed Web of Science ®Google Scholar
• Chen, Z. (2022), “Robust Tests for Combining p-values under Arbitrary Dependency Structures,” Scientific Reports, 12, 1–8. DOI: 10.1038/s41598-022-07094-7.
   Web of Science ®Google Scholar
• De Vito, S., Massera, E., Piga, M., Martinotto, L., and Di Francia, G. (2008), “On Field Calibration of an Electronic Nose for Benzene Estimation in an Urban Pollution Monitoring Scenario,” Sensors and Actuators B: Chemical, 129, 750–757. DOI: 10.1016/j.snb.2007.09.060.
   Web of Science ®Google Scholar
• Deo, C. M. (1972), “Some Limit Theorems for Maxima of Absolute Values of Gaussian Sequences,” Sankhyā: The Indian Journal of Statistics, Series A, 34, 289–292.
   Google Scholar
• Donoho, D., and Jin, J. (2004), “Higher Criticism for Detecting Sparse Heterogeneous Mixtures,” The Annals of Statistics, 32, 962–994. DOI: 10.1214/009053604000000265.
   Web of Science ®Google Scholar
• Edgington, E. S. (1972), “An Additive Method for Combining Probability Values from Independent Experiments,” The Journal of Psychology, 80, 351–363. DOI: 10.1080/00223980.1972.9924813.
   Web of Science ®Google Scholar
• Eidelman, E., Twum-Ampofo, J., Ansari, J., and Siddiqui, M. M. (2017), “The Metabolic Phenotype of Prostate Cancer,” Frontiers in Oncology, 7, 131. DOI: 10.3389/fonc.2017.00131.
   PubMed Web of Science ®Google Scholar
• Fisher, R. (1932), Statistical Methods for Research Workers, Edinburgh and London: Oliver and Boyd.
   Google Scholar
• Geerdens, C., Acar, E. F., and Janssen, P. (2018), “Conditional Copula Models for Right-Censored Clustered Event Time Data,” Biostatistics, 19, 247–262. DOI: 10.1093/biostatistics/kxx034.
   PubMed Web of Science ®Google Scholar
• Genest, C., and MacKay, J. (1986), “The Joy of Copulas: Bivariate Distributions with Uniform Marginals,” The American Statistician, 40, 280–283.
   Web of Science ®Google Scholar
• Gorfine, M., Schlesinger, M., and Hsu, L. (2020), “K-sample Omnibus Non-proportional Hazards Tests based on Right-Censored Data,” Statistical Methods in Medical Research, 29, 2830–2850. DOI: 10.1177/0962280220907355.
   PubMed Web of Science ®Google Scholar
• Honda, K., and Taniguchi, T. (2006), “IRFS: Master Regulators of Signalling by Toll-Like Receptors and Cytosolic Pattern-Recognition Receptors,” Nature Reviews Immunology, 6, 644–658. DOI: 10.1038/nri1900.
   PubMed Web of Science ®Google Scholar
• Hu, X., Zhang, W., Zhang, S., Ma, S., and Li, Q. (2016), “Group-Combined p-values with Applications to Genetic Association Studies,” Bioinformatics, 32, 2737–2743. DOI: 10.1093/bioinformatics/btw314.
   PubMed Web of Science ®Google Scholar
• Johnstone, I. M. (2001), “On the Distribution of the Largest Eigenvalue in Principal Components Analysis,” The Annals of Statistics, 29, 295–327. DOI: 10.1214/aos/1009210544.
   Web of Science ®Google Scholar
• Khalid, F., Hasan, S. R., Hasan, O., and Shafique, M. (2020), “Simcom: Statistical Sniffing of Inter-Module Communications for Runtime Hardware Trojan Detection,” Microprocessors and Microsystems, 77, 103122. DOI: 10.1016/j.micpro.2020.103122.
   Web of Science ®Google Scholar
• Lee, S., Zou, F., and Wright, F. A. (2014), “Convergence of Sample Eigenvalues, Eigenvectors, and Principal Component Scores for Ultra-High Dimensional Data,” Biometrika, 101, 484–490. DOI: 10.1093/biomet/ast064.
   PubMed Web of Science ®Google Scholar
• Li, X., Li, Z., Zhou, H., Gaynor, S. M., Liu, Y., Chen, H., Sun, R., Dey, R., Arnett, D. K., Aslibekyan, S., Ballantyne, C. M., Bielak, L. F., Blangero, J., Boerwinkle, E., Bowden, D. W., Broome, J. G., Conomos, M. P., Correa, A., Adrienne Cupples, L., Curran, J. E., Freedman, B. I., Guo, X., Hindy, G., Irvin, M. R., Kardia, S. L. R., Kathiresan, S., Khan, A. T., Kooperberg, C. L., Laurie, C. C., Shirley Liu, X., Mahaney, M. C., Manichaikul, A. W., Martin, L. W., Mathias, R. A., McGarvey, S. T., Mitchell, B. D., Montasser, M. E., Moore, J. E., Morrison, A. C., O’Connell, J. R., Palmer, N. D., Pampana, A., Peralta, J. M., Peyser, P. A., Psaty, B. M., Redline, S., Rice, K. M., Rich, S. S., Smith, J. A., Tiwari, H. K., Tsai, M. Y., Vasan, R. S., Wang, F. F., Weeks, D. E., Weng, Z., Wilson, J. G., Yanek, L. R., NHLBI Trans-Omics for Precision Medicine (TOPMed) Consortium, TOPMed Lipids Working Group, Neale, B. M., Sunyaev, S. R., Abecasis, G. R., Rotter, J. I., Willer, C. J., Peloso, G. M., Natarajan, P., and Lin, X. (2020), “Dynamic Incorporation of Multiple in Silico Functional Annotations Empowers Rare Variant Association Analysis of Large Whole-Genome Sequencing Studies at Scale,” Nature Genetics, 52, 969–983. DOI: 10.1038/s41588-020-0676-4.
   PubMed Web of Science ®Google Scholar
• Li, Z. Li, X., Liu, Y., Shen, J., Chen, H., Zhou, H., Morrison, A. C., Boerwinkle, E., and Lin, X. (2019), “Dynamic Scan Procedure for Detecting Rare-Variant Association Regions in Whole-Genome Sequencing Studies,” The American Journal of Human Genetics, 104, 802–814. DOI: 10.1016/j.ajhg.2019.03.002.
   PubMed Web of Science ®Google Scholar
• Li, Z., Li, X., Zhou, H., Gaynor, S. M., Selvaraj, M. S., Arapoglou, T., Quick, C., Liu, Y., Chen, H., Sun, R., Dey, R., Arnett, D. K., Bielak, L. F., Bis, J. C., Blackwell, T. W., Blangero, J., Boerwinkle, E., Bowden, D. W., Brody, J. A., Cade, B. E., Conomos, M. P., Correa, A., Adrienne Cupples, L., Curran, J. E., de Vries, P. S., Duggirala, R., Freedman, B. I., Göring, H. H. H., Guo, X., Kalyani, R. R., Kooperberg, C., Kral, B. G., Lange, L. A., Manichaikul, A., Martin, L. W., Mitchell, B. D., Montasser, M. E., Morrison, A. C., Naseri, T., O’Connell, J. R., Palmer, N. D., Peyser, P. A., Psaty, B. M., Raffield, L. M., Redline, S., Reiner, A. P., Sefuiva Reupena, M., Rice, K. M., Rich, S. S., Smith, J. A., Taylor, K. D., Vasan, R. S., Weeks, D. E., Wilson, J. G., Yanek, L. R., Zhao, W., NHLBI Trans-Omics for Precision Medicine (TOPMed) Consortium, TOPMed Lipids Working Group, Rotter, J. I., Willer, C. J., Natarajan, P., Peloso, G. M., and Lin, X. (2021), “A Framework for Detecting Noncoding Rare Variant Associations of Large-Scale Whole-Genome Sequencing Studies,” bioRxiv.
   Google Scholar
• Lipták, T. (1958), “On the Combination of Independent Tests,” Magyar Tud Akad Mat Kutato Int Kozl, 3, 171–197.
   Google Scholar
• Liu, Y., Chen, S., Li, Z., Morrison, A. C., Boerwinkle, E., and Lin, X. (2019), “Acat: A Fast and Powerful p Value Combination Method for Rare-Variant Analysis in Sequencing Studies,” The American Journal of Human Genetics, 104, 410–421. DOI: 10.1016/j.ajhg.2019.01.002.
   PubMed Web of Science ®Google Scholar
• Liu, Y., and Xie, J. (2020), “Cauchy Combination Test: A Powerful Test with Analytic p-value Calculation under Arbitrary Dependency Structures,” Journal of the American Statistical Association, 115, 393–402. DOI: 10.1080/01621459.2018.1554485.
   PubMed Web of Science ®Google Scholar
• Liu, Z., and Lin, X. (2019), “A Geometric Perspective on the Power of Principal Component Association Tests in Multiple Phenotype Studies,” Journal of the American Statistical Association, 114, 975–990. DOI: 10.1080/01621459.2018.1513363.
   PubMed Web of Science ®Google Scholar
• McCaw, Z. R., Lane, J. M., Saxena, R., Redline, S., and Lin, X. (2020), “Operating Characteristics of the Rank-based Inverse Normal Transformation for Quantitative Trait Analysis in Genome-Wide Association Studies,” Biometrics, 76, 1262–1272. DOI: 10.1111/biom.13214.
   PubMed Web of Science ®Google Scholar
• Meyer, C. (2013), “The Bivariate Normal Copula,” Communications in Statistics-Theory and Methods, 42, 2402–2422. DOI: 10.1080/03610926.2011.611316.
   Web of Science ®Google Scholar
• Pakshirajan, R., and Hebbar, H. V. (1977), “Limit Theorems for Extremes of Absolute Values of Gaussian Sequences,” Sankhyā: The Indian Journal of Statistics, Series A, 39, 191–195.
   Google Scholar
• Pearson, K. (1933), “On a Method of Determining Whether a Sample of Size n Supposed to have been Drawn from a Parent Population having a Known Probability Integral has Probably Been Drawn at Random,” Biometrika, 25, 379–410. DOI: 10.1093/biomet/25.3-4.379.
   Google Scholar
• Ren, S., Wei, G.-H., Liu, D., Wang, L., Hou, Y., Zhu, S., Peng, L., Zhang, Q., Cheng, Y., Su, H., Zhou, X., Zhang, J., Li, F., Zheng, H., Zhao, Z., Yin, C., He, Z., Gao, X., Zhau, H. E., Chu, C.-Y., Wu, J. B., Collins, C., Volik, S. V., Bell, R., Huang, J., Wu, K., Xu, D., Ye, D., Yu, Y., Zhu, L., Qiao, M., Lee, H.-M., Yang, Y., Zhu, Y., Shi, X., Chen, R., Wang, Y., Xu, W., Cheng, Y., Xu, C., Gao, X., Zhou, T., Yang, B., Hou, J., Liu, L., Zhang, Z., Zhu, Y., Qin, C., Shao, P., Pang, J., Chung, L. W. K., Xu, J., Wu, C.-L., Zhong, W., Xu, X., Li, Y., Zhang, X., Wang, J., Yang, H., Wang, J., Huang, H., and Sun, Y. (2018), “Whole-Genome and Transcriptome Sequencing of Prostate Cancer Identify New Genetic Alterations Driving Disease Progression,” European Urology, 73, 322–339. DOI: 10.1016/j.eururo.2017.08.027.
   PubMed Web of Science ®Google Scholar
• Runge, J. (2018), “Conditional Independence Testing based on a Nearest-Neighbor Estimator of Conditional Mutual Information,” in International Conference on Artificial Intelligence and Statistics, pp. 938–947. PMLR.
   Google Scholar
• Shi, Y., Zhang, W., Liu, A., and Li, Q. (2022), “Distance-based Regression Analysis for Measuring Associations,” Journal of Systems Science & Complexity. DOI: 10.1007/s11424-022-2070-z..
   Web of Science ®Google Scholar
• Shtivelman, E., Beer, T. M., and Evans, C. P. (2014), “Molecular Pathways and Targets in Prostate Cancer,” Oncotarget, 5, 7217–7259. DOI: 10.18632/oncotarget.2406.
   PubMed Web of Science ®Google Scholar
• Singh, D., Febbo, P. G., Ross, K., Jackson, D. G., Manola, J., Ladd, C., Tamayo, P., Renshaw, A. A., D’Amico, A. V., Richie, J. P., Lander, E. S., Loda, M., Kantoff, P. W., Golub, T. R., and Sellers, W. R. (2002), “Gene Expression Correlates of Clinical Prostate Cancer Behavior,” Cancer Cell, 1, 203–209. DOI: 10.1016/S1535-6108(02)00030-2.
   PubMed Web of Science ®Google Scholar
• Sun, R., and Lin, X. (2020), “Genetic Variant Set-based Tests using the Generalized Berk–Jones Statistic with Application to a Genome-Wide Association Study of Breast Cancer,” Journal of the American Statistical Association, 115, 1079–1091. DOI: 10.1080/01621459.2019.1660170.
   PubMed Web of Science ®Google Scholar
• Tippett, L. H. C. (1931), The Methods of Statistics. An Introduction Mainly for Workers in the Biological Sciences, London: Williams and Norgate, Ltd.
   Google Scholar
• Xu, D., Wang, C., Kiryluk, K., Buxbaum, J. D., and Ionita-Laza, I. (2020), “Co-localization between Sequence Constraint and Epigenomic Information Improves Interpretation of Whole-Genome Sequencing Data,” The American Journal of Human Genetics, 106, 513–524. DOI: 10.1016/j.ajhg.2020.03.003.
   PubMed Web of Science ®Google Scholar
• Zhang, J.-T., Guo, J., Zhou, B., and Cheng, M.-Y. (2020), “A Simple Two-Sample Test in High Dimensions Based on l 2-Norm,” Journal of the American Statistical Association, 115, 1011–1027. DOI: 10.1080/01621459.2019.1604366.
   Web of Science ®Google Scholar