Abstract

A hypothesis testing procedure is considered asymptotically correlation-robust (ACR) if data

correlations have a diminishing impact on type I error control at higher significance levels. This property is crucial for analyzing large datasets with complex correlations, such as those in whole-genome

sequencing studies. Since such data often require stringent significance thresholds, correlation-robust

tests allow the use of independence approximations to reduce computational complexity while maintaining accurate type I error control. This study demonstrates that a broad range of supremum-based

p-value combination tests – such as the classic minP, Simes, Higher Criticism, and some phi-divergence

tests – are ACR when the data exhibit asymptotically independent tails, a condition satisfied by Gaussianity and various non-Gaussian dependencies characterized by appropriate pairwise copulas. A the-

oretical power analysis further demonstrates that, in the stringent-significance regime, the supremumbased p-value combination tests and the equal-weight Cauchy Combination Test possess the same

first-order asymptotic power under the dependence conditions that guarantee ACR. Furthermore, we

systematically investigate the non-asymptotic properties of these tests under a variety of linkage disequilibria among SNPs across the full set of genes in the human genome through extensive simulations

and a gene-based SNP-set analysis of femoral neck bone mineral density.

Key words and phrases: Correlation robustness, global hypothesis testing, p-value combination, SNP- set test, whole genome sequencing study

Information

Preprint No.SS-2025-0263
Manuscript IDSS-2025-0263
Complete AuthorsXiaohui Chen, Fangfang Wang, Hong Zhang, Zheyang Wu
Corresponding AuthorsZheyang Wu
Emailszheyangwu@wpi.edu

References

  1. Berk, R. H. and D. H. Jones (1979). Goodness-of-fit test statistics that dominate the kolmogorov statistics. Probability Theory and Related Fields 47(1), 47–59.
  2. Block, H. W., T. H. Savits, and J. Wang (2008). Negative dependence and the simes inequality. Journal of statistical planning and inference 138(12), 4107–4110.
  3. Devlin, B. and K. Roeder (1999). Genomic control for association studies. Biometrics 55(4), 997–1004.
  4. Donoho, D. L. and J. Jin (2004). Higher criticism for detecting sparse heterogeneous mixtures. The Annals of Statistics 32(3), 962–994.
  5. Donoho, D. L. and J. Jin (2008, Sep 30). Higher criticism thresholding: Optimal feature selection when useful features are rare and weak. Proceedings of the National Academy of Sciences of the United States of America 105(39), 14790–14795.
  6. Estrada, K., U. Styrkarsdottir, E. Evangelou, Y.-H. Hsu, E. L. Duncan, E. E. Ntzani, et al. (2012). Genome-wide meta-analysis identifies 56 bone mineral density loci and reveals 14 loci associated with risk of fracture. Nature genetics 44(5), 491–501.
  7. Fang, Y., C. Chang, Y. Park, and G. C. Tseng (2023). Heavy-tailed distribution for combining dependent p-values with asymptotic robustness. Statistica Sinica 33, 1115–1142.
  8. God´ınez-Rub´ı, M. and D. Ortu˜no-Sahag´un (2020). mir-615 fine-tunes growth and development and has a role in cancer and in neural repair. Cells 9(7), 1566.
  9. Ingster, Y. I. and I. A. Suslina (2000). Minimax nonparametric hypothesis testing for ellipsoids and besov bodies. ESAIM: Probability and Statistics 4, 53–135.
  10. Jager, L. and J. A. Wellner (2007). Goodness-of-fit tests via phi-divergences. The Annals of Statistics 35(5), 2018– 2053.
  11. Li, W. V. and Q.-M. Shao (2002). A normal comparison inequality and its applications. Probability Theory and Related Fields 122(4), 494–508.
  12. Liu, Y. and J. Xie (2020). Cauchy combination test: a powerful test with analytic p-value calculation under arbitrary dependency structures. Journal of the American Statistical Association 115(529), 393–402.
  13. Long, M., Z. Li, W. Zhang, and Q. Li (2023). The cauchy combination test under arbitrary dependence structures. The American Statistician 77(2), 134–142.
  14. Pu, Y., F. Zhao, W. Cai, X. Meng, Y. Li, and S. Cai (2016). Mir-193a-3p and mir-193a-5p suppress the metastasis of human osteosarcoma cells by down-regulating rab27b and srr, respectively. Clinical & experimental metastasis 33, 359–372.
  15. Sarkar, S. K. (1998). Some probability inequalities for ordered mtp2 random variables: a proof of the simes conjecture. Annals of Statistics 26(2), 494–504.
  16. Sarkar, S. K. and C.-K. Chang (1997). The simes method for multiple hypothesis testing with positively dependent test statistics. Journal of the American Statistical Association 92(440), 1601–1608.
  17. Simes, R. J. (1986). An improved bonferroni procedure for multiple tests of significance. Biometrika 73(3), 751–754.
  18. Sun, L., P. Wang, Z. Zhang, K. Zhang, Z. Xu, S. Li, and J. Mao (2020). Microrna-615 functions as a tumor suppressor in osteosarcoma through the suppression of hk2. Oncology Letters 20(5), 1–1.
  19. Vovk, V. and R. Wang (2020). Combining p-values via averaging. Biometrika 107(4), 791–808.
  20. Wilson, D. J. (2019). The harmonic mean p-value for combining dependent tests. Proceedings of the National Academy
  21. Zhang, H., J. Jin, and Z. Wu (2020). Distributions and power of optimal signal-detection statistics in finite case. IEEE Transactions on Signal Processing 68, 1021–1033.
  22. Zhang, H., M. Liu, J. Jin, and Z. Wu (2023). Signal-noise ratio of genetic associations and statistical power of snp-set tests. Annals of Applied Statistics 17(3), 2410–2431.
  23. Zhang, H. and Z. Wu (2022, March). The general goodness-of-fit tests for correlated data. Computational Statistics
  24. & Data Analysis 167, 107379.
  25. Worcester Polytechnic Institute, Worcester, MA, USA

Acknowledgments

We acknowledge partial financial support from NSF grants DMS-2113570 and DMS-2515791.

Supplementary Materials

The Supplementary Materials include additional discussions, proofs of main results, and

extra numerical studies. The supplementary file, top gene results.xlsx, lists the top-hit genes

identified in the GEFOS2012-FN study.

Supplementary materials are available for download.