Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Statistical Applications in Genetics and Molecular Biology

Editor-in-Chief: Sanguinetti, Guido


IMPACT FACTOR 2018: 0.536
5-year IMPACT FACTOR: 0.764

CiteScore 2018: 0.49

SCImago Journal Rank (SJR) 2018: 0.316
Source Normalized Impact per Paper (SNIP) 2018: 0.342

Mathematical Citation Quotient (MCQ) 2017: 0.04

Online
ISSN
1544-6115
See all formats and pricing
More options …
Volume 12, Issue 4

Issues

Volume 10 (2011)

Volume 9 (2010)

Volume 6 (2007)

Volume 5 (2006)

Volume 4 (2005)

Volume 2 (2003)

Volume 1 (2002)

The mid p-value in exact tests for Hardy-Weinberg equilibrium

Jan Graffelman
  • Corresponding author
  • Department of Statistics and Operations Research, Universitat Politècnica de Catalunya, Avinguda Diagonal 647, 08028 Barcelona, Spain
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Victor Moreno
  • Cancer Prevention Program, Catalan Institute of Oncology (ICO) Bellvitge Biomedical Research Institute (IDIBELL), Faculty of Medicine and CIBERESP, Department of Clinical Sciences, University of Barcelona (UB), Gran Via 199, 08908 L’Hospitalet del Llobregat (Barcelona), Spain
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2013-08-03 | DOI: https://doi.org/10.1515/sagmb-2012-0039

Abstract

Objective: Exact tests for Hardy-Weinberg equilibrium are widely used in genetic association studies. We evaluate the mid p-value, unknown in the genetics literature, as an alternative for the standard p-value in the exact test.

Method: The type 1 error rate and the power of the exact test are calculated for different sample sizes, sigificance levels, minor allele counts and degrees of deviation from equilibrium. Three different p-value are considered: the standard two-sided p-value, the doubled one-sided p-value and the mid p-value. Practical implications of using the mid p-value are discussed with HapMap datasets and a data set on colon cancer.

Results: The mid p-value is shown to have a type 1 error rate that is always closer to the nominal level, and to have better power. Differences between the standard p-value and the mid p-value can be large for insignificant results, and are smaller for significant results. The analysis of empirical databases shows that the mid p-value uncovers more significant markers, and that the equilibrium null distribution is not tenable for both databases.

Conclusion: The standard exact p-value is overly conservative, in particular for small minor allele frequencies. The mid p-value ameliorates this problem by bringing the rejection rate closer to the nominal level, at the price of ocasionally exceeding the nominal level.

Keywords: Levene-Haldane distribution; power; single nucleotide polymorphism; type I error rate

References

  • Agresti, A. (2002): Categorical data analysis. New York: John Wiley & Sons, second edition.Google Scholar

  • Attia, J., A. Thakkinstian, P. McElduff, E. Milne, S. Dawson, R. J. Scott, N. de Klerk, B. Armstrong and J. Thompson (2010): “Detecting genotyping error using measures of degree of Hardy-Weinberg disequilibrium,” Stat. Appl. Genet. Mol. Biol., 9, doi: 10.2202/1544-6115.1463.Web of ScienceCrossrefGoogle Scholar

  • Ayres, K. L. and D. J. Balding (1998): “Measuring departures from Hardy-Weinberg: a markov chain monte carlo method for estimating the inbreeding coefficient,” Heredity, 80, 769–777.Google Scholar

  • Barnard, G. A. (1989): “On alleged gains in power from lower p-values,” Stat. Med., 8, 1469–1477.PubMedGoogle Scholar

  • Berry, G. and P. Armitage (1995): “Mid-p confidence intervals: a brief review,” J. Roy. Stat. Soc. D, 44, 417–423.Google Scholar

  • Chakraborty, R. and Y. Zhong (1994): “Statistical power of an exact test of Hardy-Weinberg proportions of genotypic data at a multiallelic locus,” Hum. Hered., 44, 1–9.CrossrefGoogle Scholar

  • Elston, R. C. and R. Forthofer (1977): “Testing for Hardy-Weinberg equilibrium in small samples,” Biometrics, 33, 536–542.Google Scholar

  • Emigh, T. H. (1980): “A comparison of tests for Hardy-Weinberg equilibrium,” Biometrics, 36, 627–642.Google Scholar

  • Graffelman, J. (2010): “The number of markers in the hapmap project: some notes on chi-square and exact tests for Hardy-Weinberg equilibrium,” Am. J. Hum. Genet., 86, 813–818.Web of ScienceGoogle Scholar

  • Graffelman, J. and J. Morales-Camarena (2008): “Graphical tests for Hardy-Weinberg equilibrium based on the ternary plot,” Hum. Hered., 65, 77–84.Web of ScienceGoogle Scholar

  • Guo, W. S. and E. A. Thompson (1992): “Performing the exact test of Hardy-Weinberg proportion for multiple alleles,” Biometrics, 48, 361–372.PubMedGoogle Scholar

  • Haldane, J. B. S. (1954): “An exact test for randomness of mating,” J. Genet., 52, 631–635.Google Scholar

  • Hirji, K. F. (1991): “A comparison of exact, mid-p, and score tests for matched case-control studies,” Biometrics, 47, 487–496.PubMedGoogle Scholar

  • Hosking, L., S. Lumsden, K. Lewis, A. Yeo, L. McCarthy, A. Bansal, J. Riley, I. Purvis, and C. Xu (2004): “Detection of genotyping errors by Hardy-Weinberg equilibrium testing,” Eur. J. Hum. Genet., 12, 395–399.CrossrefGoogle Scholar

  • Lancaster, H. O. (1961): “Significance tests in discrete distributions,” J. Am. Stat. Assoc., 56, 223–234.Google Scholar

  • Landi, S., F. Gemignania, V. Moreno, L. Gioia-Patricola, A. Chabrier, E. Guino, M. Navarro, J. de Oca, F. Capella and F. Canzian (2005): “A comprehensive analysis of phase i and phase ii metabolism gene polymorphisms and risk of colorectal cancer,” Pharmacogenetics and Genomics, 15, 535–546.Google Scholar

  • Lee, W. C. (2003): “Searching for disease-susceptibility loci by testing for Hardy-Weinberg disequilibrium in a gene bank of affected individuals,” Am. J. Epidemiol., 158, 397–400.Google Scholar

  • Levene, H. (1949): “On a matching problem arising in genetics,” Ann. Math. Stat., 20, 91–94.Google Scholar

  • Lindley, D. V. (1988): Statistical inference concerning Hardy-Weinberg equilibrium. In Bernardo, J. M., M. H. DeGroot, D. V. Lindley and A. F. M. Smith, (Eds.), Bayesian Statistics, 3, Oxford: Oxford University Press, pp. 307–326.Google Scholar

  • Okamoto, M. and G. Ishii (1961): “Test of independence in intraclass 2×2 tables,” Biometrika, 48, 181–190.Google Scholar

  • Rohlfs, R. V. and B. S. Weir (2008): “Distributions of Hardy-Weinberg equilibrium test statistics,” Genetics, 180, 1609–1616.Web of ScienceGoogle Scholar

  • Salanti, G., G. Amountza, E. E. Ntzani and J. P. A. Ioannidis (2005): “Hardy-Weinberg equilibrium in genetic association studies: an empirical evaluation of reporting, deviations, and power,” Eur. J. Hum. Genet., 13, 840–848.CrossrefGoogle Scholar

  • Shoemaker, J., I. Painter and B. S. Weir (1998): “A bayesian characterization of Hardy-Weinberg disequilibrium,” Genetics, 149, 2079–2088.Google Scholar

  • Smith, C. A. B. (1986): “Chi-squared tests with small numbers,” Ann. Hum. Genet., 50, 163–167.PubMedGoogle Scholar

  • The International HapMap Consortium (2003): “The international hapmap project,” Nature, 426, 789–796.Google Scholar

  • The International HapMap Consortium (2005): “A haplotype map of the human genome,” Nature, 437, 1299–1320.Google Scholar

  • The International HapMap Consortium (2007): “A second generation human haplotype map of over 3.1 million snps,” Nature, 449, 851–861.Web of ScienceGoogle Scholar

  • Wakefield, J. (2010): “Bayesian methods for examining Hardy-Weinberg equilibrium,” Biometrics, 66, 257–265.Web of SciencePubMedGoogle Scholar

  • Weir, B. S. (1996): Genetic Data Analysis II. Massachusetts: Sinauer Associates.Google Scholar

  • Wigginton, J. E., D. J. Cutler and G. R. Abecasis (2005): “A note on exact tests of Hardy-Weinberg equilibrium,” Am. J. Hum. Genet., 76, 887–893.Web of ScienceGoogle Scholar

  • Yates, F. (1984): “Tests of significance for 2×2 contingency tables,” J. Roy. Stat. Soc A., 147, 426–463.Google Scholar

  • Yu, C., S. Zhang, C. Zhou, and S. Sile (2009): “A likelihood ratio test of population Hardy-Weinberg equilibrium of case-control studies,” Genet. Epidemiol., 33, 275–280.PubMedWeb of ScienceGoogle Scholar

About the article

Corresponding author: Jan Graffelman, Department of Statistics and Operations Research, Universitat Politècnica de Catalunya, Avinguda Diagonal 647, 08028 Barcelona, Spain, Phone: +34-934011739, Fax: +34-934016575


Published Online: 2013-08-03

Published in Print: 2013-08-01


Citation Information: Statistical Applications in Genetics and Molecular Biology, Volume 12, Issue 4, Pages 433–448, ISSN (Online) 1544-6115, ISSN (Print) 2194-6302, DOI: https://doi.org/10.1515/sagmb-2012-0039.

Export Citation

©2013 by Walter de Gruyter Berlin Boston.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Arthur Gilly, Daniel Suveges, Karoline Kuchenbaecker, Martin Pollard, Lorraine Southam, Konstantinos Hatzikotoulas, Aliki-Eleni Farmaki, Thea Bjornland, Ryan Waples, Emil V. R. Appel, Elisabetta Casalone, Giorgio Melloni, Britt Kilian, Nigel W. Rayner, Ioanna Ntalla, Kousik Kundu, Klaudia Walter, John Danesh, Adam Butterworth, Inês Barroso, Emmanouil Tsafantakis, George Dedoussis, Ida Moltke, and Eleftheria Zeggini
Nature Communications, 2018, Volume 9, Number 1
[2]
Benjamin N Sacks, Zachary T Lounsberry, and Mark J Statham
Journal of Heredity, 2018
[3]
Patrick Rubin-Delanchy, Nicholas A Heard, and Daniel J Lawson
Journal of the American Statistical Association, 2018, Page 1
[4]
Jan Graffelman and Bruce S. Weir
Molecular Ecology Resources, 2018
[5]
Arkan Abadi, Akram Alyass, Sebastien Robiou du Pont, Ben Bolker, Pardeep Singh, Viswanathan Mohan, Rafael Diaz, James C. Engert, Salim Yusuf, Hertzel C. Gerstein, Sonia S. Anand, and David Meyre
The American Journal of Human Genetics, 2017, Volume 101, Number 6, Page 925
[7]
Kelin Xu, Li Jin, and Momiao Xiong
BMC Genomics, 2017, Volume 18, Number 1
[8]
Jan Graffelman, Deepti Jain, and Bruce Weir
Human Genetics, 2017, Volume 136, Number 6, Page 727
[9]
Jan Graffelman, Milagros Sánchez, Samantha Cook, Victor Moreno, and Francesc Calafell
PLoS ONE, 2013, Volume 8, Number 12, Page e83316
[10]
Mark T.W. Ebbert, Kevin L. Boehme, Mark E. Wadsworth, Lyndsay A. Staley, Shubhabrata Mukherjee, Paul K. Crane, Perry G. Ridge, and John S.K. Kauwe
Alzheimer's & Dementia, 2016, Volume 12, Number 2, Page 121
[11]
R. K. Waples, J. E. Seeb, and L. W. Seeb
Molecular Ecology, 2017, Volume 26, Number 16, Page 4131
[13]
Aldo Córdova-Palomera, Marcel A. de Reus, Mar Fatjó-Vilas, Carles Falcón, Nuria Bargalló, Martijn P. van den Heuvel, and Lourdes Fañanás
Brain Imaging and Behavior, 2017, Volume 11, Number 1, Page 62

Comments (0)

Please log in or register to comment.
Log in