Calculation and Use of the Hardy‐Weinberg Model in Association Studies

Kelli Ryckman1, Scott M. Williams1

1 Vanderbilt University, Nashville, Tennessee
Publication Name:  Current Protocols in Human Genetics
Unit Number:  Unit 1.18
DOI:  10.1002/0471142905.hg0118s57
Online Posting Date:  April, 2008
GO TO THE FULL TEXT: PDF or HTML at Wiley Online Library


Hardy‐Weinberg equilibrium (HWE) is an important tool for understanding population structure. If certain assumptions are met, genotype and allele frequencies can be estimated from one generation to the next. In genetic association studies, HWE principles have been applied to detect genotyping error and disease susceptibility loci. The focus of this unit is to review the key principles and assumptions of HWE. There is a brief discussion on how the significance of HWE is tested, and a review of current applications of HWE in association studies. The applications discussed include estimating penetrance, evaluating genotyping errors, testing for population stratification, and testing for association. Curr. Protoc. Hum. Genet. 57:1.18.1‐1.18.11. © 2008 by John Wiley & Sons, Inc.

Keywords: Hardy‐Weinberg equilibrium; genetic association; genotyping; population structure; penetrance

PDF or HTML at Wiley Online Library

Table of Contents

  • Introduction
  • Basic Assumptions and Priniciples of HWE
  • Violating the Assumptions of HWE
  • Testing for HWE
  • Current Applications of HWE in Human Genetics
  • Analyzing Data
  • Summary
  • Literature Cited
  • Figures
PDF or HTML at Wiley Online Library


PDF or HTML at Wiley Online Library



Literature Cited

Literature Cited
   Akey, J.M., Zhang, K., Xiong, M., Doris, P., and Jin, L. 2001. The effect that genotyping errors have on the robustness of common linkage‐disequilibrium measures. Am. J. Hum. Genet. 68: 1447‐1456.
   Cox, D.G. and Kraft, P. 2006. Quantification of the power of Hardy‐Weinberg equilibrium testing to detect genotyping error. Hum. Hered. 61: 10‐14.
   Devlin, B. and Roeder, K. 1999. Genomic control for association studies. Biometrics 55: 997‐1004.
   Emigh, T. 1980. A comparison of tests for Hardy‐Weinberg equilibrium. Biometrics 36: 627‐642.
   Feder, J.N., Gnirke, A., Thomas, W., Tsuchihashi, Z., Ruddy, D.A., Basava, A., Dormishian, F., Domingo, R. Jr., Ellis, M.C., Fullan, A., Hinton, L.M., Jones, N.L., Kimmel, B.E., Kronmal, G.S., Lauer, P., Lee, V.K., Loeb, D.B., Mapa, F.A., McClelland, E., Meyer, N.C., Mintier, G.A., Moeller, N., Moore, T., Morikang, E., Prass, C.E., Quintana, L., Starnes, S.M., Schatzman, R.C., Brunke, K.J., Drayna, D.T., Risch, N.J., Bacon, B.R., and Wolff, R.K. 1996. A novel MHC class I‐like gene is mutated in patients with hereditary haemochromatosis. Nat. Genet. 13: 399‐408.
   Gomes, I., Collins, A., Lonjou, C., Thomas, N.S., Wilkinson, J., Watson, M., and Morton, N. 1999. Hardy‐Weinberg quality control. Ann. Hum. Genet. 63: 535‐538.
   Guo, S.W. and Thompson, E.A. 1992. Performing the exact test of Hardy‐Weinberg proportion for multiple alleles. Biometrics 48: 361‐372.
   Hardy, G.H. 1908. Mendelian proportions in a mixed population. Science 18: 49‐50.
   Hartl, D.L. and Clark, A.G. 1997. Principles of population genetics. Sinauer Associates, Sunderland, Mass.
   Hernandez, J.L. and Weir, B.S. 1989. A disequilibrium coefficient approach to Hardy‐Weinberg testing. Biometrics 45: 53‐70.
   Hirschhorn, J.N. 2005. Genetic approaches to studying common diseases and complex traits. Pediatr. Res. 57: 74R‐77R.
   Hoh, J., Wille, A., and Ott, J. 2001. Trimming, weighting, and grouping SNPs in human case‐control association studies. Genome Res. 11: 2115‐2119.
   Hosking, L., Lumsden, S., Lewis, K., Yeo, A., McCarthy, L., Bansal, A., Riley, J., Purvis, I., and Xu, C.F. 2004. Detection of genotyping errors by Hardy‐Weinberg equilibrium testing. Eur. J. Hum. Genet. 12: 395‐399.
   Leal, S.M. 2005. Detection of genotyping errors and pseudo‐SNPs via deviations from Hardy‐Weinberg equilibrium. Genet. Epidemiol. 29: 204‐214.
   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.
   Moore, J.H. 2003. The ubiquitous nature of epistasis in determining susceptibility to common human diseases. Hum. Hered. 56: 73‐82.
   Nance, W.E. and Kearsey, M.J. 2004. Relevance of connexin deafness (DFNB1) to human evolution. Am. J. Hum. Genet. 74: 1081‐1087.
   Nielsen, D.M., Ehm, M.G., and Weir, B.S. 1998. Detecting marker‐disease association by testing for Hardy‐Weinberg disequilibrium at a marker locus. Am. J. Hum. Genet. 63: 1531‐1540.
   Pritchard, J.K. and Rosenberg, N.A. 1999. Use of unlinked genetic markers to detect population stratification in association studies. Am. J. Hum. Genet. 65: 220‐228.
   Salanti, G., Amountza, G., Ntzani, E.E., and Ioannidis, J.P. 2005. Hardy‐Weinberg equilibrium in genetic association studies: An empirical evaluation of reporting, deviations, and power. Eur. J. Hum. Genet. 13: 840‐848.
   Sasieni, P.D. 1997. From genotypes to genes: Doubling the sample size. Biometrics 53: 1253‐1261.
   Soares, M.L., Coelho, T., Sousa, A., Batalov, S., Conceicao, I., Sales‐Luis, M.L., Ritchie, M.D., Williams, S.M., Nievergelt, C.M., Schork, N.J., Saraiva, M.J., and Buxbaum, J.N. 2005. Susceptibility and modifier genes in Portuguese transthyretin V30M amyloid polyneuropathy: Complexity in a single‐gene disease. Hum. Mol. Genet. 14: 543‐553.
   Song, K. and Elston, R.C. 2006. A powerful method of combining measures of association and Hardy‐Weinberg disequilibrium for fine‐mapping in case‐control studies. Stat. Med. 25: 105‐126.
   Templeton, A. 2006. Population Genetics and Microevolutionary Theory. John Wiley & Sons, Hoboken, N. J.
   Tsai, C.T., Lai, L.P., Lin, J.L., Chiang, F.T., Hwang, J.J., Ritchie, M.D., Moore, J.H., Hsu, K.L., Tseng, C.D., Liau, C.S., and Tseng, Y.Z. 2004. Renin‐angiotensin system gene polymorphisms and atrial fibrillation. Circulation 109: 1640‐1646.
   Watson, D., Klohnen, E.C., Casillas, A., Simms, E.N., Haig, J., and Berry, D.S. 2004. Match makers and deal breakers: Analyses of assortative mating in newlywed couples. J. Pers. 72: 1029‐1068.
   Weinberg, W. 1908. Über den Nachweis der Vererbung beim Menschen. Jahreshefte des Vereins für vaterländische Naturkunde in Württemberg. 64:368–382. [English Version: 1963. On the demonstration of heredity in man. In Papers on Human Genetics (S.H. Boyer, ed.) pp. 4‐15. Prentice‐Hall, Englewood Cliffs, N.J.]
   Weir, B.S. 1996. Genetic Data Analysis II. Sinauer Associates, Sunderland, Mass.
   Wigginton, J.E., Cutler, D.J., and Abecasis, G.R. 2005. A note on exact tests of Hardy‐Weinberg equilibrium. Am. J. Hum. Genet. 76: 887‐893.
   Williams, S.M., Addy, J.H., Phillips, J.A. III, Dai, M., Kpodonu, J., Afful, J., Jackson, H., Joseph, K., Eason, F., Murray, M.M., Epperson, P., Aduonum, A., Wong, L.J., Jose, P.A., and Felder, R.A.. 2000. Combinations of variations in multiple genes are associated with hypertension. Hypertension 36: 2‐6.
   Williams, S.M., Haines, J.L., and Moore, J.H. 2004a. The use of animal models in the study of complex disease: All else is never equal or why do so many human studies fail to replicate animal findings? Bioessays 26: 170‐179.
   Williams, S.M., Ritchie, M.D., Phillips, J.A. III, Dawson, E., Prince, M., Dzhura, E., Willis, A., Semenya, A., Summar, M., White, B.C., Addy, J.H., Kpodonu, J., Wong, L.J., Felder, R.A., Jose, P.A., and Moore, J.H. 2004b. Multilocus analysis of hypertension: A hierarchical approach. Hum. Hered. 57: 28‐38.
   Wittke‐Thompson, J.K., Pluzhnikov, A., and Cox, N.J. 2005. Rational inferences about departures from Hardy‐Weinberg equilibrium. Am. J. Hum. Genet. 76: 967‐986.
   Zou, G.Y. and Donner, A. 2006. The merits of testing Hardy‐Weinberg equilibrium in the analysis of unmatched case‐control data: A cautionary note. Ann. Hum. Genet. 70: 923‐933.
PDF or HTML at Wiley Online Library