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Estimating Disequilibrium Coefficients

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Statistical Human Genetics

Part of the book series: Methods in Molecular Biology ((MIMB,volume 1666))

Abstract

Gametic phase disequilibrium is the nonrandom association of alleles within gametes. Linkage disequilibrium (LD) describes the special case of deviation from independence between alleles at two linked genetic loci. Estimation of allelic LD requires knowledge of haplotypes. Genotype-based LD measures dispense with the haplotype estimation step and avoid bias in LD estimation. In this chapter, the most important measures for allelic and genotypic LD are introduced. The use of software packages for LD estimation is illustrated.

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References

  1. Wang X, Elston RC, Zhu X (2010) The meaning of interaction. Hum Hered 70:269–277

    Article  PubMed  PubMed Central  Google Scholar 

  2. Ziegler A, König IR (2010) A statistical approach to genetic epidemiology: concepts and applications. Wiley-VCH, Weinheim

    Book  Google Scholar 

  3. Weir BS (1979) Inferences about linkage disequilibrium. Biometrics 35:235–254

    Article  CAS  PubMed  Google Scholar 

  4. Wellek S, Ziegler A (2009) A genotype-based approach to assessing the association between single nucleotide polymorphisms. Hum Hered 67:128–139

    Article  CAS  PubMed  Google Scholar 

  5. Robbins RB (1918) Some applications of mathematics to breeding problems III. Genetics 3:375–389

    PubMed  PubMed Central  CAS  Google Scholar 

  6. Hill WG, Weir BS (1994) Maximum-likelihood estimation of gene location by linkage disequilibrium. Am J Hum Genet 54:705–714

    PubMed  PubMed Central  CAS  Google Scholar 

  7. Lewontin RC (1964) The interaction of selection and linkage. I. General considerations; heterotic models. Genetics 49:49–67

    PubMed  PubMed Central  CAS  Google Scholar 

  8. Levin ML, Bertell R (1978) Re—simple estimation of population attributable risk from case-control studies. Am J Epidemiol 108:78–79

    PubMed  CAS  Google Scholar 

  9. Levin ML (1953) The occurrence of lung cancer in man. Acta Unio Int Contra Cancrum 9:531–541

    PubMed  CAS  Google Scholar 

  10. Kaplan N, Weir BS (1992) Expected behavior of conditional linkage disequilibrium. Am J Hum Genet 51:333–343

    PubMed  PubMed Central  CAS  Google Scholar 

  11. Yule GU (1900) On the association of attributes in statistics: with illustrations from the material of the childhood society. Phil Transact Roy Soc London A 194:257–319

    Article  Google Scholar 

  12. Devlin B, Risch N (1995) A comparison of linkage disequilibrium measures for fine-scale mapping. Genomics 29:311–322

    Article  CAS  PubMed  Google Scholar 

  13. Weir BS (1996) Genetic data analysis II: methods for discrete population genetic data. Sinauer Associates, Inc., Sunderland, MA

    Google Scholar 

  14. Weir BS, Cockerham CC (1979) Estimation of linkage disequilibrium in randomly mating populations. Heredity 42:105–111

    Article  Google Scholar 

  15. Mueller JC (2004) Linkage disequilibrium for different scales and applications. Brief Bioinform 5:355–364

    Article  CAS  PubMed  Google Scholar 

  16. Nielsen DM et al (2004) Effect of two- and three-locus linkage disequilibrium on the power to detect marker/phenotype associations. Genetics 168:1029–1040

    Article  PubMed  PubMed Central  Google Scholar 

  17. Nothnagel M, Furst R, Rohde K (2002) Entropy as a measure for linkage disequilibrium over multilocus haplotype blocks. Hum Hered 54:186–198

    Article  CAS  PubMed  Google Scholar 

  18. Zhang L, Liu JF, Deng HW (2009) A multilocus linkage disequilibrium measure based on mutual information theory and its applications. Genetica 137:355–364

    Article  PubMed  Google Scholar 

  19. Liu Z, Lin S (2005) Multilocus LD measure and tagging SNP selection with generalized mutual information. Genet Epidemiol 29:353–364

    Article  PubMed  PubMed Central  Google Scholar 

  20. Gorelick R, Laubichler MD (2004) Decomposing multilocus linkage disequilibrium. Genetics 166:1581–1583

    Article  PubMed  PubMed Central  Google Scholar 

  21. Rogers AR, Huff C (2009) Linkage disequilibrium between loci with unknown phase. Genetics 182:839–844

    Article  PubMed  PubMed Central  Google Scholar 

  22. Kim Y, Feng S, Zeng ZB (2008) Measuring and partitioning the high-order linkage disequilibrium by multiple order Markov chains. Genet Epidemiol 32:301–312

    Article  PubMed  Google Scholar 

  23. Feng S, Wang SC (2010) Summarizing and quantifying multilocus linkage disequilibrium patterns with multi-order Markov chain models. J Biopharm Stat 20:441–453

    Article  PubMed  Google Scholar 

  24. Genomes Project C et al (2015) A global reference for human genetic variation. Nature 526:68–74

    Article  CAS  Google Scholar 

  25. Chang CC et al (2015) Second-generation PLINK: rising to the challenge of larger and richer datasets. Gigascience 4:7

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  26. Purcell S, Chang C. PLINK v1.90b3.45. https://www.cog-genomics.org/plink2

  27. Coronary Artery Disease C et al (2009) Large scale association analysis of novel genetic loci for coronary artery disease. Arterioscler Thromb Vasc Biol 29:774–780

    Article  CAS  Google Scholar 

  28. Purcell S et al (2007) PLINK: a tool set for whole-genome association and population-based linkage analyses. Am J Hum Genet 81:559–575

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  29. Gaunt TR, Rodriguez S, Day IN (2007) Cubic exact solutions for the estimation of pairwise haplotype frequencies: implications for linkage disequilibrium analyses and a web tool “CubeX”. BMC Bioinformatics 8:428

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. Graffelman J, Moreno V (2013) The mid p-value in exact tests for Hardy-Weinberg equilibrium. Stat Appl Genet Mol Biol 12:433–448

    Article  PubMed  Google Scholar 

  31. R Core Team (2016) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/

    Google Scholar 

  32. Clayton D (2015) snpStats: SnpMatrix and XSnpMatrix classes and methods. R package version 1.24.0

    Google Scholar 

  33. Clayton D, Leung HT (2007) An R package for analysis of whole-genome association studies. Hum Hered 64:45–51

    Article  PubMed  Google Scholar 

  34. Slatkin M, Excoffier L (1996) Testing for linkage disequilibrium in genotypic data using the expectation-maximization algorithm. Heredity 76:377–383

    Article  PubMed  Google Scholar 

  35. Shin J-H et al (2006) LDheatmap: an R function for graphical display of pairwise linkage disequilibria between single nucleotide polymorphisms. J Stat Soft 16: Code Snippet 3

    Google Scholar 

  36. Luna A, Nicodemus KK (2007) snp.plotter: an R-based SNP/haplotype association and linkage disequilibrium plotting package. Bioinformatics 23:774–776

    Article  CAS  PubMed  Google Scholar 

  37. Aulchenko YS et al (2007) GenABEL: an R library for genome-wide association analysis. Bioinformatics 23:1294–1296

    Article  CAS  PubMed  Google Scholar 

  38. Karssen LC, van Duijn CM, Aulchenko YS (2016) The GenABEL project for statistical genomics. F1000Res 5:914

    Article  PubMed  PubMed Central  Google Scholar 

  39. Warnes G (2013) Genetics: population genetics. R Package Version 1.3.8.1. https://CRAN.R-project.org/package=genetics

  40. Lewin A (2008) LDtests: exact tests for linkage lisequilibrium and Hardy-Weinberg equilibrium. R package Version 1.0

    Google Scholar 

  41. Kulinskaya E, Lewin A (2009) Testing for linkage and Hardy-Weinberg disequilibrium. Ann Hum Genet 73:253–262

    Article  CAS  PubMed  Google Scholar 

  42. Thomson G, Single RM (2014) Conditional asymmetric linkage disequilibrium (ALD): extending the biallelic r2 measure. Genetics 198:321–331

    Article  PubMed  PubMed Central  Google Scholar 

  43. Mangin B et al (2012) Novel measures of linkage disequilibrium that correct the bias due to population structure and relatedness. Heredity 108:285–291

    Article  CAS  PubMed  Google Scholar 

  44. Desrousseaux D et al (2013) LDcorSV: linkage disequilibrium corrected by the structure and the relatedness. R Package Version 131. https://CRAN.R-project.org/package=LDcorSV

  45. Barrett JC (2009) Haploview: visualization and analysis of SNP genotype data. Cold Spring Harb Protoc. pdb ip71

    Google Scholar 

  46. Barrett JC et al (2005) Haploview: analysis and visualization of LD and haplotype maps. Bioinformatics 21:263–265

    Article  CAS  PubMed  Google Scholar 

  47. Abecasis GR, Cookson WOC (2000) GOLD—graphical overview of linkage disequilibrium. Bioinformatics 16:182–183

    Article  CAS  PubMed  Google Scholar 

  48. Pruim RJ et al (2010) LocusZoom: regional visualization of genome-wide association scan results. Bioinformatics 26:2336–2337

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  49. Sved JA (2009) Linkage disequilibrium and its expectation in human populations. Twin Res Hum Genet 12:35–43

    Article  PubMed  Google Scholar 

  50. Morton NE, Collins A (1998) Tests and estimates of allelic association in complex inheritance. Proc Natl Acad Sci U S A 95:11389–11393

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  51. Chen YG, Lin CH, Sabatti C (2006) Volume measures for linkage disequilibrium. BMC Genet 7:54–62

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  52. VanLiere JM, Rosenberg NA (2008) Mathematical properties of the r(2) measure of linkage disequilibrium. Theor Popul Biol 74:130–137

    Article  PubMed  PubMed Central  Google Scholar 

  53. Teare MD et al (2002) Sampling distribution of summary linkage disequilibrium measures. Ann Hum Genet 66:223–233

    Article  CAS  PubMed  Google Scholar 

  54. Tenesa A et al (2004) Extent of linkage disequilibrium in a Sardinian sub-isolate: sampling and methodological considerations. Hum Mol Genet 13:25–33

    Article  CAS  PubMed  Google Scholar 

  55. Gabriel SB et al (2002) The structure of haplotype blocks in the human genome. Science 296:2225–2229

    Article  CAS  PubMed  Google Scholar 

  56. Hedrick PW (1987) Gametic disequilibrium measures—proceed with caution. Genetics 117:331–341

    PubMed  PubMed Central  CAS  Google Scholar 

  57. Wray NR (2005) Allele frequencies and the r2 measure of linkage disequilibrium: impact on design and interpretation of association studies. Twin Res Hum Genet 8:87–94

    Article  PubMed  Google Scholar 

  58. Lehesjoki AE et al (1993) Linkage disequilibrium mapping in progressive myoclonus epilepsy of Unverricht-Lundborg type. Am J Hum Genet 53:1029–1029

    Google Scholar 

  59. Terwilliger JD (1995) A powerful likelihood method for the analysis of linkage disequilibrium between trait loci and one or more polymorphic marker loci. Am J Hum Genet 56:777–787

    PubMed  PubMed Central  CAS  Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Medizinische Biometrie und Epidemiologie, Universitätsklinikum Hamburg-Eppendorf, Martinistraße 52, Hamburg, 20246, Germany

    Maren Vens

  2. Institut für Medizinische Biometrie und Statistik & Zentrum für klinische Studien, Universität zu Lübeck, Universitätsklinikum Schleswig-Holstein, Campus Lübeck, Ratzeburger Allee 160, Lübeck, 23562, Germany

    Andreas Ziegler

Authors
  1. Maren Vens
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  2. Andreas Ziegler
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Correspondence to Maren Vens .

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Editors and Affiliations

  1. Case Western Reserve University, Cleveland, OH, USA

    Robert C. Elston

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Vens, M., Ziegler, A. (2017). Estimating Disequilibrium Coefficients. In: Elston, R. (eds) Statistical Human Genetics. Methods in Molecular Biology, vol 1666. Humana Press, New York, NY. https://doi.org/10.1007/978-1-4939-7274-6_7

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  • DOI: https://doi.org/10.1007/978-1-4939-7274-6_7

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  • Publisher Name: Humana Press, New York, NY

  • Print ISBN: 978-1-4939-7273-9

  • Online ISBN: 978-1-4939-7274-6

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