Markov Chain Monte Carlo Linkage Analysis Methods

  • Robert P. Igo
  • Yuqun LuoJr.
  • Shili LinEmail author


As alluded to in the chapter “Linkage Analysis of Qualitative Traits”, neither the Elston–Steward algorithm nor the Lander–Green approach is amenable to genetic data from large complex pedigrees and a large number of markers. In such cases, Monte Carlo estimation methods provide a viable alternative to the exact solutions. Two types of Monte Carlo methods have been developed for linkage analysis, haplotype inference, and other kinds of genetic analysis. They are Markov chain Monte Carlo (MCMC) methods and Monte Carlo methods that are based on independent samples. Approaches based on Markov chain Monte Carlo methods are more widely applicable; there is practically no limit on the size or complexity of the pedigrees, nor on the number of markers to be considered simultaneously. In this chapter, we will review the basic principles of MCMC methods for multipoint linkage analysis with extended pedigrees. Both simulations and application to data from the Framingham study will be used to compare and contrast three MCMC software packages: LOKI, MORGAN, and SIMWALK.


Quantitative Trait Locus Markov Chain Monte Carlo Linkage Analysis Binary Trait Continuous Trait 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



We thank Joseph Rothstein, Yun Ju Sung, and Ellen Wijsman for their valuable advice. This work was supported in part by NSF grant DMS-0112050 and NIH grants R01-HG002657 and RO1-HG003054. GAW is supported by NIH grant R01 GM031575. Some of the results of this paper were obtained by using the program package S.A.G.E., which is supported by a U.S. Public Health Service Resource Grant (RR03655) from the National Center for Research Resources. We also acknowledge the Framingham Heart Study for their permission to use the GAW 13 data, and we thank the Framingham Heart Study Investigators for their contributions and the NHLBI for collection of the Framingham Study data.


  1. 1.
    Abecasis GR, Cherny SS, Cookson WO, Cardon LR (2002) Merlin – rapid analysis of dense genetic maps using sparse gene flow trees. Nat Genet 30:97–101CrossRefPubMedGoogle Scholar
  2. 2.
    Atwood LD, Heard-Costa NL (2003) Limits of fine-mapping a quantitative trait. Genet Epidemiol 24:99–106CrossRefPubMedGoogle Scholar
  3. 3.
    Biswas S, Lin S (2006) A Bayesian approach for incorporating variable rates of heterogeneity in linkage analysis. J Am Stat Assoc 101:1341–1351CrossRefGoogle Scholar
  4. 4.
    Biswas S, Papachristou C, Irwin MC, Lin S (2003) Linkage analysis of the simulated data – evaluations and comparisons of methods. BMC Genet 31 (Suppl 1):S70CrossRefGoogle Scholar
  5. 5.
    Bonney G (1986) Regressive logistic models for familial disease and other binary traits. Biometrics 42:611–625CrossRefPubMedGoogle Scholar
  6. 6.
    Chen W-M, Abecasis GR (2007) Family-based association tests for genomewide association scans. Am J Hum Genet 81:913–926CrossRefPubMedGoogle Scholar
  7. 7.
    Cottingham R, Idury RM, Schffer AA (1993) Faster sequential genetic linkage computations. Am J Hum Genet 53:252–263PubMedGoogle Scholar
  8. 8.
    Cupples LA, Yang Q, Demissie S, Copenhafer D, Levy D, FraminghamHeartStudyInvestigators (2003) Desription of the Framingham Heart Study data for Genetic Analysis Workshop 13. BMC Genet 4(Suppl. 1):S2Google Scholar
  9. 9.
    Dietter J, Spiegel A, an Mey D, Pflug H-J, Al-Kateb H, Hoffmann K, Wienker TF, Strauch K (2004) Efficient two-trait-locus linkage analysis through program optimization and parallelization: application to hypercholesterolemia. Eur J Hum. Genet 12:542–550Google Scholar
  10. 10.
    Ding J, Lin S, Liu Y (2006) Monte Carlo pedigree disequilibrium test for markers on the X chromosome. Am J Hum Genet 79:567–573CrossRefPubMedGoogle Scholar
  11. 11.
    Elston RC, Stewart J (1971) A general model for the analysis of pedigree data. Hum Hered 21:523–542CrossRefPubMedGoogle Scholar
  12. 12.
    Fishelson M, Geiger D (2002) Exact genetic linkage computations for general pedigrees. Bioinformatics 18:S189–S198PubMedGoogle Scholar
  13. 13.
    George AW, Thompson EA (2002) Multipoint linkage analyses for disease mapping in extended pedigrees: a Markov chain Monte Carlo approach. Technical report no. 405, Department of Statistics, University of Washington, Seattle, WAGoogle Scholar
  14. 14.
    George AW, Thompson EA (2003) Discovering disease genes: multipoint linkage analysis via a new Markov chain Monte Carlo approach. Stat Sci 18:515–531CrossRefGoogle Scholar
  15. 15.
    George AW, Basu S, Li N, Rothstein JH, Sieberts SK, Stewart W, Wijsman EM, Thompson EA (2003) Approaches to mapping genetically correlated complex traits. BMC Genet 4 (Suppl 1):S71CrossRefPubMedGoogle Scholar
  16. 16.
    George AW, Wijsman EM, Thompson EA (2005) MCMC multilocus lod scores: application of a new approach. Hum Hered 59:98–108CrossRefPubMedGoogle Scholar
  17. 17.
    Green PJ (1995) Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82:711–732CrossRefGoogle Scholar
  18. 18.
    Grundy SM, Cleeman JI, Daniels SR, Donato KA, Eckel RH, Franklin BA, Gordon DJ, Krauss RM, Savage PJ, Smith SC, Spertus JA, Costa F (2005) Diagnosis and management of the metabolic syndrome. Circulation 112:2735–2752CrossRefPubMedGoogle Scholar
  19. 19.
    Heath SC (1997) Markov chain Monte Carlo segregation and linkage analysis for oligogenic models. Am J Hum Genet 61:748–760CrossRefPubMedGoogle Scholar
  20. 20.
    Horne BD, Malhotra A, Camp NJ (2003) Comparison of linkage analysis methods for genome-wide scanning of extended pedigrees, with application to the TG/HDL-C ratio in the Framingham Heart Study. BMC Genet 4(Suppl. 1):S93CrossRefPubMedGoogle Scholar
  21. 21.
    Igo RP Jr, Chapman NH, Berninger VW, Matsushita M, Brkanac Z, Rothstein JH, Holzman T, Neilsen K, Raskind WH, Wijsman EM (2006) Genomewide scan for real-word reading subphenotypes of dyslexia: novel chromosome 13 locus and genetic complexity. Am J Med Genet (Neuropsychiatr Genet) 141B:15–27CrossRefGoogle Scholar
  22. 22.
    Igo RP, Jr, Chapman NH, Wijsman EM (2006) Segregation analysis of a complex quantitative trait: approaches for identifying influential data points. Hum Hered 61:80–86CrossRefPubMedGoogle Scholar
  23. 23.
    Igo RP, Jr, Wijsman EM (2008) Empirical significance values for linkage analysis: trait simulation using posterior model distributions from MCMC oligogenic segregation analysis. Genet Epidemiol 32:119–131CrossRefPubMedGoogle Scholar
  24. 24.
    Irwin M, Cox N, Kong A (1994) Sequential imputation for multipoint linkage analysis. Proc Natl Acad Sci USA 91:11684–11688CrossRefPubMedGoogle Scholar
  25. 25.
    Kass RE, Rafferty AE (1995) Bayes factors. J Am Stat Assoc 90:773–795CrossRefGoogle Scholar
  26. 26.
    Kong A, Liu JS, Wong WH (1994) Sequential imputations and Bayesian missing data problems. J Am Stat Assoc 89:278–288CrossRefGoogle Scholar
  27. 27.
    Kruglyak L, Daly MJ, Reeve-Daly MP, Lander ES (1996) Parametric and nonparametric linkage analysis: a unified multipoint approach. Am J Hum Genet 58:1347–1363PubMedGoogle Scholar
  28. 28.
    Lander E, Green P (1987) Construction of multilocus genetic linkage maps in humans. Proc Natl Acad Sci USA 84:2363–2367CrossRefPubMedGoogle Scholar
  29. 29.
    Lange K, Sobel E (1991) A random walk method for computing genetic location scores. Am J Hum Genet 49:1320–1334PubMedGoogle Scholar
  30. 30.
    Lathrop GM, Lalouel JM, Julier C, Ott J (1984) Strategies for multilocus linkage analysis in humans. Proc Natl Acad Sci USA 81:3443–3446CrossRefPubMedGoogle Scholar
  31. 31.
    Lin S (2000) Monte Carlo methods for linkage analysis of two-locus disease models. Ann Hum Genet 64:519–532CrossRefPubMedGoogle Scholar
  32. 32.
    Lin S, Skrivanek Z, Irwin M (2003) Haplotyping using SIMPLE: caution on ignoring interference. Genet Epidemiol 25:384–387CrossRefPubMedGoogle Scholar
  33. 33.
    Luo Y, Lin S, Irwin ME (2001) Two-locus modeling of asthma in a Hutterite pedigree via Markov chain Monte Carlo. Genet Epidemiol 21(Suppl 1):S24–S29PubMedGoogle Scholar
  34. 34.
    Luo Y, Lin S (2003) Finding starting points for Markov chain Monte Carlo analysis of genetic data from large and complex pedigrees. Genet Epidemiol 25:14–24CrossRefPubMedGoogle Scholar
  35. 35.
    MacCluer JW, Vandeberg JL, Read B, Ryder OA (1986) Pedigree analysis by computer simulation. Zoo Biol 5:147–160CrossRefGoogle Scholar
  36. 36.
    O’Connell JR (2001) Rapid multipoint linkage analysis via inheritance vectors in the Elston–Stewart algorithm. Hum Hered 51:226–240CrossRefPubMedGoogle Scholar
  37. 37.
    Pritchard JK, Stephens M, Donnelly P (2000) Inference of population structure using multilocus genotype data. Genetics 155:945–959PubMedGoogle Scholar
  38. 38.
    Risch N, Merikangas K (1996) The future of genetic studies of complex human diseases. Science 273:1516–1517CrossRefPubMedGoogle Scholar
  39. 39.
    Robert CP, Casella G (2004). Monte Carlo statistical methods. Springer-Verlag, New YorkGoogle Scholar
  40. 40.
    S.A.G.E. (2007) Statistical analysis for genetic epidemiology, version 5.4.
  41. 41.
    Shearman AM, Ordovas JM, Cupples LA, Schaefer EJ, Harmon MD, Shao Y, Keen JD, DeStefano AL, Joost O, Wilson PWF, Housman DE, Myers RH (2000) Evidence for a gene influencing the TG/HDL-C ratio on chromosome 7q32.3-qter: a genome-wide scan in the Framingham Study. Hum Mol Genet 9:1315–1320CrossRefPubMedGoogle Scholar
  42. 42.
    Sieh W, Basu S, Fu AQ, Rothstein JH, Scheet PA, Sterward WCL, Sung YJ, Thompson EA, Wijsman EM (2005) Comparison of marker types and map assumptions using Markov chain Monte Carlo-based linkage analysis of COGA data. BMC Genet 6(Suppl 1):S11CrossRefPubMedGoogle Scholar
  43. 43.
    Skrivanek Z, Lin S, Irwin M (2003) Linkage analysis with sequential imputation. Genet Epidemiol 25:25–35CrossRefPubMedGoogle Scholar
  44. 44.
    Sobel E, Lange K (1996) Descent graphs in pedigree analysis: applications to haplotyping, location scores, and marker-sharing statistics. Am J Hum Genet 58:1323–1337PubMedGoogle Scholar
  45. 45.
    Sobel E, Sengul H, Weeks DE (2001) Multipoint estimation of identity-by-descent probabilities at arbitrary positions among marker loci on general pedigrees. Hum Hered 52:121–131CrossRefPubMedGoogle Scholar
  46. 46.
    Sung YJ, Thompson EA, Wijsman EM (2007) MCMC-based linkage analysis for complex traits on general pedigrees: multipoint analysis with a two-locus model and polygenic component. Genet Epidemiol 31:103–114CrossRefPubMedGoogle Scholar
  47. 47.
    Thompson EA (1995) Monte Carlo in genetic analysis. Technical report no. 294, Department of Statistics, University of Washington, Seattle, WAGoogle Scholar
  48. 48.
    Thompson EA (2000) Statistical inferences from genetic data on pedigrees, vol. 6. IMS, Beachwood, OHGoogle Scholar
  49. 49.
    Thompson EA (2005) MCMC in the analysis of genetic data on pedigrees. In: Liang F, Wang J-S, Kendall W (eds) Markov Chain Monte Carlo: innovations and applications. World Scientific, SingaporeGoogle Scholar
  50. 50.
    Wijsman EM, Amos CI (1997) Genetic analysis of simulated oligogenic traits in nuclear and extended pedigrees: summary of GAW10 contributions. Genet Epidemiol 14:719–735CrossRefPubMedGoogle Scholar
  51. 51.
    Thompson EA, Heath SC (1999) Estimation of conditional multilocus gene identity among relatives. In: Seillier-Moiseiwitsch F (ed) Statistics in molecular biology and genetics: selected proceedings of the 1997 Joint AMS-IMS-SIAM Summer Conference on Statistics in Molecular Biology. Institute of Mathematical Studies, Hayward, CAGoogle Scholar
  52. 52.
    Wijsman EM, Yu D (2004) Joint oligogenic segregation and linkage analysis using Bayesian Markov chain Monte Carlo methods. Mol Biotechnol 28:205–226CrossRefPubMedGoogle Scholar
  53. 53.
    Wijsman EM, Rothstein J, Thompson EA (2006) Multipoint linkage analysis with many multiallelic or dense diallelic markers: Markov chain-Monte Carlo provides practical approaches for genome scans on general pedigrees. Am J Hum Genet 79:846–858CrossRefPubMedGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Epidemiology and Biostatistics, Division of Genetics and Molecular EpidemiologyCase Western Reserve UniversityClevelandUSA
  2. 2.Department of StatisticsThe Ohio State UniversityClevelandUSA

Personalised recommendations