Skip to main content
Book cover

Epistasis pp 257–268Cite as

Epistasis Analysis Using Information Theory

Part of the Methods in Molecular Biology book series (MIMB,volume 1253)

Abstract

Here we introduce entropy-based measures derived from information theory for detecting and characterizing epistasis in genetic association studies. We provide a general overview of the methods and highlight some of the modifications that have greatly improved its power for genetic analysis. We end with a few published studies of complex human diseases that have used these measures.

Key words

  • Epistasis
  • Information theory
  • Entropy
  • Association studies
  • Genetic analysis
  • Gene–gene interaction

This is a preview of subscription content, access via your institution.

Protocol
USD   49.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-1-4939-2155-3_13
  • Chapter length: 12 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   109.00
Price excludes VAT (USA)
  • ISBN: 978-1-4939-2155-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   149.99
Price excludes VAT (USA)
Hardcover Book
USD   179.99
Price excludes VAT (USA)
Learn about institutional subscriptions
Fig. 1

Springer Nature is developing a new tool to find and evaluate Protocols. Learn more

References

  1. Phillips PC (2008) Epistasis – the essential role of gene interactions in the structure and evolution of genetic systems. Nat Rev Genet 9:855–867

    CrossRef  CAS  PubMed Central  PubMed  Google Scholar 

  2. Phillips PC (1998) The language of gene interaction. Genetics 149:1167–1171

    CAS  PubMed Central  PubMed  Google Scholar 

  3. Cordell HJ (2002) Epistasis: what it means, what it doesn’t mean, and statistical methods to detect it in humans. Hum Mol Genet 11:2463–2468

    CrossRef  CAS  PubMed  Google Scholar 

  4. Cordell HJ (2009) Detecting gene–gene interactions that underlie human diseases. Nat Rev Genet 10:392–404

    CrossRef  CAS  PubMed Central  PubMed  Google Scholar 

  5. Moore JH (2003) The ubiquitous nature of epistasis in determining susceptibility to common human diseases. Hum Hered 56:73–82

    CrossRef  PubMed  Google Scholar 

  6. Moore JH (2005) A global view of epistasis. Nat Genet 37:13–14

    CrossRef  CAS  PubMed  Google Scholar 

  7. Moore JH, Williams SM (2005) Traversing the conceptual divide between biological and statistical epistasis: systems biology and a more modern synthesis. Bioessays 27:637–646

    CrossRef  CAS  PubMed  Google Scholar 

  8. Tyler AL, Asselbergs FW, Williams SM et al (2009) Shadows of complexity: what biological networks reveal about epistasis and pleiotropy. Bioessays 31:220–227

    CrossRef  PubMed Central  PubMed  Google Scholar 

  9. Cowper-Sal lari R, Cole MD, Karagas MR et al (2011) Layers of epistasis: genome-wide regulatory networks and network approaches to genome-wide association studies. Wiley Interdiscip Rev Syst Biol Med 3:513–526

    CrossRef  CAS  PubMed Central  PubMed  Google Scholar 

  10. Moore JH, Williams SM (2009) Epistasis and its implications for personal genetics. Am J Hum Genet 85:309–320

    CrossRef  CAS  PubMed Central  PubMed  Google Scholar 

  11. Millstein J, Conti DV, Gilliland FD et al (2006) A testing framework for identifying susceptibility genes in the presence of epistasis. Am J Hum Genet 78:15–27

    CrossRef  CAS  PubMed Central  PubMed  Google Scholar 

  12. Kooperberg C, Ruczinski I (2005) Identifying interacting SNPs using Monte Carlo logic regression. Genet Epidemiol 28:157–170

    CrossRef  PubMed  Google Scholar 

  13. Kooperberg C, Ruczinski I, LeBlanc ML et al (2001) Sequence analysis using logic regression. Genet Epidemiol 21(Suppl 1):S626–S631

    PubMed  Google Scholar 

  14. Schwender H, Ruczinski I (2010) Logic regression and its extensions. Adv Genet 72:25–45

    CrossRef  PubMed  Google Scholar 

  15. Hahn LW, Ritchie MD, Moore JH (2003) Multifactor dimensionality reduction software for detecting gene–gene and gene–environment interactions. Bioinformatics 19:376–382

    CrossRef  CAS  PubMed  Google Scholar 

  16. Ritchie MD, Hahn LW, Roodi N et al (2001) Multifactor-dimensionality reduction reveals high-order interactions among estrogen-metabolism genes in sporadic breast cancer. Am J Hum Genet 69:138–147

    CrossRef  CAS  PubMed Central  PubMed  Google Scholar 

  17. Hahn LW, Moore JH (2004) Ideal discrimination of discrete clinical endpoints using multilocus genotypes. In Silico Biol 4:183–194

    CAS  PubMed  Google Scholar 

  18. Ritchie MD, Hahn LW, Moore JH (2003) Power of multifactor dimensionality reduction for detecting gene–gene interactions in the presence of genotyping error, missing data, phenocopy, and genetic heterogeneity. Genet Epidemiol 24:150–157

    CrossRef  PubMed  Google Scholar 

  19. Moore JH (2004) Computational analysis of gene–gene interactions using multifactor dimensionality reduction. Expert Rev Mol Diagn 4:795–803

    CrossRef  CAS  PubMed  Google Scholar 

  20. Moore JH (2010) Detecting, characterizing, and interpreting nonlinear gene–gene interactions using multifactor dimensionality reduction. Adv Genet 72:101–116

    CrossRef  PubMed  Google Scholar 

  21. Velez DR, White BC, Motsinger AA et al (2007) A balanced accuracy function for epistasis modeling in imbalanced datasets using multifactor dimensionality reduction. Genet Epidemiol 31:306–315

    CrossRef  PubMed  Google Scholar 

  22. Pattin KA, White BC, Barney N et al (2009) A computationally efficient hypothesis testing method for epistasis analysis using multifactor dimensionality reduction. Genet Epidemiol 33:87–94

    CrossRef  PubMed Central  PubMed  Google Scholar 

  23. Moore JH (2007) Genome-wide analysis of epistasis using multifactor dimensionality reduction: feature selection and construction in the domain of human genetics. In: Zhu X, Davidson I (eds) Knowledge discovery and data mining: challenges and realities. IGI Global, Hershey, PA, pp 17–30

    CrossRef  Google Scholar 

  24. Moore JH (2008) Bases, bits and disease: a mathematical theory of human genetics. Eur J Hum Genet 16:143–144

    CrossRef  PubMed  Google Scholar 

  25. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423

    CrossRef  Google Scholar 

  26. McGill WJ (1954) Multivariate information transmission. Psychometrika 19:97–116

    CrossRef  Google Scholar 

  27. Jakulin A, Bratko I (2003) Analyzing attribute dependencies. In: Lavrač N, Gamberger D, Todorovski L et al (eds) Knowledge discovery in databases: PKDD 2003. Springer, Berlin, pp 229–240

    Google Scholar 

  28. Moore JH, Gilbert JC, Tsai C-T et al (2006) A flexible computational framework for detecting, characterizing, and interpreting statistical patterns of epistasis in genetic studies of human disease susceptibility. J Theor Biol 241:252–261

    CrossRef  PubMed  Google Scholar 

  29. Hu T, Chen Y, Kiralis JW et al (2013) ViSEN: methodology and software for visualization of statistical epistasis networks. Genet Epidemiol 37(3):283–285

    CrossRef  PubMed Central  PubMed  Google Scholar 

  30. Demšar J, Curk T, Erjavec A et al (2013) Orange: data mining toolbox in python. J Mach Learn Res 14:2349–2353

    Google Scholar 

  31. Cover TM, Thomas JA (2006) Elements of information theory. Wiley-Interscience, Hoboken, NJ

    Google Scholar 

  32. Fan R, Zhong M, Wang S et al (2011) Entropy-based information gain approaches to detect and to characterize gene–gene and gene–environment interactions/correlations of complex diseases. Genet Epidemiol 35:706–721

    CrossRef  CAS  PubMed Central  PubMed  Google Scholar 

  33. Hu T, Andrew AS, Karagas MR et al (2013) Statistical epistasis networks reduce the computational complexity of searching three-locus genetic models. Pac Symp Biocomput 397–408

    Google Scholar 

  34. Hu T, Sinnott-Armstrong NA, Kiralis JW et al (2011) Characterizing genetic interactions in human disease association studies using statistical epistasis networks. BMC Bioinformatics 12:364

    CrossRef  CAS  PubMed Central  PubMed  Google Scholar 

  35. McKinney BA, Reif DM, White BC et al (2007) Evaporative cooling feature selection for genotypic data involving interactions. Bioinformatics 23:2113–2120

    CrossRef  CAS  PubMed Central  PubMed  Google Scholar 

  36. Dong C, Chu X, Wang Y et al (2008) Exploration of gene–gene interaction effects using entropy-based methods. Eur J Hum Genet 16:229–235

    CrossRef  CAS  PubMed  Google Scholar 

  37. Kang G, Yue W, Zhang J et al (2008) An entropy-based approach for testing genetic epistasis underlying complex diseases. J Theor Biol 250:362–374

    CrossRef  CAS  PubMed  Google Scholar 

  38. Wu C, Li S, Cui Y (2012) Genetic association studies: an information content perspective. Curr Genomics 13:566–573

    CrossRef  CAS  PubMed Central  PubMed  Google Scholar 

  39. Chanda P, Zhang A, Brazeau D et al (2007) Information-theoretic metrics for visualizing gene–environment interactions. Am J Hum Genet 81:939–963

    CrossRef  CAS  PubMed Central  PubMed  Google Scholar 

  40. Sucheston L, Chanda P, Zhang A et al (2010) Comparison of information-theoretic to statistical methods for gene–gene interactions in the presence of genetic heterogeneity. BMC Genomics 11:487

    CrossRef  PubMed Central  PubMed  Google Scholar 

  41. Chanda P, Zhang A, Ramanathan M (2011) Modeling of environmental and genetic interactions with AMBROSIA, an information-theoretic model synthesis method. Heredity 107:320–327

    CrossRef  CAS  PubMed Central  PubMed  Google Scholar 

  42. Tritchler DL, Sucheston L, Chanda P et al (2011) Information metrics in genetic epidemiology. Stat Appl Genet Mol Biol 10, Article 12

    Google Scholar 

  43. Hu T, Chen Y, Kiralis JW et al (2013) An information-gain approach to detecting three-way epistatic interactions in genetic association studies. J Am Med Inform Assoc 20:630–636

    CrossRef  PubMed Central  PubMed  Google Scholar 

  44. Anastassiou D (2007) Computational analysis of the synergy among multiple interacting genes. Mol Syst Biol 3:83

    CrossRef  PubMed Central  PubMed  Google Scholar 

  45. Varadan V, Miller DM 3rd, Anastassiou D (2006) Computational inference of the molecular logic for synaptic connectivity in C. elegans. Bioinformatics 22:e497–e506

    CrossRef  CAS  PubMed  Google Scholar 

  46. Chechik G, Globerson A, Tishby N et al (2002) Group redundancy measures reveal redundancy reduction in the auditory pathway. In: Becker S, Ghaharamani Z, Dietterich TG (eds) Advances in neural information processing systems. MIT Press, Cambridge, MA, pp 173–180

    Google Scholar 

  47. West D (2007) Introduction to graph theory. Prentice Hall PTR, Upper Saddle River, NJ

    Google Scholar 

  48. Newman MEJ (2010) Networks: an introduction. Oxford University Press, Oxford, UK

    CrossRef  Google Scholar 

  49. Andrew AS, Nelson HH, Kelsey KT et al (2006) Concordance of multiple analytical approaches demonstrates a complex relationship between DNA repair gene SNPs, smoking and bladder cancer susceptibility. Carcinogenesis 27:1030–1037

    CrossRef  CAS  PubMed  Google Scholar 

  50. Urbanowicz RJ, Andrew AS, Karagas MR et al (2013) Role of genetic heterogeneity and epistasis in bladder cancer susceptibility and outcome: a learning classifier system approach. J Am Med Inform Assoc 20:603–612

    CrossRef  PubMed Central  PubMed  Google Scholar 

  51. Andrew AS, Gui J, Sanderson AC et al (2009) Bladder cancer SNP panel predicts susceptibility and survival. Hum Genet 125:527–539

    CrossRef  PubMed Central  PubMed  Google Scholar 

  52. Hu T, Pan Q, Andrew AS et al (2014) Functional genomics annotation of a statistical epistasis network associated with bladder cancer susceptibility. BioData Min 7:5

    CrossRef  PubMed Central  PubMed  Google Scholar 

  53. Moore JH, Asselbergs FW, Williams SM (2010) Bioinformatics challenges for genome-wide association studies. Bioinformatics 26:445–455

    CrossRef  CAS  PubMed Central  PubMed  Google Scholar 

  54. Purcell S, Neale B, Todd-Brown K et al (2007) PLINK: a tool set for whole-genome association and population-based linkage analyses. Am J Hum Genet 81:559–575

    CrossRef  CAS  PubMed Central  PubMed  Google Scholar 

  55. Greene CS, Hill DP, Moore JH (2010) Environmental sensing of expert knowledge in a computational evolution system for complex problem solving in human genetics. In: Riolo R, O’Reilly U-M, McConaghy T (eds) Genetic programming theory and practice VII. Springer, New York, USA, pp 19–36

    CrossRef  Google Scholar 

  56. Moore JH, Andrews PC, Barney N et al (2008) Development and evaluation of an open-ended computational evolution system for the genetic analysis of susceptibility to common human diseases. In: Marchiori E, Moore JH (eds) Evolutionary computation, machine learning and data mining in bioinformatics. Springer, Berlin, pp 129–140

    CrossRef  Google Scholar 

  57. Moore JH, Greene CS, Andrews PC et al (2009) Does complexity matter? artificial evolution, computational evolution and the genetic analysis of epistasis in common human diseases. Genetic programming theory and practice VI. Springer, New York, USA, pp 1–19

    Google Scholar 

Download references

Acknowledgements

This work was supported by National Institutes of Health (NIH) grants AI59694, EY022300, GM103534, GM103506, LM009012, LM010098, and LM011360.

Author information

Authors and Affiliations

  1. Department of Community and Family Medicine, Geisel School of Medicine, DHMC, One Medical Center Drive, HB 7937, Lebanon, NH, 03756, USA

    Jason H. Moore

  2. Department of Genetics, Geisel School of Medicine, DHMC, Lebanon, NH, USA

    Ting Hu

  3. Department of Genetics, Institute for Quantitative Biomedical Sciences, Geisel School of Medicine, Hanover, NH, USA

    Jason H. Moore

Authors
  1. Jason H. Moore
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ting Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jason H. Moore .

Editor information

Editors and Affiliations

  1. Department of Genetics, Institute of Quantitative Biomedical Sciences, Geisel School of Medicine, Hanover, New Hampshire, USA

    Jason H. Moore

  2. Department of Genetics, Institute of Quantitative Biomedical Sciences, Geisel School of Medicine, Hanover, New Hampshire, USA

    Scott M. Williams

Rights and permissions

Reprints and Permissions

Copyright information

© 2015 Springer Science+Business Media New York

About this protocol

Cite this protocol

Moore, J.H., Hu, T. (2015). Epistasis Analysis Using Information Theory. In: Moore, J., Williams, S. (eds) Epistasis. Methods in Molecular Biology, vol 1253. Humana Press, New York, NY. https://doi.org/10.1007/978-1-4939-2155-3_13

Download citation

  • DOI: https://doi.org/10.1007/978-1-4939-2155-3_13

  • Published:

  • Publisher Name: Humana Press, New York, NY

  • Print ISBN: 978-1-4939-2154-6

  • Online ISBN: 978-1-4939-2155-3

  • eBook Packages: Springer Protocols