Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Bayesian inference of epistatic interactions in case-control studies

Abstract

Epistatic interactions among multiple genetic variants in the human genome may be important in determining individual susceptibility to common diseases. Although some existing computational methods for identifying genetic interactions have been effective for small-scale studies, we here propose a method, denoted 'bayesian epistasis association mapping' (BEAM), for genome-wide case-control studies. BEAM treats the disease-associated markers and their interactions via a bayesian partitioning model and computes, via Markov chain Monte Carlo, the posterior probability that each marker set is associated with the disease. Testing this on an age-related macular degeneration genome-wide association data set, we demonstrate that the method is significantly more powerful than existing approaches and that genome-wide case-control epistasis mapping with many thousands of markers is both computationally and statistically feasible.

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

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Comparison between BEAM (B), the stepwise B-stat (S), the stepwise logistic regression (L) and the 2-d.f. χ2 test (C) on six disease models.
Figure 2: Impact of MAF discrepancy and LD on the powers of BEAM (B), the stepwise B-stat (S), the stepwise logistic regression (L) and the 2-d.f. χ2 test (C).
Figure 3: Posterior probabilities of association for each marker in the AMD data set, obtained by running BEAM for 108 iterations and taking samples at every 105 iterations.
Figure 4: Comparison of BEAM (B), the stepwise B-stat (S), the stepwise logistic regression (L) and the 2-d.f. χ2 test (C) on the 100,000-SNP data sets.
Figure 5: Comparison of BEAM (B), MDR (M), logic regression (R), BGTA (T) and the 2-d.f. χ2 test (C) on model 4.

References

  1. Moore, J.H. & Williams, S.M. New strategies for identifying gene-gene interactions in hypertension. Ann. Med. 34, 88–95 (2002).

    Article  CAS  Google Scholar 

  2. Ritchie, M.D. et al. Multifactor-dimensionality reduction reveals high-order interactions among estrogen-metabolism genes in sporadic breast cancer. Am. J. Hum. Genet. 69, 138–147 (2001).

    Article  CAS  Google Scholar 

  3. Zee, R.Y. et al. Multi-locus interactions predict risk for post-PTCA restenosis: an approach to the genetic analysis of common complex disease. Pharmacogenomics J. 2, 197–201 (2002).

    Article  CAS  Google Scholar 

  4. Williams, S.M. et al. Multilocus analysis of hypertension: a hierarchical approach. Hum. Hered. 57, 28–38 (2004).

    Article  Google Scholar 

  5. Tsai, C.T. et al. Renin-angiotensin system gene polymorphisms and atrial fibrillation. Circulation 109, 1640–1646 (2004).

    Article  CAS  Google Scholar 

  6. Cho, Y.M. et al. Multifactor-dimensionality reduction shows a two-locus interaction associated with Type 2 diabetes mellitus. Diabetologia 47, 549–554 (2004).

    Article  CAS  Google Scholar 

  7. Nelson, M.R., Kardia, S.L., Ferrell, R.E. & Sing, C.F. A combinatorial partitioning method to identify multilocus genotypic partitions that predict quantitative trait variation. Genome Res. 11, 458–470 (2001).

    Article  CAS  Google Scholar 

  8. Culverhouse, R., Klein, T. & Shannon, W. Detecting epistatic interactions contributing to quantitative traits. Genet. Epidemiol. 27, 141–152 (2004).

    Article  Google Scholar 

  9. Cook, N.R., Zee, R.Y. & Ridker, P.M. Tree and spline based association analysis of gene-gene interaction models for ischemic stroke. Stat. Med. 23, 1439–1453 (2004).

    Article  Google Scholar 

  10. Kooperberg, C. & Ruczinski, I. Identifying interaction SNPs using Monte Carlo logic regression. Genet. Epidemiol. 28, 157–170 (2005).

    Article  Google Scholar 

  11. Zheng, T., Wang, H. & Lo, S.H. Backward genotype-trait association (BGTA) - based dissection of complex traits in case-control design. Hum. Hered. 62, 196–212 (2006).

    Article  Google Scholar 

  12. Marchini, J., Donnelly, P. & Cardon, L.R. Genome-wide strategies for detecting multiple loci that influence complex diseases. Nat. Genet. 37, 413–417 (2005).

    Article  CAS  Google Scholar 

  13. Klein, R.J. et al. Complement factor H polymorphism in age-related macular degeneration. Science 308, 385–389 (2005).

    Article  CAS  Google Scholar 

  14. Culverhouse, R., Suarez, B.K., Lin, J. & Reich, T. A perspective on epistasis: limits of models displaying no main effect. Am. J. Hum. Genet. 70, 461–471 (2002).

    Article  Google Scholar 

  15. Zondervan, K.T. & Cardon, L.R. The complex interplay among factors that influence allelic association. Nat. Rev. Genet. 5, 89–100 (2004).

    Article  CAS  Google Scholar 

  16. Collins, A., Lonjou, C. & Morton, N.E. Genetic epidemiology of single-nucleotide polymorphism. Proc. Natl. Acad. Sci. USA 96, 15173–15177 (1999).

    Article  CAS  Google Scholar 

  17. Kruglyak, L. Prospects for whole-genome linkage disequilibrium mapping of common disease genes. Nat. Genet. 22, 139–144 (1999).

    Article  CAS  Google Scholar 

  18. Wang, W.Y.S., Barratt, B.J., Clayton, D.G. & Todd, J.A. Genome-wide association studies: theoretical and practical concerns. Nat. Rev. Genet. 6, 109–118 (2005).

    Article  CAS  Google Scholar 

  19. Liu, J.S. Monte Carlo Strategies in Scientific Computing (Springer, New York, 2001).

    Google Scholar 

Download references

Acknowledgements

This work was supported in part by US National Institutes of Health grant R01HG002518-06, US National Science Foundation grant DMS-0204674 and a grant from the National Science Foundation of China (10228102). We thank J. Hoh for providing us the AMD data set and T. Niu for discussions.

Author information

Authors and Affiliations

Authors

Contributions

Y.Z. and J.S.L. designed the statistical models and simulation studies together. Y.Z. implemented the method and wrote the software. Both authors contributed to the writing of the manuscript.

Corresponding author

Correspondence to Jun S Liu.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Text and Figures

Supplementary Methods, Supplementary Figures 1–4, Supplementary Table 1 (PDF 367 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Zhang, Y., Liu, J. Bayesian inference of epistatic interactions in case-control studies. Nat Genet 39, 1167–1173 (2007). https://doi.org/10.1038/ng2110

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/ng2110

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing