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.

  • Brief Communication
  • Published:

Efficient multivariate linear mixed model algorithms for genome-wide association studies

Nature Methods volume 11, pages 407–409 (2014) Cite this article

View saved research

Abstract

Multivariate linear mixed models (mvLMMs) are powerful tools for testing associations between single-nucleotide polymorphisms and multiple correlated phenotypes while controlling for population stratification in genome-wide association studies. We present efficient algorithms in the genome-wide efficient mixed model association (GEMMA) software for fitting mvLMMs and computing likelihood ratio tests. These algorithms offer improved computation speed, power and P-value calibration over existing methods, and can deal with more than two phenotypes.

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

Access options

Access through your institution

Buy this article

  • Purchase on SpringerLink
  • Instant access to the full article PDF.

39,95 €

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Statistical benefits of the mvLMM algorithm implemented in GEMMA.

Similar content being viewed by others

Explore related subjects

Discover the latest articles and news in related subjects.

References

  1. Henderson, C.R. Applications of Linear Models in Animal Breeding (University of Guelph, 1984).

  2. Price, A.L. et al. PLoS Genet. 7, e1001317 (2011).

    Article  CAS  Google Scholar 

  3. Korte, A. et al. Nat. Genet. 44, 1066–1071 (2012).

    Article  CAS  Google Scholar 

  4. Lee, S.H., Yang, J., Goddard, M.E., Visscher, P.M. & Wray, N.R. Bioinformatics 28, 2540–2542 (2012).

    Article  CAS  Google Scholar 

  5. Trzaskowski, M., Yang, J., Visscher, P.M. & Plomin, R. Mol. Psychiatry 10.1038/mp.2012.191 (29 January 2013).

  6. Vattikuti, S., Guo, J. & Chow, C.C. PLoS Genet. 8, e1002637 (2012).

    Article  CAS  Google Scholar 

  7. Amos, C.I. Am. J. Hum. Genet. 54, 535–543 (1994).

    CAS  PubMed  PubMed Central  Google Scholar 

  8. Kruuk, L.E. Phil. Trans. R. Soc. Lond. B 359, 873–890 (2004).

    Article  Google Scholar 

  9. Meyer, K., Johnston, D.J. & Graser, H.U. Aust. J. Agric. Res. 55, 195–210 (2004).

    Article  Google Scholar 

  10. Meyer, K. Genet. Sel. Evol. 23, 67–83 (1991).

    Article  Google Scholar 

  11. Kang, H.M. et al. Nat. Genet. 42, 348–354 (2010).

    Article  CAS  Google Scholar 

  12. Lippert, C. et al. Nat. Methods 8, 833–835 (2011).

    Article  CAS  Google Scholar 

  13. Pirinen, M., Donnelly, P. & Spencer, C.C.A. Ann. Appl. Stat. 7, 369–390 (2013).

    Article  Google Scholar 

  14. Yu, J.M. et al. Nat. Genet. 38, 203–208 (2006).

    Article  CAS  Google Scholar 

  15. Zhang, Z.W. et al. Nat. Genet. 42, 355–360 (2010).

    Article  CAS  Google Scholar 

  16. Zhou, X., Carbonetto, P. & Stephens, M. PLoS Genet. 9, e1003264 (2013).

    Article  CAS  Google Scholar 

  17. Zhou, X. & Stephens, M. Nat. Genet. 44, 821–824 (2012).

    Article  CAS  Google Scholar 

  18. Banerjee, S., Yandell, B.S. & Yi, N.J. Genetics 179, 2275–2289 (2008).

    Article  Google Scholar 

  19. Ferreira, M.A.R. & Purcell, S.M. Bioinformatics 25, 132–133 (2009).

    Article  CAS  Google Scholar 

  20. Kim, S. & Xing, E.P. PLoS Genet. 5, e1000587 (2009).

    Article  Google Scholar 

  21. O'reilly, P.F. et al. PLoS One 7, e34861 (2012).

    Article  CAS  Google Scholar 

  22. Stephens, M. PLoS One 8, e65245 (2013).

    Article  CAS  Google Scholar 

  23. Yang, J.A., Lee, S.H., Goddard, M.E. & Visscher, P.M. Am. J. Hum. Genet. 88, 76–82 (2011).

    Article  CAS  Google Scholar 

  24. Meyer, K. J. Zhejiang Univ. Sci. B 8, 815–821 (2007).

    Article  Google Scholar 

  25. Gilmour, A.R., Thompson, R. & Cullis, B.R. Biometrics 51, 1440–1450 (1995).

    Article  Google Scholar 

  26. Meyer, K. PX × AI: Algorithmics for better convergence in restricted maximum likelihood estimation. in 8th World Congress on Genetics Applied to Livestock Production (Belo Horizonte, Brasil, 2006).

  27. Kang, H.M. et al. Genetics 178, 1709–1723 (2008).

    Article  Google Scholar 

  28. Kostem, E. & Eskin, E. Am. J. Hum. Genet. 92, 558–564 (2013).

    Article  CAS  Google Scholar 

  29. Runcie, D.E. & Mukherjee, S. Genetics 194, 753–767 (2013).

    Article  Google Scholar 

  30. Listgarten, J. et al. Nat. Methods 9, 525–526 (2012).

    Article  CAS  Google Scholar 

  31. Bennett, B.J. et al. Genome Res. 20, 281–290 (2010).

    Article  CAS  Google Scholar 

  32. Sabatti, C. et al. Nat. Genet. 41, 35–46 (2009).

    Article  CAS  Google Scholar 

  33. Purcell, S. et al. Am. J. Hum. Genet. 81, 559–575 (2007).

    Article  CAS  Google Scholar 

  34. Astle, W. & Balding, D.J. Stat. Sci. 24, 451–471 (2009).

    Article  Google Scholar 

  35. Hayes, B.J., Visscher, P.M. & Goddard, M.E. Genet. Res. 91, 143–143 (2009).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

This research was supported in part by US National Institutes of Health (NIH) grant HL092206 (principal investigator, Y. Gilad) and NIH grant HG02585 to M.S. We thank A.J. Lusis for making the mouse genotype and phenotype data available, and the NFBC1966 Study Investigators for making the NFBC1966 data available. The NFBC1966 study is conducted and supported by the National Heart, Lung, and Blood Institute (NHLBI) in collaboration with the Broad Institute, University of California Los Angeles, University of Oulu, and the National Institute for Health and Welfare in Finland. This manuscript was not prepared in collaboration with investigators of the NFBC1966 study and does not necessarily reflect their views or those of their host institutions.

Author information

Authors and Affiliations

  1. Department of Human Genetics, University of Chicago, Chicago, Illinois, USA

    Xiang Zhou & Matthew Stephens

  2. Department of Statistics, University of Chicago, Chicago, Illinois, USA

    Xiang Zhou & Matthew Stephens

Authors
  1. Xiang Zhou
    View author publications

    Search author on:PubMed Google Scholar

  2. Matthew Stephens
    View author publications

    Search author on:PubMed Google Scholar

Contributions

X.Z. and M.S. conceived the idea and designed the study. X.Z. developed the algorithms, implemented the software and performed the analyses. X.Z. and M.S. wrote the paper.

Corresponding authors

Correspondence to Xiang Zhou or Matthew Stephens.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Text and Figures (download PDF )

Supplementary Figures 1–8, Supplementary Tables 1 and 2, and Supplementary Note (PDF 1889 kb)

Supplementary Software (download ZIP )

GEMMA version 0.94. (ZIP 24880 kb)

Source data

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, X., Stephens, M. Efficient multivariate linear mixed model algorithms for genome-wide association studies. Nat Methods 11, 407–409 (2014). https://doi.org/10.1038/nmeth.2848

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue date:

  • DOI: https://doi.org/10.1038/nmeth.2848

Search

Advanced 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