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

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.

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

References

  1. 1

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

  2. 2

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

    CAS  Article  Google Scholar 

  3. 3

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

    CAS  Article  Google Scholar 

  4. 4

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

    CAS  Article  Google Scholar 

  5. 5

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

  6. 6

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

    CAS  Article  Google Scholar 

  7. 7

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

    CAS  PubMed  PubMed Central  Google Scholar 

  8. 8

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

    Article  Google Scholar 

  9. 9

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

    Article  Google Scholar 

  10. 10

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

    Article  Google Scholar 

  11. 11

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

    CAS  Article  Google Scholar 

  12. 12

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

    CAS  Article  Google Scholar 

  13. 13

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

    Article  Google Scholar 

  14. 14

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

    CAS  Article  Google Scholar 

  15. 15

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

    CAS  Article  Google Scholar 

  16. 16

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

    CAS  Article  Google Scholar 

  17. 17

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

    CAS  Article  Google Scholar 

  18. 18

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

    Article  Google Scholar 

  19. 19

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

    CAS  Article  Google Scholar 

  20. 20

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

    Article  Google Scholar 

  21. 21

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

    CAS  Article  Google Scholar 

  22. 22

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

    CAS  Article  Google Scholar 

  23. 23

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

    CAS  Article  Google Scholar 

  24. 24

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

    Article  Google Scholar 

  25. 25

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

    Article  Google Scholar 

  26. 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. 27

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

    Article  Google Scholar 

  28. 28

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

    CAS  Article  Google Scholar 

  29. 29

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

    Article  Google Scholar 

  30. 30

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

    CAS  Article  Google Scholar 

  31. 31

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

    CAS  Article  Google Scholar 

  32. 32

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

    CAS  Article  Google Scholar 

  33. 33

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

    CAS  Article  Google Scholar 

  34. 34

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

    Article  Google Scholar 

  35. 35

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

    CAS  Article  Google Scholar 

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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.

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Authors

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.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Text and Figures

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

Supplementary Software

GEMMA version 0.94. (ZIP 24880 kb)

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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

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