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Efficiently controlling for case-control imbalance and sample relatedness in large-scale genetic association studies

Nature Genetics volumeΒ 50,Β pages 1335–1341 (2018)Cite this article

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Abstract

In genome-wide association studies (GWAS) for thousands of phenotypes in large biobanks, most binary traits have substantially fewer cases than controls. Both of the widely used approaches, the linear mixed model and the recently proposed logistic mixed model, perform poorly; they produce large type I error rates when used to analyze unbalanced case-control phenotypes. Here we propose a scalable and accurate generalized mixed model association test that uses the saddlepoint approximation to calibrate the distribution of score test statistics. This method, SAIGE (Scalable and Accurate Implementation of GEneralized mixed model), provides accurate P values even when case-control ratios are extremely unbalanced. SAIGE uses state-of-art optimization strategies to reduce computational costs; hence, it is applicable to GWAS for thousands of phenotypes by large biobanks. Through the analysis of UK Biobank data of 408,961 samples from white British participants with European ancestry for > 1,400 binary phenotypes, we show that SAIGE can efficiently analyze large sample data, controlling for unbalanced case-control ratios and sample relatedness.

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Fig. 1: Manhattan plots of GWAS results for four binary phenotypes with various case-control ratios in the UK Biobank.
Fig. 2: Quantile–quantile plots of GWAS results for four binary phenotypes with various case-control ratios in the UK Biobank.

References

  1. Bush, W. S., Oetjens, M. T. & Crawford, D. C. Unravelling the human genome-phenome relationship using phenome-wide association studies. Nat. Rev. Genet. 17, 129–145 (2016).

    ArticleΒ  CASΒ  Google ScholarΒ 

  2. Denny, J. C. et al. Systematic comparison of phenome-wide association study of electronic medical record data and genome-wide association study data. Nat. Biotechnol. 31, 1102–1110 (2013).

    ArticleΒ  CASΒ  Google ScholarΒ 

  3. Kang, H. M. et al. Variance component model to account for sample structure in genome-wide association studies. Nat. Genet. 42, 348–354 (2010).

    ArticleΒ  CASΒ  Google ScholarΒ 

  4. Zhang, Z. et al. Mixed linear model approach adapted for genome-wide association studies. Nat. Genet. 42, 355–360 (2010).

    ArticleΒ  CASΒ  Google ScholarΒ 

  5. Yang, J., Lee, S. H., Goddard, M. E. & Visscher, P. M. GCTA: a tool for genome-wide complex trait analysis. Am. J. Hum. Genet. 88, 76–82 (2011).

    ArticleΒ  CASΒ  Google ScholarΒ 

  6. Lippert, C. et al. FaST linear mixed models for genome-wide association studies. Nat. Methods 8, 833–835 (2011).

    ArticleΒ  CASΒ  Google ScholarΒ 

  7. Zhou, X. & Stephens, M. Genome-wide efficient mixed-model analysis for association studies. Nat. Genet. 44, 821–824 (2012).

    ArticleΒ  CASΒ  Google ScholarΒ 

  8. Loh, P. R. et al. Efficient Bayesian mixed-model analysis increases association power in large cohorts. Nat. Genet. 47, 284–290 (2015).

    ArticleΒ  CASΒ  Google ScholarΒ 

  9. Chen, H. et al. Control for population structure and relatedness for binary traits in genetic association studies via logistic mixed models. Am. J. Hum. Genet. 98, 653–666 (2016).

    ArticleΒ  CASΒ  Google ScholarΒ 

  10. Ma, C., Blackwell, T., Boehnke, M. & Scott, L. J., GoT2D investigators. Recommended joint and meta-analysis strategies for case-control association testing of single low-count variants. Genet. Epidemiol 37, 539–550 (2013).

    ArticleΒ  Google ScholarΒ 

  11. Kuonen, D. Saddlepoint approximations for distributions of quadratic forms in normal variables. Biometrika 86, 4 (1999).

  12. Dey, R., Schmidt, E. M., Abecasis, G. R. & Lee, S. A fast and accurate algorithm to test for binary phenotypes and its application to PheWAS. Am. J. Hum. Genet. 101, 37–49 (2017).

    ArticleΒ  CASΒ  Google ScholarΒ 

  13. Kaasschieter, E. F. Preconditioned conjugate gradients for solving singular systems. J. Comput. Appl. Math. 24, 265–275 (1988).

    ArticleΒ  Google ScholarΒ 

  14. Sudlow, C. et al. UK Biobank: an open access resource for identifying the causes of a wide range of complex diseases of middle and old age. PLoS Med. 12, e1001779 (2015).

    ArticleΒ  Google ScholarΒ 

  15. Bycroft, C. et al. Genome-wide genetic data on ~500,000 UK Biobank participants. Preprint at bioRxiv, https://doi.org/10.1101/166298 (2017).

  16. Gilmour, A. R., Thompson, R. & Cullis, B. R. Average information REML: an efficient algorithm for variance parameter estimation in linear mixed models. Biometrics 51, 1440–1450 (1995).

    ArticleΒ  Google ScholarΒ 

  17. Aulchenko, Y. S., Ripke, S., Isaacs, A. & van Duijn, C. M. GenABEL: an R library for genome-wide association analysis. Bioinformatics 23, 1294–1296 (2007).

    ArticleΒ  CASΒ  Google ScholarΒ 

  18. Svishcheva, G. R., Axenovich, T. I., Belonogova, N. M., van Duijn, C. M. & Aulchenko, Y. S. Rapid variance components-based method for whole-genome association analysis. Nat. Genet. 44, 1166–1170 (2012).

    ArticleΒ  CASΒ  Google ScholarΒ 

  19. McCarthy, S. et al. A reference panel of 64,976 haplotypes for genotype imputation. Nat. Genet. 48, 1279–1283 (2016).

    ArticleΒ  CASΒ  Google ScholarΒ 

  20. Nelis, M. et al. Genetic structure of Europeans: a view from the North-East. PLoS One 4, e5472 (2009).

    ArticleΒ  Google ScholarΒ 

  21. Shameer, K. et al. A genome- and phenome-wide association study to identify genetic variants influencing platelet count and volume and their pleiotropic effects. Hum. Genet. 133, 95–109 (2014).

    ArticleΒ  Google ScholarΒ 

  22. Yang, J., Zaitlen, N. A., Goddard, M. E., Visscher, P. M. & Price, A. L. Advantages and pitfalls in the application of mixed-model association methods. Nat. Genet. 46, 100–106 (2014).

    ArticleΒ  Google ScholarΒ 

  23. Listgarten, J. et al. Improved linear mixed models for genome-wide association studies. Nat. Methods 9, 525–526 (2012).

    ArticleΒ  CASΒ  Google ScholarΒ 

  24. Breslow, N. E. & Clayton, D. G. Approximate inference in generalized linear mixed models. J. Am. Stat. Assoc 88, 9–25 (1993).

    Google ScholarΒ 

  25. Hestenes, M. R. & Stiefel, E. Methods of conjugate gradients for solving linear systems. J. Res. Natl Bur. Stand. 49, 409–436 (1952).

    ArticleΒ  Google ScholarΒ 

  26. Imhof, J. P. Computing the distribution of quadratic forms in normal variables. Biometrika 48, 419–426 (1961).

    ArticleΒ  Google ScholarΒ 

  27. Abecasis, G. R., Cherny, S. S., Cookson, W. O. & Cardon, L. R. Merlinβ€”rapid analysis of dense genetic maps using sparse gene flow trees. Nat. Genet. 30, 97–101 (2002).

    ArticleΒ  CASΒ  Google ScholarΒ 

  28. de Villemereuil, P., Schielzeth, H., Nakagawa, S. & Morrissey, M. General methods for evolutionary quantitative genetic inference from generalized mixed models. Genetics 204, 1281–1294 (2016).

    ArticleΒ  Google ScholarΒ 

  29. Bulik-Sullivan, B. K. et al. LD Score regression distinguishes confounding from polygenicity in genome-wide association studies. Nat. Genet. 47, 291–295 (2015).

    ArticleΒ  CASΒ  Google ScholarΒ 

Download references

Acknowledgements

This research has been conducted using the UK Biobank Resource under application number 24460. S.L. and R.D. were supported by NIH R01 HG008773. C.J.W. was supported by NIH R35 HL135824. W.Z. was supported by the University of Michigan Rackham Predoctoral Fellowship. J.B.N. was supported by the Danish Heart Foundation and the Lundbeck Foundation. J.C.D., A.G., L.A.B., and W.-Q.W. were supported by NIH R01 LM010685 and U2C OD023196.

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Author notes

  1. These authors contributed equally: Cristen J. Willer and Seunggeun Lee.

Authors and Affiliations

  1. Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, MI, USA

    Wei Zhou,Β Brooke N. WolfordΒ &Β Cristen J. Willer

  2. Center for Statistical Genetics, University of Michigan School of Public Health, Ann Arbor, MI, USA

    Wei Zhou,Β Lars G. Fritsche,Β Rounak Dey,Β Brooke N. Wolford,Β Jonathon LeFaive,Β Peter VandeHaar,Β Sarah A. Gagliano,Β Hyun Min Kang,Β Goncalo R. AbecasisΒ &Β Seunggeun Lee

  3. Department of Internal Medicine, Division of Cardiology, University of Michigan Medical School, Ann Arbor, MI, USA

    Jonas B. Nielsen,Β Maoxuan LinΒ &Β Cristen J. Willer

  4. K. G. Jebsen Center for Genetic Epidemiology, Department of Public Health and Nursing, Norwegian University of Science and Technology, Trondheim, Norway

    Lars G. Fritsche,Β Maiken E. GabrielsenΒ &Β Kristian Hveem

  5. Department of Biostatistics, University of Michigan School of Public Health, Ann Arbor, MI, USA

    Lars G. Fritsche,Β Rounak Dey,Β Jonathon LeFaive,Β Peter VandeHaar,Β Sarah A. Gagliano,Β Hyun Min Kang,Β Goncalo R. AbecasisΒ &Β Seunggeun Lee

  6. Department of Biomedical Informatics, Vanderbilt University, Nashville, TN, USA

    Aliya Gifford,Β Lisa A. Bastarache,Β Wei-Qi WeiΒ &Β Joshua C. Denny

  7. Department of Medicine, Vanderbilt University Medical Center, Nashville, TN, USA

    Joshua C. Denny

  8. HUNT Research Centre, Department of Public Health and General Practice, Norwegian University of Science and Technology, Levanger, Norway

    Kristian Hveem

  9. Department of Human Genetics, University of Michigan Medical School, Ann Arbor, MI, USA

    Cristen J. Willer

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Contributions

W.Z., C.J.W., and S.L. designed the experiments. W.Z. and S.L. performed the experiments. J.B.N., L.G.F., A.G., L.A.B., W.-Q.W., and J.C.D. constructed the phenotypes for the UK Biobank data. W.Z., J.L., S.A.G., B.N.W., M.L., H.M.K., C.J.W., S.L., and G.R.A. analyzed the UK Biobank data. P.V. created the PheWeb. M.E.G. and K.H. provided the data. W.Z., J.B.N., A.G., J.C.D., R.D., C.J.W., and S.L. wrote the manuscript.

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Correspondence to Cristen J. Willer or Seunggeun Lee.

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Zhou, W., Nielsen, J.B., Fritsche, L.G. et al. Efficiently controlling for case-control imbalance and sample relatedness in large-scale genetic association studies. Nat Genet 50, 1335–1341 (2018). https://doi.org/10.1038/s41588-018-0184-y

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