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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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.

Author information

Author notes

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


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

    • Wei Zhou
    • , Brooke N. Wolford
    •  & Cristen J. Willer
  2. Center for Statistical Genetics, University of Michigan School of Public Health, Ann Arbor, MI, USA

    • Wei Zhou
    • , Lars G. Fritsche
    • , Rounak Dey
    • , Brooke N. Wolford
    • , Jonathon LeFaive
    • , Peter VandeHaar
    • , Sarah A. Gagliano
    • , Hyun Min Kang
    • , Goncalo R. Abecasis
    •  & Seunggeun Lee
  3. Department of Internal Medicine, Division of Cardiology, University of Michigan Medical School, Ann Arbor, MI, USA

    • Jonas B. Nielsen
    • , Maoxuan Lin
    •  & 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
    • , Maiken E. Gabrielsen
    •  & Kristian Hveem
  5. Department of Biostatistics, University of Michigan School of Public Health, Ann Arbor, MI, USA

    • Lars G. Fritsche
    • , Rounak Dey
    • , Jonathon LeFaive
    • , Peter VandeHaar
    • , Sarah A. Gagliano
    • , Hyun Min Kang
    • , Goncalo R. Abecasis
    •  & Seunggeun Lee
  6. Department of Biomedical Informatics, Vanderbilt University, Nashville, TN, USA

    • Aliya Gifford
    • , Lisa A. Bastarache
    • , Wei-Qi Wei
    •  & 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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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.

Competing interests

The authors declare no competing interests.

Corresponding authors

Correspondence to Cristen J. Willer or Seunggeun Lee.

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