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


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.


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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




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).

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