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Mixed-model association for biobank-scale datasets

Nature Genetics volume 50, pages 906–908 (2018) Cite this article

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To the Editor — Despite recent work highlighting the advantages of linear mixed-model (LMM) methods for genome-wide association studies (GWAS) in datasets containing relatedness or population structure1,2,3, much uncertainty remains about best practices for optimizing GWAS power while controlling confounders. Several recent studies of the interim UK Biobank dataset4 (∼150,000 samples) removed >20% of samples by filtering for relatedness or genetic ancestry and/or used linear regression in preference to mixed-model association. These issues are exacerbated in the full UK Biobank dataset (∼500,000 samples), in which suggested sample exclusions decrease sample size by nearly 30%5. Here we release a much faster version of our BOLT-LMM Bayesian mixed-model association method3 and show that it can be applied with minimal sample exclusions and achieves greatly superior power as compared to common practices for analyzing UK Biobank data.

To verify that BOLT-LMM analyses of all European samples were robust to potential confounding due to relatedness or population structure, we performed LD score regression (LDSC) analyses7 of association statistics computed using both BOLT-LMM (on all European samples, allowing related individuals as well as population structure) and linear regression (on unrelated British samples stringently quality controlled to minimize confounding5); we ran LDSC using the baselineLD model8. We observed that, while the value of the LD score regression intercept (previously proposed as an indicator of confounding7) was generally difficult to interpret owing to attenuation bias3, which causes the intercept to rise above 1 with increasing sample size and heritability (Supplementary Fig. 2 and Supplementary Note), the ‘attenuation ratio’—(LDSC intercept – 1)/(mean χ2 – 1)—matched closely between BOLT-LMM and PC-corrected linear regression and was relatively small (Fig. 1c, Supplementary Fig. 2 and Supplementary Table 4). Across 23 traits, we observed similar mean attenuation ratios of 0.078 (standard error (s.e.) 0.006) for PC-corrected linear regression and 0.082 (0.005) for BOLT-LMM, indicating that BOLT-LMM successfully controlled for sample structure (as expected for mixed-model methods)1,2,3. In contrast, uncorrected linear regression produced a mean attenuation ratio of 0.104 (0.012), indicating confounding (Supplementary Fig. 2 and Supplementary Table 4). Similarly, PC-corrected linear regression on all European samples exhibited slightly elevated attenuation ratios (mean 0.085, s.e. 0.006; binomial P = 0.01 versus attenuation on unrelated British samples), indicating slight confounding due to relatedness (Supplementary Table 4), while still achieving lower power than BOLT-LMM (Supplementary Table 2). We note that attenuation ratios are broadly smaller under the LDSC baselineLD model8, which incorporates functional and linkage disequilibrium (LD)-related genome annotations, than under the original LDSC model (Supplementary Table 5), consistent with better model fit.

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Fig. 1: Power, calibration and speed of BOLT-LMM v2.3 in UK Biobank analyses.
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Acknowledgements

We are grateful to H. Finucane and Y. Reshef for helpful discussions. This research was conducted using the UK Biobank Resource under application 10438 and was supported by US National Institutes of Health grants R01 HG006399, R01 GM105857 and R01 MH107649 (A.L.P.), a Burroughs Wellcome Fund Career Award at the Scientific Interfaces and the Next Generation Fund at the Broad Institute of MIT and Harvard (P.-R.L.), and a Boehringer Ingelheim Fonds fellowship (A.P.S.). Computational analyses were performed on the Orchestra High-Performance Compute Cluster at Harvard Medical School, which is partially supported by grant NCRR 1S10RR028832-01.

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Authors and Affiliations

  1. Division of Genetics, Department of Medicine, Brigham and Women’s Hospital and Harvard Medical School, Boston, MA, USA

    Po-Ru Loh

  2. Program in Medical and Population Genetics, Broad Institute of MIT and Harvard, Cambridge, MA, USA

    Po-Ru Loh, Steven Gazal, Armin P. Schoech & Alkes L. Price

  3. Bioinformatics Interdepartmental Program, University of California, Los Angeles, Los Angeles, CA, USA

    Gleb Kichaev

  4. Department of Epidemiology, Harvard T.H. Chan School of Public Health, Boston, MA, USA

    Steven Gazal, Armin P. Schoech & Alkes L. Price

  5. Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, MA, USA

    Armin P. Schoech & Alkes L. Price

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  1. Po-Ru Loh
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  2. Gleb Kichaev
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  3. Steven Gazal
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  4. Armin P. Schoech
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  5. Alkes L. Price
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Contributions

P.-R.L. and A.L.P. designed the study. P.-R.L., G.K., S.G. and A.P.S. performed analyses. All authors wrote the manuscript.

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Correspondence to Po-Ru Loh or Alkes L. Price.

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The authors declare no competing interests.

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Supplementary Figures 1 and 2, Supplementary Tables 1–9 and Supplementary Note

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Loh, PR., Kichaev, G., Gazal, S. et al. Mixed-model association for biobank-scale datasets. Nat Genet 50, 906–908 (2018). https://doi.org/10.1038/s41588-018-0144-6

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