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Am J Hum Genet. 2015 May 7;96(5):720-30. doi: 10.1016/j.ajhg.2015.03.004. Epub 2015 Apr 16.

Mixed model with correction for case-control ascertainment increases association power.

Author information

1
Department of Biostatistics, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA 02115, USA; Program in Medical and Population Genetics, Broad Institute of Harvard and MIT, Cambridge, MA 02142, USA. Electronic address: tjh488@mail.harvard.edu.
2
Lung Biology Center, School of Medicine, University of California, San Francisco, San Francisco, CA 94158,USA.
3
Program in Medical and Population Genetics, Broad Institute of Harvard and MIT, Cambridge, MA 02142, USA; Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA 02115, USA.
4
Queensland Brain Institute, University of Queensland, Brisbane, QLD 4072, Australia; Diamantina Institute, University of Queensland, Brisbane, QLD 4072, Australia.
5
Queensland Brain Institute, University of Queensland, Brisbane, QLD 4072, Australia.
6
Faculty of Land and Food Resources, University of Melbourne, Melbourne, VIC 3010, Australia.
7
Program in Medical and Population Genetics, Broad Institute of Harvard and MIT, Cambridge, MA 02142, USA.
8
Department of Biostatistics, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA 02115, USA; Program in Medical and Population Genetics, Broad Institute of Harvard and MIT, Cambridge, MA 02142, USA; Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA 02115, USA. Electronic address: aprice@hsph.harvard.edu.

Abstract

We introduce a liability-threshold mixed linear model (LTMLM) association statistic for case-control studies and show that it has a well-controlled false-positive rate and more power than existing mixed-model methods for diseases with low prevalence. Existing mixed-model methods suffer a loss in power under case-control ascertainment, but no solution has been proposed. Here, we solve this problem by using a χ(2) score statistic computed from posterior mean liabilities (PMLs) under the liability-threshold model. Each individual's PML is conditional not only on that individual's case-control status but also on every individual's case-control status and the genetic relationship matrix (GRM) obtained from the data. The PMLs are estimated with a multivariate Gibbs sampler; the liability-scale phenotypic covariance matrix is based on the GRM, and a heritability parameter is estimated via Haseman-Elston regression on case-control phenotypes and then transformed to the liability scale. In simulations of unrelated individuals, the LTMLM statistic was correctly calibrated and achieved higher power than existing mixed-model methods for diseases with low prevalence, and the magnitude of the improvement depended on sample size and severity of case-control ascertainment. In a Wellcome Trust Case Control Consortium 2 multiple sclerosis dataset with >10,000 samples, LTMLM was correctly calibrated and attained a 4.3% improvement (p = 0.005) in χ(2) statistics over existing mixed-model methods at 75 known associated SNPs, consistent with simulations. Larger increases in power are expected at larger sample sizes. In conclusion, case-control studies of diseases with low prevalence can achieve power higher than that in existing mixed-model methods.

PMID:
25892111
PMCID:
PMC4570278
DOI:
10.1016/j.ajhg.2015.03.004
[Indexed for MEDLINE]
Free PMC Article

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