title: Mixed model with correction for case-control ascertainment increases association power.
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.
authors.affiliation: 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.
authors.forename: Tristan J
authors.initials: TJ
authors.lastname: Hayeck
authors.affiliation: Lung Biology Center, School of Medicine, University of California, San Francisco, San Francisco, CA 94158,USA.
authors.forename: Noah A
authors.initials: NA
authors.lastname: Zaitlen
authors.affiliation: 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.
authors.forename: Po-Ru
authors.initials: PR
authors.lastname: Loh
authors.affiliation: 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.
authors.forename: Bjarni
authors.initials: B
authors.lastname: Vilhjalmsson
authors.affiliation: 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.
authors.forename: Samuela
authors.initials: S
authors.lastname: Pollack
authors.affiliation: 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.
authors.forename: Alexander
authors.initials: A
authors.lastname: Gusev
authors.affiliation: Queensland Brain Institute, University of Queensland, Brisbane, QLD 4072, Australia; Diamantina Institute, University of Queensland, Brisbane, QLD 4072, Australia.
authors.forename: Jian
authors.initials: J
authors.lastname: Yang
authors.affiliation: Queensland Brain Institute, University of Queensland, Brisbane, QLD 4072, Australia.
authors.forename: Guo-Bo
authors.initials: GB
authors.lastname: Chen
authors.affiliation: Faculty of Land and Food Resources, University of Melbourne, Melbourne, VIC 3010, Australia.
authors.forename: Michael E
authors.initials: ME
authors.lastname: Goddard
authors.affiliation: Queensland Brain Institute, University of Queensland, Brisbane, QLD 4072, Australia; Diamantina Institute, University of Queensland, Brisbane, QLD 4072, Australia.
authors.forename: Peter M
authors.initials: PM
authors.lastname: Visscher
authors.affiliation: Program in Medical and Population Genetics, Broad Institute of Harvard and MIT, Cambridge, MA 02142, USA.
authors.forename: Nick
authors.initials: N
authors.lastname: Patterson
authors.affiliation: 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.
authors.forename: Alkes L
authors.initials: AL
authors.lastname: Price
mesh_terms: D016022:Case-Control Studies; D002874:Chromosome Mapping; D003198:Computer Simulation; D056726:Genetic Association Studies; D006801:Humans; D008957:Models, Genetic; D008962:Models, Theoretical; D009103:Multiple Sclerosis / Q000235:genetics / Q000473:pathology; D010641:Phenotype; D020641:Polymorphism, Single Nucleotide; D018401:Sample Size