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Genet Epidemiol. 2019 Mar;43(2):189-206. doi: 10.1002/gepi.22177. Epub 2018 Dec 9.

Linear mixed models for association analysis of quantitative traits with next-generation sequencing data.

Author information

Division of Biostatistics, Department of Preventive Medicine, University of Tennessee Health Science Center, Memphis, Tennessee.
Computational and Statistical Genomics Branch, National Human Genome Research Institute, National Institutes of Health (NIH), Bethesda, Maryland.
Department of Biochemistry and Molecular Biology, School of Basic Medicine, Kunming Medical University, Kunming, Yunnan, China.
Department of Biostatistics, Bioinformatics, and Biomathematics, Georgetown University Medical Center, Washington, District of Columbia.
Department of Human Genetics, David Geffen School of Medicine, University of California, Los Angeles, California.
Department of Biostatistics, Graduate School of Public Health, University of Pittsburgh, Pittsburgh, Pennsylvania.
Department of Human Genetics, Graduate School of Public Health, University of Pittsburgh, Pittsburgh, Pennsylvania.
Department of Genetics, University of Pennsylvania, Philadelphia, Pennsylvania.
Department de Mathematiques et de Statistique, Universite Laval, Quebec, Canada.
Department of Statistics and Actuarial Science, Waterloo, Ontario, Quebec, Canada.
Human Genetics Branch and Genetic Basis of Mood and Anxiety Disorders Section, University of Waterloo, National Institute of Mental Health, NIH, Bethesda, Maryland.
Department of Medicine, Baylor College of Medicine, Houston, Texas.
Human Genetics Center, University of Texas-Houston, Houston, Texas.


We develop linear mixed models (LMMs) and functional linear mixed models (FLMMs) for gene-based tests of association between a quantitative trait and genetic variants on pedigrees. The effects of a major gene are modeled as a fixed effect, the contributions of polygenes are modeled as a random effect, and the correlations of pedigree members are modeled via inbreeding/kinship coefficients. <mml:math xmlns:mml=""><mml:mi>F</mml:mi></mml:math> -statistics and χ 2 likelihood ratio test (LRT) statistics based on the LMMs and FLMMs are constructed to test for association. We show empirically that the <mml:math xmlns:mml=""><mml:mi>F</mml:mi></mml:math> -distributed statistics provide a good control of the type I error rate. The <mml:math xmlns:mml=""><mml:mi>F</mml:mi></mml:math> -test statistics of the LMMs have similar or higher power than the FLMMs, kernel-based famSKAT (family-based sequence kernel association test), and burden test famBT (family-based burden test). The <mml:math xmlns:mml=""><mml:mi>F</mml:mi></mml:math> -statistics of the FLMMs perform well when analyzing a combination of rare and common variants. For small samples, the LRT statistics of the FLMMs control the type I error rate well at the nominal levels <mml:math xmlns:mml=""><mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.01</mml:mn></mml:math> and <mml:math xmlns:mml=""><mml:mn>0.05</mml:mn></mml:math> . For moderate/large samples, the LRT statistics of the FLMMs control the type I error rates well. The LRT statistics of the LMMs can lead to inflated type I error rates. The proposed models are useful in whole genome and whole exome association studies of complex traits.


common variants; complex diseases; functional data analysis; functional linear mixed models; linear mixed models; rare variants

[Available on 2020-03-01]
[Indexed for MEDLINE]

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