A Kernel of Truth. Statistical Advances in Polygenic Variance Component Models for Complex Human Pedigrees.

John Blangero, Vincent P. Diego, Thomas D. Dyer, Marcio Almeida, Juan Peralta, Jack W. Kent, Jeff T. Williams, Laura Almasy, Harald H.H. GÖring

    Research output: Chapter in Book/Report/Conference proceedingChapter

    44 Scopus citations

    Abstract

    Statistical genetic analysis of quantitative traits in large pedigrees is a formidable computational task due to the necessity of taking the nonindependence among relatives into account. With the growing awareness that rare sequence variants may be important in human quantitative variation, heritability and association study designs involving large pedigrees will increase in frequency due to the greater chance of observing multiple copies of rare variants among related individuals. Therefore, it is important to have statistical genetic test procedures that utilize all available information for extracting evidence regarding genetic association. Optimal testing for marker/phenotype association involves the exact calculation of the likelihood ratio statistic which requires the repeated inversion of potentially large matrices. In a whole genome sequence association context, such computation may be prohibitive. Toward this end, we have developed a rapid and efficient eigensimplification of the likelihood that makes analysis of family data commensurate with the analysis of a comparable sample of unrelated individuals. Our theoretical results which are based on a spectral representation of the likelihood yield simple exact expressions for the expected likelihood ratio test statistic (ELRT) for pedigrees of arbitrary size and complexity. For heritability, the ELRT is-∑ln1+h2λgi-1,where h2 and λgi are, respectively, the heritability and eigenvalues of the pedigree-derived genetic relationship kernel (GRK). For association analysis of sequence variants, the ELRT is given byELRThq2>0:unrelateds-ELRTht2>0:pedigrees-ELRThr2>0:pedigrees,where ht 2, hq 2, and hr 2 are the total, quantitative trait nucleotide, and residual heritabilities, respectively. Using these results, fast and accurate analytical power analyses are possible, eliminating the need for computer simulation. Additional benefits of eigensimplification include a simple method for calculation of the exact distribution of the ELRT under the null hypothesis which turns out to differ from that expected under the usual asymptotic theory. Further, when combined with the use of empirical GRKs-estimated over a large number of genetic markers-our theory reveals potential problems associated with nonpositive semidefinite kernels. These procedures are being added to our general statistical genetic computer package, SOLAR.

    Original languageEnglish (US)
    Title of host publicationAdvances in Genetics
    PublisherAcademic Press Inc.
    Pages1-31
    Number of pages31
    DOIs
    StatePublished - 2013

    Publication series

    NameAdvances in Genetics
    Volume81
    ISSN (Print)0065-2660

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    Keywords

    • Association analysis
    • Eigensimplification
    • Eigenvalues
    • Heritability
    • Human pedigrees
    • Power analysis
    • Variance component models

    ASJC Scopus subject areas

    • Genetics

    Cite this

    Blangero, J., Diego, V. P., Dyer, T. D., Almeida, M., Peralta, J., Kent, J. W., Williams, J. T., Almasy, L., & GÖring, H. H. H. (2013). A Kernel of Truth. Statistical Advances in Polygenic Variance Component Models for Complex Human Pedigrees. In Advances in Genetics (pp. 1-31). (Advances in Genetics; Vol. 81). Academic Press Inc.. https://doi.org/10.1016/B978-0-12-407677-8.00001-4