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Statistical Inference in Mixed Models and Analysis of Twin and Family Data

Authors

  • Xueqin Wang,

    1. Department of Statistics, School of Mathematics & Computational Science, Sun Yat-Sen University, Guangzhou, 510275, China
    2. State Key Laboratory of Ophthalmology, Zhongshan Ophthalmic Center, Sun Yat-Sen University, Guangzhou, 510080, China
    3. Zhongshan Medical School, Sun Yat-Sen University, Guangzhou, 510080, China
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  • Xiaobo Guo,

    1. Department of Statistics, School of Mathematics & Computational Science, Sun Yat-Sen University, Guangzhou, 510275, China
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  • Mingguang He,

    1. State Key Laboratory of Ophthalmology, Zhongshan Ophthalmic Center, Sun Yat-Sen University, Guangzhou, 510080, China
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  • Heping Zhang

    Corresponding author
    1. Department of Statistics, School of Mathematics & Computational Science, Sun Yat-Sen University, Guangzhou, 510275, China
    2. Department of Epidemiology and Public Health, Yale University School of Medicine, New Haven, Connecticut 06520-8034, U.S.A.
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email: heping.zhang@yale.edu

Abstract

Summary Analysis of data from twin and family studies provides the foundation for studies of disease inheritance. The development of advanced theory and computational software for general linear models has generated considerable interest for using mixed-effect models to analyze twin and family data, as a computationally more convenient and theoretically more sound alternative to the classical structure equation modeling. Despite the long history of twin and family data analysis, some fundamental questions remain unanswered. We addressed two important issues. One is to determine the necessary and sufficient conditions for the identifiability in the mixed-effects models for twin and family data. The other is to derive the asymptotic distribution of the likelihood ratio test, which is novel due to the fact that the standard regularity conditions are not satisfied. We considered a series of specific yet important examples in which we demonstrated how to formulate mixed-effect models to appropriately reflect the data, and our key idea is the use of the Cholesky decomposition. Finally, we applied our method and theory to provide a more precise estimate of the heritability of two data sets than the previously reported estimate.

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