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A Constrained Generalized Functional Linear Model for Multi-Loci Genetic Mapping

Author

Listed:
  • Jiayu Huang

    (Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11790, USA)

  • Jie Yang

    (Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11790, USA)

  • Zhangrong Gu

    (Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11790, USA)

  • Wei Zhu

    (Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11790, USA)

  • Song Wu

    (Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11790, USA)

Abstract

In genome-wide association studies (GWAS), efficient incorporation of linkage disequilibria (LD) among densely typed genetic variants into association analysis is a critical yet challenging problem. Functional linear models (FLM), which impose a smoothing structure on the coefficients of correlated covariates, are advantageous in genetic mapping of multiple variants with high LD. Here we propose a novel constrained generalized FLM (cGFLM) framework to perform simultaneous association tests on a block of linked SNPs with various trait types, including continuous, binary and zero-inflated count phenotypes. The new cGFLM applies a set of inequality constraints on the FLM to ensure model identifiability under different genetic codings. The method is implemented via B-splines, and an augmented Lagrangian algorithm is employed for parameter estimation. For hypotheses testing, a test statistic that accounts for the model constraints was derived, following a mixture of chi-square distributions. Simulation results show that cGFLM is effective in identifying causal loci and gene clusters compared to several competing methods based on single markers and SKAT-C. We applied the proposed method to analyze a candidate gene-based COGEND study and a large-scale GWAS data on dental caries risk.

Suggested Citation

  • Jiayu Huang & Jie Yang & Zhangrong Gu & Wei Zhu & Song Wu, 2021. "A Constrained Generalized Functional Linear Model for Multi-Loci Genetic Mapping," Stats, MDPI, vol. 4(3), pages 1-28, June.
    • Handle: RePEc:gam:jstats:v:4:y:2021:i:3:p:33-577:d:582512
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    References listed on IDEAS

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    1. Martin Ridout & John Hinde & Clarice G. B. Demétrio, 2001. "A Score Test for Testing a Zero‐Inflated Poisson Regression Model Against Zero‐Inflated Negative Binomial Alternatives," Biometrics, The International Biometric Society, vol. 57(1), pages 219-223, March.
    2. Nadezhda M Belonogova & Gulnara R Svishcheva & James F Wilson & Harry Campbell & Tatiana I Axenovich, 2018. "Weighted functional linear regression models for gene-based association analysis," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-14, January.
    3. Xinsheng Liu, 2007. "Likelihood Ratio Test for and Against Nonlinear Inequality Constraints," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(1), pages 93-108, February.
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