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Locating Multiple Interacting Quantitative Trait Loci with the Zero-Inflated Generalized Poisson Regression

Author

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  • Erhardt Vinzenz

    (Technische Universität München)

  • Bogdan Malgorzata

    (Wroclaw University of Technology and Purdue University)

  • Czado Claudia

    (Technische Universität München)

Abstract

We consider the problem of locating multiple interacting quantitative trait loci (QTL) influencing traits measured in counts. In many applications the distribution of the count variable has a spike at zero. Zero-inflated generalized Poisson regression (ZIGPR) allows for an additional probability mass at zero and hence an improvement in the detection of significant loci. Classical model selection criteria often overestimate the QTL number. Therefore, modified versions of the Bayesian Information Criterion (mBIC and EBIC) were successfully used for QTL mapping. We apply these criteria based on ZIGPR as well as simpler models. An extensive simulation study shows their good power detecting QTL while controlling the false discovery rate. We illustrate how the inability of the Poisson distribution to account for over-dispersion leads to an overestimation of the QTL number and hence strongly discourages its application for identifying factors influencing count data. The proposed method is used to analyze the mice gallstone data of Lyons et al. (2003). Our results suggest the existence of a novel QTL on chromosome 4 interacting with another QTL previously identified on chromosome 5. We provide the corresponding code in R.

Suggested Citation

  • Erhardt Vinzenz & Bogdan Malgorzata & Czado Claudia, 2010. "Locating Multiple Interacting Quantitative Trait Loci with the Zero-Inflated Generalized Poisson Regression," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-27, June.
    • Handle: RePEc:bpj:sagmbi:v:9:y:2010:i:1:n:26
    DOI: 10.2202/1544-6115.1545
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    References listed on IDEAS

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    1. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    2. Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
    3. Baierl, Andreas & Futschik, Andreas & Bogdan, Malgorzata & Biecek, Przemyslaw, 2007. "Locating multiple interacting quantitative trait loci using robust model selection," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6423-6434, August.
    4. Zehua Chen & Jianbin Liu, 2009. "Mixture Generalized Linear Models for Multiple Interval Mapping of Quantitative Trait Loci in Experimental Crosses," Biometrics, The International Biometric Society, vol. 65(2), pages 470-477, June.
    5. Karl W. Broman & Terence P. Speed, 2002. "A model selection approach for the identification of quantitative trait loci in experimental crosses," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 641-656, October.
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    2. Zak-Szatkowska, Malgorzata & Bogdan, Malgorzata, 2011. "Modified versions of the Bayesian Information Criterion for sparse Generalized Linear Models," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2908-2924, November.

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