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Bivariate Poisson models with varying offsets: an application to the paired mitochondrial DNA dataset

Author

Listed:
  • Su Pei-Fang

    (Department of Statistics, National Cheng Kung University, Tainan 70101, Taiwan)

  • Mau Yu-Lin

    (Department of Statistics, National Cheng Kung University, Tainan 70101, Taiwan)

  • Guo Yan

    (Center for Quantitative Sciences, Vanderbilt University, Nashville, TN 37232, USA)

  • Li Chung-I

    (Department of Statistics, National Cheng Kung University, Tainan 70101, Taiwan)

  • Liu Qi

    (Center for Quantitative Sciences, Vanderbilt University, Nashville, TN 37232, USA)

  • Boice John D.

    (National Council on Radiation Protection Measurements, Bethesda, MD 20814, USA)

  • Shyr Yu

    (Center for Quantitative Sciences, Vanderbilt University, Nashville, TN 37232, USA)

Abstract

To assess the effect of chemotherapy on mitochondrial genome mutations in cancer survivors and their offspring, a study sequenced the full mitochondrial genome and determined the mitochondrial DNA heteroplasmic (mtDNA) mutation rate. To build a model for counts of heteroplasmic mutations in mothers and their offspring, bivariate Poisson regression was used to examine the relationship between mutation count and clinical information while accounting for the paired correlation. However, if the sequencing depth is not adequate, a limited fraction of the mtDNA will be available for variant calling. The classical bivariate Poisson regression model treats the offset term as equal within pairs; thus, it cannot be applied directly. In this research, we propose an extended bivariate Poisson regression model that has a more general offset term to adjust the length of the accessible genome for each observation. We evaluate the performance of the proposed method with comprehensive simulations, and the results show that the regression model provides unbiased parameter estimations. The use of the model is also demonstrated using the paired mtDNA dataset.

Suggested Citation

  • Su Pei-Fang & Mau Yu-Lin & Guo Yan & Li Chung-I & Liu Qi & Boice John D. & Shyr Yu, 2017. "Bivariate Poisson models with varying offsets: an application to the paired mitochondrial DNA dataset," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 16(1), pages 47-58, March.
    • Handle: RePEc:bpj:sagmbi:v:16:y:2017:i:1:p:47-58:n:5
    DOI: 10.1515/sagmb-2016-0040
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    References listed on IDEAS

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    1. Dimitris Karlis, 2003. "An EM algorithm for multivariate Poisson distribution and related models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(1), pages 63-77.
    2. Jung, Robert C & Winkelmann, Rainer, 1993. "Two Aspects of Labor Mobility: A Bivariate Poisson Regression Approach," Empirical Economics, Springer, vol. 18(3), pages 543-556.
    3. Felix Famoye, 2010. "On the bivariate negative binomial regression model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(6), pages 969-981.
    4. Bermúdez, Lluís & Karlis, Dimitris, 2012. "A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3988-3999.
    5. Karlis, Dimitris & Ntzoufras, Ioannis, 2005. "Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i10).
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