Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Statistical Applications in Genetics and Molecular Biology

Editor-in-Chief: Sanguinetti, Guido

IMPACT FACTOR 2018: 0.536
5-year IMPACT FACTOR: 0.764

CiteScore 2018: 0.49

SCImago Journal Rank (SJR) 2018: 0.316
Source Normalized Impact per Paper (SNIP) 2018: 0.342

Mathematical Citation Quotient (MCQ) 2018: 0.02

See all formats and pricing
More options …
Volume 16, Issue 1


Volume 10 (2011)

Volume 9 (2010)

Volume 6 (2007)

Volume 5 (2006)

Volume 4 (2005)

Volume 2 (2003)

Volume 1 (2002)

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

Pei-Fang Su / Yu-Lin Mau / Yan Guo / Chung-I Li / Qi Liu / John D. Boice / Yu Shyr
Published Online: 2017-03-01 | DOI: https://doi.org/10.1515/sagmb-2016-0040


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.

This article offers supplementary material which is provided at the end of the article.

Keywords: DNA dataset; EM algorithm; offset; paired count data; sequence quality


  • Andrews, R. M., I. Kubacka, P. F. Chinnery, R. N. Lightowlers, D. M. Turnbull and N. Howell (1999): “Reanalysis and revision of the Cambridge reference sequence for human mitochondrial DNA,” Nat. Genet., 23, 147.CrossrefGoogle Scholar

  • Bermúdez, L. and D. Karlis (2012): “A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking,” Comput. Stat. Data Anal., 56, 3988–3999.Google Scholar

  • Famoye, F. (2010): “On the bivariate negative binomial regression model,” J. Appl. Stat., 37, 969–981.Google Scholar

  • Guo, Y., Q. Cai, D. Samuels, F. Ye, J. Long, C. Li, J. Winther, E. J. Tawn, M. Stovall, P. Lähteenmäki, N. Malila, S. Levy, C. Shaffer, Y. Shyr, X. Shu, and J. Boice (2012): “The use of next generation sequencing technology to study the effect of radiation therapy on mitochondrial DNA mutation,” Mutat. Res., 744, 154–160.Google Scholar

  • Johnson, N., S. Kotz, and N. Balakrishnan (1997): Discrete multivariate distributions, Wiley, New York.Google Scholar

  • Jung, R. and R. Winkelmann (1993): “Two aspects of labor mobility: a bivariate Poisson regression approach,” Empir. Econ., 18, 543–556.Google Scholar

  • Karlis, D. (2003): “An em algorithm for multivariate Poisson distribution and related models,” J. Appl. Stat., 30, 63–77.Google Scholar

  • Karlis, D. and L. Meligkotsidou (2005): “Multivariate Poisson regression with covariance structure,” Stat. Comput., 15, 255–265.Google Scholar

  • Karlis, D. and I. Ntzoufras (2005): “Bivariate Poisson and diagonal inflated bivariate Poisson regression models in r,” J. Stat. Softw., 14, 1–36.Google Scholar

  • Karlis, D. and L. Ntzoufras (2003): “Analysis of sports data by using bivariate Poisson models,” Statistician, 52, 381–393.Google Scholar

  • Kawamura, K. (1985): “A note on the recurrent relations for the bivariate Poisson distribution,” Kodai Math. J., 8, 70–78.Google Scholar

  • Kocherlakota, S. and K. Kocherlakota (2001): “Regression in the bivariate Poisson distribution,” Commun. Stat. Theory Methods, 30, 815–825.Google Scholar

  • McLachlan, G. and T. Krishnan (1997): The EM algorithm and extensions, Wiley, New York.Google Scholar

  • Pakendorf, B. and M. Stoneking (2005): “Mitochondrial DNA and human evolution,” Annu. Rev. Genomics Hum. Genet., 6, 165–183.Google Scholar

  • Robinson, M. and A. Oshlack (2010): “A scaling normalization method for differential pression analysis of RNA-seq data,” Genome Biol., 11, R25.CrossrefGoogle Scholar

  • Srivastava, S. and L. Chen (2010): “A two-parameter generalized Poisson model to improve the analysis of RNA-seq data,” Nucleic Acids Res., 38, e170.CrossrefGoogle Scholar

  • Verma, M. and D. Kumar (2007): “Application of mitochondrial genome information in cancer epidemiology,” Clin. Chim. Acta, 383, 41–50.Google Scholar

  • Wang, L., Z. Feng, X. Wang, X. Wang, and X. Zhang (2010): “Degseq: an R package for identifying differentially expressed genes from RNA-seq data,” Bioinformatics, 26, 136–138.Google Scholar

About the article

Published Online: 2017-03-01

Published in Print: 2017-03-01

Citation Information: Statistical Applications in Genetics and Molecular Biology, Volume 16, Issue 1, Pages 47–58, ISSN (Online) 1544-6115, ISSN (Print) 2194-6302, DOI: https://doi.org/10.1515/sagmb-2016-0040.

Export Citation

©2017 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Supplementary Article Materials

Comments (0)

Please log in or register to comment.
Log in