IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0167568.html
   My bibliography  Save this article

Analysis of Practical Identifiability of a Viral Infection Model

Author

Listed:
  • Van Kinh Nguyen
  • Frank Klawonn
  • Rafael Mikolajczyk
  • Esteban A Hernandez-Vargas

Abstract

Mathematical modelling approaches have granted a significant contribution to life sciences and beyond to understand experimental results. However, incomplete and inadequate assessments in parameter estimation practices hamper the parameter reliability, and consequently the insights that ultimately could arise from a mathematical model. To keep the diligent works in modelling biological systems from being mistrusted, potential sources of error must be acknowledged. Employing a popular mathematical model in viral infection research, existing means and practices in parameter estimation are exemplified. Numerical results show that poor experimental data is a main source that can lead to erroneous parameter estimates despite the use of innovative parameter estimation algorithms. Arbitrary choices of initial conditions as well as data asynchrony distort the parameter estimates but are often overlooked in modelling studies. This work stresses the existence of several sources of error buried in reports of modelling biological systems, voicing the need for assessing the sources of error, consolidating efforts in solving the immediate difficulties, and possibly reconsidering the use of mathematical modelling to quantify experimental data.

Suggested Citation

  • Van Kinh Nguyen & Frank Klawonn & Rafael Mikolajczyk & Esteban A Hernandez-Vargas, 2016. "Analysis of Practical Identifiability of a Viral Infection Model," PLOS ONE, Public Library of Science, vol. 11(12), pages 1-16, December.
  • Handle: RePEc:plo:pone00:0167568
    DOI: 10.1371/journal.pone.0167568
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0167568
    Download Restriction: no

    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0167568&type=printable
    Download Restriction: no

    File URL: https://libkey.io/10.1371/journal.pone.0167568?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Hana M Dobrovolny & Micaela B Reddy & Mohamed A Kamal & Craig R Rayner & Catherine A A Beauchemin, 2013. "Assessing Mathematical Models of Influenza Infections Using Features of the Immune Response," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-20, February.
    2. Mullen, Katharine M. & Ardia, David & Gil, David L. & Windover, Donald & Cline, James, 2011. "DEoptim: An R Package for Global Optimization by Differential Evolution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i06).
    3. Simon N. Wood, 2011. "Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 3-36, January.
    4. Amber M Smith & Frederick R Adler & Julie L McAuley & Ryan N Gutenkunst & Ruy M Ribeiro & Jonathan A McCullers & Alan S Perelson, 2011. "Effect of 1918 PB1-F2 Expression on Influenza A Virus Infection Kinetics," PLOS Computational Biology, Public Library of Science, vol. 7(2), pages 1-12, February.
    5. Ma, Shuangge & Kosorok, Michael R., 2005. "Robust semiparametric M-estimation and the weighted bootstrap," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 190-217, September.
    6. Benjamin P Holder & Philippe Simon & Laura E Liao & Yacine Abed & Xavier Bouhy & Catherine A A Beauchemin & Guy Boivin, 2011. "Assessing the In Vitro Fitness of an Oseltamivir-Resistant Seasonal A/H1N1 Influenza Strain Using a Mathematical Model," PLOS ONE, Public Library of Science, vol. 6(3), pages 1-11, March.
    7. Liang, Hua & Wu, Hulin, 2008. "Parameter Estimation for Differential Equation Models Using a Framework of Measurement Error in Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1570-1583.
    8. Ryan N Gutenkunst & Joshua J Waterfall & Fergal P Casey & Kevin S Brown & Christopher R Myers & James P Sethna, 2007. "Universally Sloppy Parameter Sensitivities in Systems Biology Models," PLOS Computational Biology, Public Library of Science, vol. 3(10), pages 1-8, October.
    9. J. O. Ramsay & G. Hooker & D. Campbell & J. Cao, 2007. "Parameter estimation for differential equations: a generalized smoothing approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 741-796, November.
    10. Mark Girolami & Ben Calderhead, 2011. "Riemann manifold Langevin and Hamiltonian Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(2), pages 123-214, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Golchi, Shirin & Campbell, David A., 2016. "Sequentially Constrained Monte Carlo," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 98-113.
    2. Hanwen Huang & Andreas Handel & Xiao Song, 2020. "A Bayesian approach to estimate parameters of ordinary differential equation," Computational Statistics, Springer, vol. 35(3), pages 1481-1499, September.
    3. E. Zanini & E. Eastoe & M. J. Jones & D. Randell & P. Jonathan, 2020. "Flexible covariate representations for extremes," Environmetrics, John Wiley & Sons, Ltd., vol. 31(5), August.
    4. Gianluca Frasso & Jonathan Jaeger & Philippe Lambert, 2016. "Parameter estimation and inference in dynamic systems described by linear partial differential equations," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(3), pages 259-287, July.
    5. Mu Niu & Joe Wandy & Rónán Daly & Simon Rogers & Dirk Husmeier, 2021. "R package for statistical inference in dynamical systems using kernel based gradient matching: KGode," Computational Statistics, Springer, vol. 36(1), pages 715-747, March.
    6. Hulin Wu & Hongqi Xue & Arun Kumar, 2012. "Numerical Discretization-Based Estimation Methods for Ordinary Differential Equation Models via Penalized Spline Smoothing with Applications in Biomedical Research," Biometrics, The International Biometric Society, vol. 68(2), pages 344-352, June.
    7. Shizhe Chen & Ali Shojaie & Daniela M. Witten, 2017. "Network Reconstruction From High-Dimensional Ordinary Differential Equations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1697-1707, October.
    8. Ahn, Kwang Woo & Chan, Kung-Sik, 2014. "Approximate conditional least squares estimation of a nonlinear state-space model via an unscented Kalman filter," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 243-254.
    9. Ying Zhu, 2021. "Phase transitions in nonparametric regressions," Papers 2112.03626, arXiv.org, revised Nov 2023.
    10. Christian A Tiemann & Joep Vanlier & Maaike H Oosterveer & Albert K Groen & Peter A J Hilbers & Natal A W van Riel, 2013. "Parameter Trajectory Analysis to Identify Treatment Effects of Pharmacological Interventions," PLOS Computational Biology, Public Library of Science, vol. 9(8), pages 1-15, August.
    11. Mu Niu & Benn Macdonald & Simon Rogers & Maurizio Filippone & Dirk Husmeier, 2018. "Statistical inference in mechanistic models: time warping for improved gradient matching," Computational Statistics, Springer, vol. 33(2), pages 1091-1123, June.
    12. Bin Zhu & Peter X.-K. Song & Jeremy M.G. Taylor, 2011. "Stochastic Functional Data Analysis: A Diffusion Model-Based Approach," Biometrics, The International Biometric Society, vol. 67(4), pages 1295-1304, December.
    13. González Javier & Vujačić Ivan & Wit Ernst, 2013. "Inferring latent gene regulatory network kinetics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(1), pages 109-127, March.
    14. Tao Lu & Yangxin Huang & Min Wang & Feng Qian, 2014. "A refined parameter estimating approach for HIV dynamic model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(8), pages 1645-1657, August.
    15. Zhou, Jie, 2015. "Detection of influential measurement for ordinary differential equation with application to HIV dynamics," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 324-332.
    16. Carey, M. & Ramsay, J.O., 2021. "Fast stable parameter estimation for linear dynamical systems," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    17. Benham, Tim & Duan, Qibin & Kroese, Dirk P. & Liquet, Benoît, 2017. "CEoptim: Cross-Entropy R Package for Optimization," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i08).
    18. Liu, Baisen & Wang, Liangliang & Nie, Yunlong & Cao, Jiguo, 2019. "Bayesian inference of mixed-effects ordinary differential equations models using heavy-tailed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 233-246.
    19. Nanshan, Muye & Zhang, Nan & Xun, Xiaolei & Cao, Jiguo, 2022. "Dynamical modeling for non-Gaussian data with high-dimensional sparse ordinary differential equations," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    20. Baisen Liu & Liangliang Wang & Yunlong Nie & Jiguo Cao, 2021. "Semiparametric Mixed-Effects Ordinary Differential Equation Models with Heavy-Tailed Distributions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 428-445, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0167568. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.