IDEAS home Printed from https://ideas.repec.org/a/plo/pcbi00/1008248.html
   My bibliography  Save this article

Testing structural identifiability by a simple scaling method

Author

Listed:
  • Mario Castro
  • Rob J de Boer

Abstract

Successful mathematical modeling of biological processes relies on the expertise of the modeler to capture the essential mechanisms in the process at hand and on the ability to extract useful information from empirical data. A model is said to be structurally unidentifiable, if different quantitative sets of parameters provide the same observable outcome. This is typical (but not exclusive) of partially observed problems in which only a few variables can be experimentally measured. Most of the available methods to test the structural identifiability of a model are either too complex mathematically for the general practitioner to be applied, or require involved calculations or numerical computation for complex non-linear models. In this work, we present a new analytical method to test structural identifiability of models based on ordinary differential equations, based on the invariance of the equations under the scaling transformation of its parameters. The method is based on rigorous mathematical results but it is easy and quick to apply, even to test the identifiability of sophisticated highly non-linear models. We illustrate our method by example and compare its performance with other existing methods in the literature.Author summary: Theoretical Biology is a useful approach to explain, generate hypotheses, or discriminate among competing theories. A well-formulated model has to be complex enough to capture the relevant mechanisms of the problem, and simple enough to be fitted to data. Structural identifiability tests aim to recognize, in advance, if the structure of the model allows parameter fitting even with unlimited high-quality data. Available methods require advanced mathematical skills, or are too costly for high-dimensional non-linear models. We propose an analytical method based on scale invariance of the equations. It provides definite answers to the structural identifiability problem while being simple enough to be performed in a few lines of calculations without any computational aid. It favorably compares with other existing methods.

Suggested Citation

  • Mario Castro & Rob J de Boer, 2020. "Testing structural identifiability by a simple scaling method," PLOS Computational Biology, Public Library of Science, vol. 16(11), pages 1-15, November.
  • Handle: RePEc:plo:pcbi00:1008248
    DOI: 10.1371/journal.pcbi.1008248
    as

    Download full text from publisher

    File URL: https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1008248
    Download Restriction: no

    File URL: https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1008248&type=printable
    Download Restriction: no

    File URL: https://libkey.io/10.1371/journal.pcbi.1008248?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. Alejandro F Villaverde & Antonio Barreiro & Antonis Papachristodoulou, 2016. "Structural Identifiability of Dynamic Systems Biology Models," PLOS Computational Biology, Public Library of Science, vol. 12(10), pages 1-22, October.
    2. Andrew F Brouwer & Rafael Meza & Marisa C Eisenberg, 2017. "Parameter estimation for multistage clonal expansion models from cancer incidence data: A practical identifiability analysis," PLOS Computational Biology, Public Library of Science, vol. 13(3), pages 1-18, March.
    3. Walter, Eric & Pronzato, Luc, 1996. "On the identifiability and distinguishability of nonlinear parametric models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 42(2), pages 125-134.
    4. Tim Maiwald & Helge Hass & Bernhard Steiert & Joep Vanlier & Raphael Engesser & Andreas Raue & Friederike Kipkeew & Hans H Bock & Daniel Kaschek & Clemens Kreutz & Jens Timmer, 2016. "Driving the Model to Its Limit: Profile Likelihood Based Model Reduction," PLOS ONE, Public Library of Science, vol. 11(9), pages 1-18, September.
    5. Nicolette Meshkat & Christine Er-zhen Kuo & Joseph DiStefano III, 2014. "On Finding and Using Identifiable Parameter Combinations in Nonlinear Dynamic Systems Biology Models and COMBOS: A Novel Web Implementation," PLOS ONE, Public Library of Science, vol. 9(10), pages 1-14, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Benjamin B. Policicchio & Erwing Fabian Cardozo-Ojeda & Cuiling Xu & Dongzhu Ma & Tianyu He & Kevin D. Raehtz & Ranjit Sivanandham & Adam J. Kleinman & Alan S. Perelson & Cristian Apetrei & Ivona Pand, 2023. "CD8+ T cells control SIV infection using both cytolytic effects and non-cytolytic suppression of virus production," Nature Communications, Nature, vol. 14(1), pages 1-13, December.

    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. Alejandro F. Villaverde, 2019. "Observability and Structural Identifiability of Nonlinear Biological Systems," Complexity, Hindawi, vol. 2019, pages 1-12, January.
    2. Kocięcki, Andrzej & Kolasa, Marcin, 2023. "A solution to the global identification problem in DSGE models," Journal of Econometrics, Elsevier, vol. 236(2).
    3. Jane Teergele & Kourosh Danai, 2015. "Selection of outputs for distributed parameter systems by identifiability analysis in the time-scale domain," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(16), pages 2939-2954, December.
    4. Song Bo & Soumya R. Sahoo & Xunyuan Yin & Jinfeng Liu & Sirish L. Shah, 2020. "Parameter and State Estimation of One-Dimensional Infiltration Processes: A Simultaneous Approach," Mathematics, MDPI, vol. 8(1), pages 1-22, January.
    5. Masud M A & Md Hamidul Islam & Khondaker A. Mamun & Byul Nim Kim & Sangil Kim, 2020. "COVID-19 Transmission: Bangladesh Perspective," Mathematics, MDPI, vol. 8(10), pages 1-19, October.
    6. Nerea Martínez & Alejandro F. Villaverde, 2020. "Nonlinear Observability Algorithms with Known and Unknown Inputs: Analysis and Implementation," Mathematics, MDPI, vol. 8(11), pages 1-27, October.
    7. Agus Hartoyo & Peter J Cadusch & David T J Liley & Damien G Hicks, 2019. "Parameter estimation and identifiability in a neural population model for electro-cortical activity," PLOS Computational Biology, Public Library of Science, vol. 15(5), pages 1-27, May.
    8. Daniel Durstewitz, 2017. "A state space approach for piecewise-linear recurrent neural networks for identifying computational dynamics from neural measurements," PLOS Computational Biology, Public Library of Science, vol. 13(6), pages 1-33, June.
    9. Philip J. Schmidt & Monica B. Emelko & Mary E. Thompson, 2020. "Recognizing Structural Nonidentifiability: When Experiments Do Not Provide Information About Important Parameters and Misleading Models Can Still Have Great Fit," Risk Analysis, John Wiley & Sons, vol. 40(2), pages 352-369, February.
    10. Matthew S. Shotwell & Richard A. Gray, 2016. "Estimability Analysis and Optimal Design in Dynamic Multi-scale Models of Cardiac Electrophysiology," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(2), pages 261-276, June.
    11. Alejandro F Villaverde & Antonio Barreiro & Antonis Papachristodoulou, 2016. "Structural Identifiability of Dynamic Systems Biology Models," PLOS Computational Biology, Public Library of Science, vol. 12(10), pages 1-22, October.
    12. Shoya Iwanami & Kosaku Kitagawa & Hirofumi Ohashi & Yusuke Asai & Kaho Shionoya & Wakana Saso & Kazane Nishioka & Hisashi Inaba & Shinji Nakaoka & Takaji Wakita & Odo Diekmann & Shingo Iwami & Koichi , 2020. "Should a viral genome stay in the host cell or leave? A quantitative dynamics study of how hepatitis C virus deals with this dilemma," PLOS Biology, Public Library of Science, vol. 18(7), pages 1-17, July.
    13. Maria Pia Saccomani & Karl Thomaseth, 2018. "The Union between Structural and Practical Identifiability Makes Strength in Reducing Oncological Model Complexity: A Case Study," Complexity, Hindawi, vol. 2018, pages 1-10, February.
    14. Xiaojun Liu & Arnaud Coutu & Stéphane Mottelet & André Pauss & Thierry Ribeiro, 2023. "Overview of Numerical Simulation of Solid-State Anaerobic Digestion Considering Hydrodynamic Behaviors, Phenomena of Transfer, Biochemical Kinetics and Statistical Approaches," Energies, MDPI, vol. 16(3), pages 1-31, January.
    15. Szép, Teodóra & van Cranenburgh, Sander & Chorus, Caspar G., 2022. "Decision Field Theory: Equivalence with probit models and guidance for identifiability," Journal of choice modelling, Elsevier, vol. 45(C).
    16. Sanjana Gupta & Robin E C Lee & James R Faeder, 2020. "Parallel Tempering with Lasso for model reduction in systems biology," PLOS Computational Biology, Public Library of Science, vol. 16(3), pages 1-22, March.

    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:pcbi00:1008248. 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: ploscompbiol (email available below). General contact details of provider: https://journals.plos.org/ploscompbiol/ .

    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.