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The Union between Structural and Practical Identifiability Makes Strength in Reducing Oncological Model Complexity: A Case Study

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  • Maria Pia Saccomani
  • Karl Thomaseth

Abstract

Mathematical models are increasingly proposed to describe tumor’s dynamic response to treatments with the aims of improving their efficacy. The most widely used are nonlinear ODE models, whose identification is often difficult due to experimental limitations. We focus on the issue of parameter estimation in model-based oncological studies. Given their complexity, many of these models are unidentifiable having an infinite number of parameter solutions. These equivalently describe experimental data but are associated with different dynamic evolution of unmeasurable variables. We propose a joint use of two different identifiability methodologies, structural identifiability and practical identifiability , which are traditionally regarded as disjoint. This new methodology provides the number of parameter solutions, the analytic relations between the unidentifiable parameters useful to reduce model complexity, a ranking between parameters revealing the most reliable estimates, and a way to disentangle the various causes of nonidentifiability. It is implementable by using available differential algebra software and statistical packages. This methodology can constitute a powerful tool for the oncologist to discover the behavior of inaccessible variables of clinical interest and to correctly address the experimental design. A complex model to study “in vivo” antitumor activity of interleukin-21 on tumor eradication in different cancers in mice is illustrated.

Suggested Citation

  • 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.
  • Handle: RePEc:hin:complx:2380650
    DOI: 10.1155/2018/2380650
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    References listed on IDEAS

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    1. Devaraj Jayachandran & Ann E Rundell & Robert E Hannemann & Terry A Vik & Doraiswami Ramkrishna, 2014. "Optimal Chemotherapy for Leukemia: A Model-Based Strategy for Individualized Treatment," PLOS ONE, Public Library of Science, vol. 9(10), pages 1-18, October.
    2. 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.
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    Cited by:

    1. Lam, Nicholas N. & Docherty, Paul D. & Murray, Rua, 2022. "Practical identifiability of parametrised models: A review of benefits and limitations of various approaches," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 202-216.
    2. Alejandro F. Villaverde, 2019. "Observability and Structural Identifiability of Nonlinear Biological Systems," Complexity, Hindawi, vol. 2019, pages 1-12, January.
    3. Hope Murphy & Gabriel McCarthy & Hana M Dobrovolny, 2020. "Understanding the effect of measurement time on drug characterization," PLOS ONE, Public Library of Science, vol. 15(5), pages 1-15, May.

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