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Computational and Applied Mathematics

, Volume 37, Issue 3, pp 2795–2815 | Cite as

Model selection and parameter estimation in tumor growth models using approximate Bayesian computation-ABC

  • José Mir Justino da Costa
  • Helcio Rangel Barreto Orlande
  • Wellington Betencurte da Silva
Article

Abstract

Cancer is one of the most fatal diseases in the world. Governments and researchers from various areas have continuously concentrated efforts to better understand the disease and propose diagnostic and treatment techniques. The use of mathematical models of tumor growth is of great importance for the development of such techniques. Due to the variety of models nowadays available in the literature, the problems of model selection and parameter estimation come into picture, aiming at suitably predicting the patient’s status of the disease. As the available data on dependent variables of existing models might not justify the use of common likelihood functions, approximate Bayesian computation (ABC) becomes a very attractive tool for model selection and model calibration (parameter estimation) in tumor growth models. In the present study, a Monte Carlo approximate Bayesian computation (ABC) algorithm is applied to select among competing models of tumor growth, with and without chemotherapy treatment. Simulated measurements are used in this work. The results obtained show that the algorithm correctly selects the model and estimates the parameters used to generate the simulated measurements.

Keywords

Model selection Parameter estimation Approximate Bayesian computation and tumor growth 

Mathematics Subject Classification

34F05 35K57 60G20 62J02 62M86 92B05 

Notes

Acknowledgements

This work has been mainly financed by FAPERJ, CAPES and CNPq. The scholarship provided by FAPEAM for Costa, J.M.J. is greatly appreciated.

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  • José Mir Justino da Costa
    • 1
  • Helcio Rangel Barreto Orlande
    • 2
  • Wellington Betencurte da Silva
    • 3
  1. 1.Department of StatisticsFederal University of Amazonas-UFAMManausBrazil
  2. 2.Department of Mechanical EngineeringFederal University of Rio de Janeiro, UFRJ Cidade UniversitáriaRio de JaneiroBrazil
  3. 3.Laboratório de Modelagem e Otimização de ProcessosFederal University of Esprito Santo-UFESAlegreBrazil

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