Model selection and parameter estimation in tumor growth models using approximate Bayesian computation-ABC
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Model selection and parameter estimation in tumor growth models using approximate Bayesian computation-ABC José Mir Justino da Costa1 · Helcio Rangel Barreto Orlande2 · Wellington Betencurte da Silva3
Received: 14 September 2016 / Revised: 1 July 2017 / Accepted: 4 July 2017 © SBMAC - Sociedade Brasileira de Matemática Aplicada de Computacional 2017
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
Communicated by Ruben Spies.
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Helcio Rangel Barreto Orlande [email protected] José Mir Justino da Costa [email protected] Wellington Betencurte da Silva [email protected]
1
Department of Statistics, Federal University of Amazonas-UFAM, Manaus, Brazil
2
Department of Mechanical Engineering, Federal University of Rio de Janeiro, UFRJ Cidade Universitária, Rio de Janeiro, RJ 21941-972, Brazil
3
Laboratório de Modelagem e Otimização de Processos, Federal University of Esprito Santo-UFES, Alegre, Brazil
123
J. M. J. da Costa et al.
Mathematics Subject Classification 34F05 · 35K57 · 60G20 · 62J02 · 62M86 · 92B05
1 Introduction The World Health Organization (WHO) estimates 27 million cases of cancer, with approximately 17 million deaths, in 2030. In Brazil, according to the National Cancer Institute (INCA), the expectation for 2016 is of 600,000 new cases. In fact, cancer is a global public health problem, which substantially demands human and financial resources. Mathematical modeling of tumor growth plays an important role for diagnostic and treatment planning of different kinds of cancer. Due to the complexity of cancer and its more than 100 different forms, correctly modeling associated physical and chemical phenomena, and the interaction of cells with chemotherapeutic agents and to predict future states of the disease are difficult tasks. Mathemat
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