Model selection and parameter estimation in tumor growth models using approximate Bayesian computation-ABC
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.
KeywordsModel selection Parameter estimation Approximate Bayesian computation and tumor growth
Mathematics Subject Classification34F05 35K57 60G20 62J02 62M86 92B05
This work has been mainly financed by FAPERJ, CAPES and CNPq. The scholarship provided by FAPEAM for Costa, J.M.J. is greatly appreciated.
- Beaumont MA, Zhang W, Balding DJ (2002) Approximate bayesian computation in population genetics. Genetics 162(4):2025–2035Google Scholar
- Burton AC (1966) Rate of growth of solid tumours as a problem of diffusion. Growth 30(2):157–176Google Scholar
- Costa JMC (2015b) Problema de estimativa de estado e de estimativa simultânea de modelos e paarâmetros em crescimento de tumores. Tese de Doutorado. Universidade Federal do Rio de Janeiro, Rio de Janeiro-UFRJGoogle Scholar
- Del Moral P, Jasra A (2007) Sequential monte carlo for bayesian computatio. Bayesian Stat 8:1–34Google Scholar
- Gatenby RA (1991) Population ecology issues in tumor growth. Cancer Res 51(10):2542–2547Google Scholar
- Gatenby RA, Gawlinski ET (1996) A reaction-diffusion model of cancer invasion. Cancer Res 56(24):5745–5753Google Scholar
- MedicinaNet (2015) www.medicinanet.com.br/pesquisas/doxorrubicina.html. Accessed 2 August 2015
- Rodrigues DS (2011) Modelagem matemtica em cancer: dinmica angiognica e quimioterapia anti-neoplsica. Dissertao de Mestrado, Universidade Estadual Paulista Jlio de Mesquita Filho, UNESP, BrasilGoogle Scholar
- Schabel FM (1969) The use of tumor growth kinetics in planning curative chemotherapy of advanced solid tumors. Cancer Res 29(12):2384–2389Google Scholar
- Toni T, Stumpf MPH (2010a) Parameter inference and model selection in signaling pathway models. In: Fenyö D (ed) Computational biology, Methods in molecular biology (methods and protocols), vol 673. Humana Press, Totowa, NJ, pp 283–295Google Scholar