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Mathematical Models for the Early Detection and Treatment of Colorectal Cancer

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Abstract

Colorectal cancer is a major cause of death for men and women in the Western world. When the cancer is detected through an awareness of the symptoms by a patient, typically it is at an advanced stage. It is possible to detect cancer at an early stage through screening and the marked differences in survival for early and late stages provide the incentive for the primary prevention or early detection of colorectal cancer. This paper considers mathematical models for colorectal cancer screening together with models for the treatment of patients. Illustrative results demonstrate that detailed attention to the processes involved in diseases, interventions and treatment enable us to combine data and expert knowledge from various sources. Thus a detailed operational model is a very useful tool in helping to make decisions about screening at national and local levels.

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References

  • Office of National Statistics, Cancer Statistics: Registrations (HMSO, London, 2000).

  • National Cancer Statistics (2000), http://cancer.gov/cancerinfo.

  • C.R. Smart, Screening and early diagnosis, Cancer Supplement 70 (1992) 1246–1251.

    CAS  Google Scholar 

  • P.B. Cotton and C.B. Williams, Practical Gastrointestinal Endoscopy third edition (Blackwell Scientic Pulications, 1990).

  • G.D. Dodd, The role of the barium enema in the detection of colonic neoplasms, Cancer, 70 (1992) 1272–1275.

    Google Scholar 

  • Eddy, Common Screening Tests, (American College of Physicians, 1991).

  • A.K. Shahani and D.M. Crease, Towards models of screening for early detection of disease, Advanced Applied Probability 9 (1977) 665–680.

    Google Scholar 

  • V. DeSenna and A.K. Shahani, A simple inspection policy for the detection of failure, European Journal of Operational Research 23 (1986) 222–227.

    Article  MathSciNet  Google Scholar 

  • R.E. Barlow and F. Proschan, Mathematical Theory of Reliability (Wiley, New York, 1965).

    Google Scholar 

  • S.K. Jones, Mathematical Modelling for Early Detection and Treatment of Cancer, PhD Thesis, School of Mathematics, University of Southampton, (1997).

  • R. Davies, K. Cooper, P. Roderick and J. Raftery, The evaluation of disease prevention and treatment using simulation models, European Journal of Operational Research 150 (2003) 53–66.

    Article  Google Scholar 

  • S.C. Brailsford, R. Davies, C.R. Canning and P. Roderick, Evaluating screening policies for the early detection of retinopathy in patients with non-insulin-dependent diabetes, Health Care Management Science 1 (1998) 1–10.

    Article  PubMed  Google Scholar 

  • M.W. Retsky, R. Demicheli, D.E. Swartzendruber, et al., Computer simulation of a breast cancer metastasis model, Breast Cancer Research and Treatment 45 (1997) 193–202.

    Article  CAS  PubMed  Google Scholar 

  • I.T. Vieira, P.R. Harper, A.K. Shahani and V. de Senna, Mother-to-child transmission of HIV: A simulation based approach for the evaluation of intervention strategies, Journal of the Operational Research Society 54 (2003) 713–722.

    Google Scholar 

  • K.D. Tocher, The Art of Simulation (English University Press, London, 1963).

  • P.H. Sugarbaker, L.L. Gunderson and R.E. Wittes, Colorectal Cancer, Chapter 25 in: V.T. DeVita, S. Hellman and S.A. Rosenberg, eds., Cancer: Principles and Practice of Oncology, 2nd Edition (1985).

  • J.A. Nelder and R. Mead, A simplex method for function minimisation, Computer Journal 7 (1965) 308–313.

    Google Scholar 

  • T. Muto, H.J.R. Bussey and B.C. Morson, The evolution of cancer of the colon and rectum, Cancer 36 (1975) 2251–2270.

    CAS  PubMed  Google Scholar 

  • S. Bolin, E. Nilsson and R. Sjödahl, Carcinoma of the colon and rectum—growth rate, Annals of Surgery 198 (1983) 151–158.

    Google Scholar 

  • S.J. Stryker, B.G. Wolff, C.E. Culp, S.D. Libbe, D.M. Ilstrup and R.L. MacCarty, Natural history of untreated colonic polyps, Gastroenterology 93 (1987) 1009–1013.

    CAS  PubMed  Google Scholar 

  • J. Austoker, Screening for colorectal cancer, British Medical Journal 304 (1994) 382–386.

    Google Scholar 

  • Office of Population Censuses and Surveys, 1992 Mortality Statistics: General. Series DH1, 27 (HMSO, London, 1994).

  • D.K. Whynes, A.R. Walker and J.D. Hardcastle, Effect of subject age on costs of screening for colorectal cancer, Journal of Epidemiology and Community Health 46 (1992) 577–581.

    CAS  PubMed  Google Scholar 

  • L. Mountney, H. Sanderson and J. Harris, in: Colorectal Cancer, Chapter 7, Health Care Assessment, 1, ed. A. Stevens, J. Raftery and Radcliffe (Medical Press Ltd., 1994).

  • W.L. England, J.J. Halls and V.B. Hunt, Strategies for screening for colorectal cancer, Medical Decision Making 7 (1989) 32–46.

    Google Scholar 

  • P. Selby, R&D priorities in cancer: Report to the NHS Central Research and Development Committee, NHS Central Research and Development Committee, 1995.

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Correspondence to P. R. Harper.

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Harper, P.R., JONES, S.K. Mathematical Models for the Early Detection and Treatment of Colorectal Cancer. Health Care Manage Sci 8, 101–109 (2005). https://doi.org/10.1007/s10729-005-0393-7

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  • DOI: https://doi.org/10.1007/s10729-005-0393-7

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