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A Computational Algorithm Associated with Patient Progress Modelling

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Abstract

Patient progress modelling, which was first introduced to provide an alternative to traditional randomised control trials, has now been used in numerous contexts including evaluation of screening programmes and assessment of the public health impact of large scale developments such as waste disposal incinerators. The method uses stochastic compartmental models whose solutions may depend on solving large sets of matrix differential equations. Although specialist software packages are available for this purpose, we propose an alternative method for deriving the solution to such equations that is simple to implement.

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References

  • Aspden P, Sutcliffe SBJ, Timothy AR, Jackson RRP (1981) An approach to treatment evaluation of Hodgkin’s disease. Omega 9(5):537–546

    Article  Google Scholar 

  • Bickart TA (1968) Matrix exponential: approximation by truncated power series. Proc IEEE 56: 872–873

    Article  Google Scholar 

  • Birkhead BG, Rankin EM, Gallivan S, Dones L (1987) A mathematical model of the development of drug resistance to cancer chemotherapy. Eur J Cancer Clin Oncol 23:1421–1427

    Article  Google Scholar 

  • Cullen MR (1985) Linear models in biology. Ellis Horwood, Chichester

    Google Scholar 

  • Horn A, Johnson CR (1985) Matrix analysis. Cambridge University Press, Cambridge

    Google Scholar 

  • Jackson RRP, Aspden P (1979) Treatment evaluation – a modelling approach with application to acute myeloid leukaemia. J Oper Res Soc 30:11–22

    Article  Google Scholar 

  • Jackson RRP, McKay VL, Malpas JS (1981) Patient progress modelling and results in Wilm’s tumour. Omega 9(5):527–536

    Article  Google Scholar 

  • Jackson RRP, Birkhead BG, Bell R, Lister TA, Gregory WM (1982) Application of Jackson, Aspden acute myeloid leukaemia model. J Oper Res Soc 33:211–216

    Article  Google Scholar 

  • Jenkins D, Sherlaw-Johnson C, Gallivan S (1994) Can additional detection of human Papillomavirus type 16 improve cervical cytological screening? J Pathol 172(Suppl):134

    Google Scholar 

  • Jenkins D, Sherlaw-Johnson C, Gallivan S (1996) Can papillomavirus testing be used to improve cervical cancer screening?. Int J Cancer 65:768–773

    Article  Google Scholar 

  • McCarthy M, Utley M (2004) Quantitative approaches to HIA. In: Kemm J, Parry J, Palmer S (eds) Health impact assessment. Oxford University Press, Oxford, pp 61–70

    Google Scholar 

  • Marcus M, Minc H (1992) A survey of matrix theory and matrix inequalities. Dover Publications, New York

    Google Scholar 

  • Moran PAP (1984) An introduction to probability theory. Clarendon Press, Oxford

    Google Scholar 

  • Pearce RM, Gallivan S, Jackson RRP (1993) Patient progress modelling for small cell lung cancer. Eur J Cancer 29(Suppl 5):734–737

    Google Scholar 

  • Rudin W (1964) Principles of mathematical analysis, 2nd edn. McGraw-Hill, New York

    Google Scholar 

  • Sherlaw-Johnson C, Gallivan S, Jenkins D, Jones M (1994) Cytological screening and management of abnormalities in prevention of cervical Cancer. J Clin Pathol 47:430–435

    Google Scholar 

  • Sherlaw-Johnson C, Gallivan S, Jenkins D (1997) Evaluating cervical cancer screening programmes for developing countries. Int J Cancer 72:210–216

    Article  Google Scholar 

  • Sherlaw-Johnson C, Gallivan S, Jenkins D (1999) Withdrawing low risk women from Cervical Screening programmes: mathematical modelling study. Brit Med J 318:356–360

    Google Scholar 

  • Utley M, Gallivan S, Biddulph J, McCarthy M, Ferguson J (2003) ARMADA – a computer model of the impact of environmental factors on health. Health Care Manag Sci 6:137–146

    Article  Google Scholar 

  • Wolfram Research Inc. (2003) Mathematica, Version 5.0. Champaign, IL

Download references

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Correspondence to S. Gallivan.

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Gallivan, S., Utley, M., Jit, M. et al. A Computational Algorithm Associated with Patient Progress Modelling. CMS 4, 283–299 (2007). https://doi.org/10.1007/s10287-006-0024-x

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