Summary
Monitoring of a cancer patient, following initial administration of a drug, provides a time sequence of measured response values constituting the level in serum of the relevant enzyme activity. The ability to model such clinical data in a rigorous way leads to (a) an improved understanding of the biological processes involved in drug uptake, (b) a measure of total absorbed dose, and (c) a prediction of the optimal time for a further stage of drug administration. A class of mathematical decay functions is studied for modelling such activity data, taking into account measurement uncertainties associated with the response values. Expressions for the uncertainties associated with the biological processes in (a) and with (b) and (c) are obtained. Applications of the model to clinical data from two hospitals are given.
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References
BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML. Evaluation of measurement data — guide to the expression of uncertainty in measurement. Joint Committee for Guides in Metrology, JCGM 100:2008. http://www.bipm.org/utils/common/documents/jcgm/JCGM1002008E.pdf.
BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML. Evaluation of measurement data — supplement 1 to the “Guide to the expression of uncertainty in measurement” — propagation of distributions using a Monte Carlo method. Joint Committee for Guides in Metrology, JCGM 101:2008. http://www.bipm.org/utils/common/documents/jcgm/JCGM1012008E.pdf.
M.G. Cox: The evaluation of key comparison data. Metrologia 39, 2002, 589–595.
M.G. Cox and P.M. Harris: SSfM Best Practice Guide No. 6, Uncertainty Evaluation. Technical Report DEM-ES-011, National Physical Laboratory, Teddington, UK, 2006. http://publications.npl.co.uk/nplweb/pdf/demes11.pdf.
A. Divoli, A. Spinelli, S. Chittenden, D. Dearnaley, and G. Flux: Whole-body dosimetry for targeted radionuclide therapy using spectral analysis. Cancer Biol. Radiopharm. 20, 2005, 66–71.
C. Elster: Calculation of uncertainty in the presence of prior knowledge. Metrologia 44, 2007, 111–116.
G.D. Flux, M.J. Guy, R. Beddows, M. Pryor, and M.A. Flower: Estimation and implications of random errors in whole-body dosimetry for targeted radionuclide therapy. Phys. Med. Biol. 47, 2002, 3211–3223.
R. Francis and R.H.J. Begent: Monoclonal antibody targeting therapy: an overview. In Targeted Therapy for Cancer K. Syrigos and K. Harrington (eds.), Oxford University Press, Oxford, 2003, 29–46.
G. Golub and V. Pereyra: Separable nonlinear least squares: the variable projection method and its applications. Inverse Problems 19, 2003, R1–R26.
C. Hindorf, S. Chittenden, L. Causer, V.J. Lewington, and H. M¨acke: Dosimetry for 90Y-DOTATOC therapies in patients with neuroendocrine tumors. Cancer Biol. Radiopharm. 22, 2007, 130–135.
IUPAC compendium of chemical terminology. http://goldbook.iupac.org/B00658.html.
E.T. Jaynes:Where do we stand on maximum entropy? In Papers on Probability, Statistics, and Statistical Physics, R.D. Rosenkrantz (ed.), Kluwer Academic, Dordrecht, The Netherlands, 1989, 210–314.
A. Mayer, R.J. Francis, S.K. Sharma, B. Tolner, C.J.S. Springer, J. Martin, G.M. Boxer, J. Bell, A.J. Green, J.A. Hartley, C. Cruickshank, J. Wren, K.A. Chester, and R.H.J. Begent: A phase I study of single administration of antibody-directed enzyme prodrug therapy with the recombinant anticarcinoembryonic antigen antibody-enzyme fusion protein MFECP1 and a bisiodo
phenol mustard prodrug. Clin. Cancer Res. 12, 2006, 6509–6516.
M.G. Stabin and J.A. Siegel: Physical models and dose factors for use in internal dose assessment. Health Phys. 85, 2003, 294.
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Cox, M.G. (2011). Modelling Clinical Decay Data Using Exponential Functions. In: Georgoulis, E., Iske, A., Levesley, J. (eds) Approximation Algorithms for Complex Systems. Springer Proceedings in Mathematics, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16876-5_8
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DOI: https://doi.org/10.1007/978-3-642-16876-5_8
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