Abstract
A method for PK/PD model development based on stochastic differential equation models is proposed. The new method has a number of advantages compared to conventional methods. In particular, the new method avoids the exhaustive trial-and-error based search often conducted to determine the most appropriate model structure, because it allows information about the appropriate model structure to be extracted directly from data. This is accomplished through quantification of the uncertainty of the individual parts of an initial model, by means of which tools for performing model diagnostics can be constructed and guidelines for model improvement provided. Furthermore, the new method allows time-variations in key parameters to be tracked and visualized graphically, which allows important functional relationships to be revealed. Using simulated data, the performance of the new method is demonstrated by means of two examples. The first example shows how, starting from a simple assumption of linear PK, the method can be used to determine the correct nonlinear model for describing the PK of a drug following an oral dose. The second example shows how, starting from a simple assumption of no drug effect, the method can be used to determine the correct model for the nonlinear effect of a drug with known PK in an indirect response model.
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References
M. O. Karlsson S. L. Beal L. B. Sheiner (1995) ArticleTitleThree new residual error models for population PK/PD analyses J. Pharmacokinet. Biopharm. 23 IssueID6 651–672 Occurrence Handle8733951
C. Cobelli J. J. DiStefano SuffixIII (1980) ArticleTitleParameter and structural identifiability concepts and ambiguities: A critical review and analysis Am. J. Physiol. 239 R7–R24 Occurrence Handle7396041
N. R. Kristensen H. Madsen S. B. Jørgensen (2004) ArticleTitleParameter estimation in stochastic grey-box models Automatica 40 IssueID2 225–237 Occurrence Handle10.1016/j.automatica.2003.10.001
N. R. Kristensen H. Madsen S. B. Jørgensen (2004) ArticleTitleA method for systematic improvement of stochastic grey-box models Comput. Chem. Eng. 28 IssueID8 1431–1449 Occurrence Handle10.1016/j.compchemeng.2004.08.004
A. H. Jazwinski (1970) Stochastic Processes and Filtering Theory Academic Press New York, USA
B. Øksendal (1998) Stochastic Differential Equations—An Introduction with Applications EditionNumber5 Springer-Verlag Berlin, Germany
P. E. Kloeden E. Platen (1992) Numerical Solution of Stochastic Differential Equations Springer–Verlag Berlin, Germany
N. R. Kristensen H. Madsen (2003) Continuous Time Stochastic Modelling-CTSM 2.3–Mathematics Guide Technical University of Denmark Lyngby, Denmark
N. R. Kristensen H. Madsen (2003) Continuous Time Stochastic Modelling-CTSM 2.3–User’s Guide Technical University of Denmark Lyngby, Denmark
S. Kotz N. L. Johnson (Eds) (1985) Encyclopedia of Statistical Sciences Wiley New York, USA
A Gelb (1974) Applied Optimal Estimation The MIT Press Cambridge, USA
G. Nicolao ParticleDe G. Sparacino C. Cobelli (1997) ArticleTitleNonparametric input estimation in physiological systems: Problems, methods, and case studies Automatica 33 IssueID5 851–870 Occurrence Handle10.1016/S0005-1098(96)00254-3
G. Sparacino G. Pillonetto M. Capello G. Nicolao ParticleDe C. Cobelli (2001) ArticleTitleWINSTODEC: A stochastic deconvolution interactive program for physiological and pharmacokinetic systems Comput. Meth. Programs Biomed. 67 67–77 Occurrence Handle10.1016/S0169-2607(00)00151-6
T. J. Hastie R. J. Tibshirani J. Friedman (2001) The Elements of Statistical Learning–Data Mining, Inference and Prediction Springer-Verlag New York, USA
T. J. Hastie R. J. Tibshirani (1990) Generalized Additive Models Chapman & Hall London, England
InstitutionalAuthorNamePharsight (2002) WinNonlin 4.0–Examples Guide Pharsight Corporation Mountain View, USA
InstitutionalAuthorNamePharsight (2002) WinNonlin 4.0–Reference Guide Pharsight Corporation Mountain View USA
R. V. Overgaard, N. Jonsson, C. W. Tornøe, and H. Madsen. Nonlinear mixed-effects models with stochastic differential equations: Implementation of an estimation algorithm. J. Pharmacokinet. Pharmacodyn., In Press, 2005.
C. W. Tornøe R. V. Overgaard H. Agersø H. A. Nielsen H. Madsen E. N. Jonsson (2005) ArticleTitleStochastic differential equations in NONMEM: Implementation, application, and comparison with ordinary differential equations Pharm. Res. 22 1247–1258 Occurrence Handle10.1007/s11095-005-5269-5 Occurrence Handle16078134
E. N. Jonsson and M. O. Karlsson. Nonlinearity detection: Advantages of nonlinear mixed-effects modelling. AAPS Pharm. Sci. 2(3): (2000).
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Kristensen, N., Madsen, H. & Ingwersen, S. Using Stochastic Differential Equations for PK/PD Model Development. J Pharmacokinet Pharmacodyn 32, 109–141 (2005). https://doi.org/10.1007/s10928-005-2105-9
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DOI: https://doi.org/10.1007/s10928-005-2105-9