Population stochastic modelling (PSM)-An R package for mixed-effects models based on stochastic differential equations

Computer Methods and Programs in Biomedicine

Volumn 94, Issue 3, 2009, Pages 279-289

  Klim, Søren ^a,c   Mortensen, Stig Bousgaard ^b,c   Kristensen, Niels Rode ^a   Overgaard, Rune Viig ^a   Madsen, Henrik ^c  

^a NOVO NORDISK A S   (Denmark)

^b H LUNDBECK A S   (Denmark)

^c TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

Mixed effect; Pharmacodynamic; Pharmacokinetic; State space models; Stochastic differential equations (SDEs)

Indexed keywords

AUTOCORRELATED; DIFFERENTIAL MODELS; ESTIMATION ALGORITHMS; ESTIMATION METHODS; FIRST ORDERS; MIXED-EFFECT; MODEL DEVELOPMENT; NATURAL VARIATIONS; NIELSEN; NOISE COMPONENTS; NON-LINEAR; OBSERVATION NOISE; STATE-SPACE FORMULATIONS; STATE-SPACE MODELS; STOCHASTIC DIFFERENTIAL EQUATIONS (SDES); STOCHASTIC MODELLING; SYSTEM EQUATIONS; SYSTEM NOISE; SYSTEMATIC MODELS; WIENER NOISE;

CELLULAR RADIO SYSTEMS; CONTROL THEORY; EQUATIONS OF STATE; ESTIMATION; GLUCOSE; MAXIMUM LIKELIHOOD ESTIMATION; MEASUREMENT THEORY; PHARMACOKINETICS; PHOTOMASKS; RANDOM PROCESSES; STATISTICAL TESTS; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC MODELS;

ORDINARY DIFFERENTIAL EQUATIONS;

ARTICLE; COMPUTER PROGRAM; HUMAN; MATHEMATICAL PARAMETERS; POPULATION; PREDICTION; STOCHASTIC MODEL;

ALGORITHMS; COMPUTATIONAL BIOLOGY; COMPUTER SIMULATION; COMPUTERS; DRUG DESIGN; HUMANS; INSULIN; LIKELIHOOD FUNCTIONS; MODELS, STATISTICAL; MODELS, THEORETICAL; PHARMACOKINETICS; PROGRAMMING LANGUAGES; SOFTWARE; STOCHASTIC PROCESSES; TECHNOLOGY, PHARMACEUTICAL;

EID: 63649145251     PISSN: 01692607     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cmpb.2009.02.001     Document Type: Article

References (16)

1. Kristensen N.R., Madsen H., and Ingwersen S.H. Using stochastic differential equations for PK/PD model development. J. Pharmacokinet. Pharmacodyn. 32 February(1) (2005) 109-141
2. Tornøe C.W., Overgaard R.V., Agersø H., Nielsen H.A., Madsen H., and Jonsson E.N. Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations. Pharm. Res. 22 August(8) (2005) 1247-1258
3. Overgaard R.V., Jonsson N., Tornøe C.W., and Madsen H. Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm. J. Pharmacokinet. Pharmacodyn. 32 February(1) (2005) 85-107
4. Picchini U., Ditlevsen S., and De Gaetano A. Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics. Math. Med. Biol. 25 June(2) (2008) 141-155
5. L.B. Sheiner, S.L. Beal, NONMEM User's Guide, NONMEM Project Group, University of California, San Francisco, 1994.
6. N.R. Kristensen, CTSM Mathematics Guide, Technical Report, Technical University of Denmark, December 2003.
7. Mortensen S.B., Klim S., Dammann B., Kristensen N.R., Madsen H., and Overgaard R.V. A Matlab framework for estimation of NLME models using stochastic differential equations: applications for estimation of insulin secretion rates. J. Pharmacokinet. Pharmacodyn. 34 October(5) (2007) 623-642
8. Tornøe C.W., Agersø H., Niclas Jonsson E., Madsen H., and Nielsen H.A. Non-linear mixed-effects pharmacokinetic/pharmacodynamic modelling in NLME using differential equations. Comput. Meth. Programs Biomed. 76 October(1) (2004) 31-40
9. Kalman R.E. New approach to linear filtering and prediction problems. Am. Soc. Mech. Eng. - Trans. - J. Basic Eng. Ser. D 82 1 (1960) 35-45
10. G. Welch, G. Bishop, http://www.cs.unc.edu/∼welch/kalman/.
11. R.V. Overgaard, Pharmacokinetic/Pharmacodynamic Modeling with a Stochastic Perspective. Insulin Secretion and Interleukin-21 Development as Case Studies, PhD Thesis, Technical University of Denmark, Informatics and Mathematical Modelling, 2006.
12. Sheiner L.B., and Beal S.L. Evaluation of methods for estimating population pharmacokinetics parameters. I. Michaelis-Menten model: routine clinical pharmacokinetic data. J. Pharmacokinet. Biopharm. 8 December(6) (1980) 553-571
13. Kailath T., Sayed A.H., and Hassibi B. Linear Estimation (2000), Prentice-Hall
14. Van Cauter E., Mestrez F., Sturis J., and Polonsky K.S. Estimation of insulin secretion rates from c-peptide levels comparison of individual and standard kinetic parameters for c-peptide clearance. Diabetes 41 March(3) (1992) 368-377
15. N.R. Kristensen, A deconvolution method for linear and nonlinear systems based on stochastic differential equations, Population Approach Group Europe, 2004.
16. S. Klim, S.B. Mortensen, PSM homepage. Internet: http://www.imm.dtu.dk/psm, June 2008.