Stochastic PK/PD modelling |
| | Abstract | This thesis describes the development of a software prototype implemented in Matlab for non-linear mixed effects modelling based on stochastic differential equations (SDEs). The setup aims at modelling measurements originating from more than one individual and it represents a powerful way of modelling systems with complicated and partially unknown dynamics. The incorporation of SDEs enables the setup to separate noise into two fundamentally different parts: uncorrelated measurement noise, arising from data collection etc. and correlated system noise, arising from model deficiencies or true random uctuation of the system. The mixed-effects model makes it possible to describe variation within a population and to estimate parameters where only few observations are available for each individual.
The setup has been implemented in a prototype, which enables maximum likelihood estimation of model parameters. The likelihood function is created using the First-Order Conditional Estimate (FOCE) used in non-linear mixed effects modelling. This is done in combination with the Extended Kalman Filter used in models with SDEs. The prototype is able to use the estimated model for prediction, filtering, smoothing and simulation for linear as well as non-linear models.
The work using the implemented prototype has focused on pharmacokinetic/ pharmacodynamic (PK/PD) modelling and has been carried out in collaboration with Novo Nordisk A/S. The prototype is compared with existing software for a range of PK models, but also used to perform analysis that is not readily doable in any other software package. Particular attention is devoted towards deconvolution of insulin secretion rate (ISR) and liver extraction of insulin based on a 24h study with three standardized meals. Moreover, an intervention model is proposed which utilizes knowledge of the three meal times and this is used for modelling of the insulin secretion rate.
Overall, the prototype has proven to be a exible and efficient tool for estimation of non-linear mixed effects models based on SDEs and has been used with success for a range of pharmacokinetic models. | | Keywords | Stochastic differential equation (SDE), non-linear mixed effects, FOCE approximation, Extended Kalman Filter, maximum likelihood estimation, insulin secretion rate, pharmacokinetic, PK/PD modelling | | Type | Master's thesis [Academic thesis] | | Year | 2006 | | Publisher | Informatics and Mathematical Modelling, Technical University of Denmark, DTU | | Address | Richard Petersens Plads, Building 321, DK-2800 Kgs. Lyngby | | Series | IMM-Thesis-2006-27 | | Note | Supervised by Henrik Madsen and Rune Viig Overgaard, IMM. External supervisor: Niels Rode Kristensen | | Electronic version(s) | [pdf] [ps] | | BibTeX data | [bibtex] | | IMM Group(s) | Mathematical Statistics |
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