Modeling and Prediction Using Stochastic Differential Equations

Research output: Chapter in Book/Report/Conference proceedingBook chapterResearchpeer-review

Abstract

Pharmacokinetic/pharmakodynamic (PK/PD) modeling for a single subject is most often performed using nonlinear models based on deterministic ordinary differential equations (ODEs), and the variation between subjects in a population of subjects is described using a population (mixed effects) setup that describes the variation between subjects. The ODE setup implies that the variation for a single subject is described by a single parameter (or vector), namely the variance (covariance) of the residuals. Furthermore the prediction of the states is given as the solution to the ODEs and hence assumed deterministic and can predict the future perfectly. A more realistic approach would be to allow for randomness in the model due to e.g., the model be too simple or errors in input. We describe a modeling and prediction setup which better reflects reality and suggests stochastic differential equations (SDEs) for modeling and forecasting. It is argued that this gives models and predictions which better reflect reality. The SDE approach also offers a more adequate framework for modeling and a number of efficient tools for model building. A software package (CTSM-R) for SDE-based modeling is briefly described.
Original languageEnglish
Title of host publicationPrediction Methods for Blood Glucose Concentration : Design, Use and Evaluation
EditorsHarald Kirchsteiger, John Bagterp Jørgensen, Eric Renard, Luigi del Re
PublisherSpringer
Publication date2016
Pages183-209
ISBN (Print)978-3-319-25911-6
ISBN (Electronic)978-3-319-25913-0
DOIs
Publication statusPublished - 2016
SeriesLecture Notes in Bioengineering
ISSN2195-271X

Cite this

Juhl, R., Møller, J. K., Jørgensen, J. B., & Madsen, H. (2016). Modeling and Prediction Using Stochastic Differential Equations. In H. Kirchsteiger, J. Bagterp Jørgensen, E. Renard, & L. del Re (Eds.), Prediction Methods for Blood Glucose Concentration: Design, Use and Evaluation (pp. 183-209). Springer. Lecture Notes in Bioengineering https://doi.org/10.1007/978-3-319-25913-0_10
Juhl, Rune ; Møller, Jan Kloppenborg ; Jørgensen, John Bagterp ; Madsen, Henrik. / Modeling and Prediction Using Stochastic Differential Equations. Prediction Methods for Blood Glucose Concentration: Design, Use and Evaluation. editor / Harald Kirchsteiger ; John Bagterp Jørgensen ; Eric Renard ; Luigi del Re. Springer, 2016. pp. 183-209 (Lecture Notes in Bioengineering).
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Juhl, R, Møller, JK, Jørgensen, JB & Madsen, H 2016, Modeling and Prediction Using Stochastic Differential Equations. in H Kirchsteiger, J Bagterp Jørgensen, E Renard & L del Re (eds), Prediction Methods for Blood Glucose Concentration: Design, Use and Evaluation. Springer, Lecture Notes in Bioengineering, pp. 183-209. https://doi.org/10.1007/978-3-319-25913-0_10

Modeling and Prediction Using Stochastic Differential Equations. / Juhl, Rune; Møller, Jan Kloppenborg; Jørgensen, John Bagterp; Madsen, Henrik.

Prediction Methods for Blood Glucose Concentration: Design, Use and Evaluation. ed. / Harald Kirchsteiger; John Bagterp Jørgensen; Eric Renard; Luigi del Re. Springer, 2016. p. 183-209 (Lecture Notes in Bioengineering).

Research output: Chapter in Book/Report/Conference proceedingBook chapterResearchpeer-review

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AB - Pharmacokinetic/pharmakodynamic (PK/PD) modeling for a single subject is most often performed using nonlinear models based on deterministic ordinary differential equations (ODEs), and the variation between subjects in a population of subjects is described using a population (mixed effects) setup that describes the variation between subjects. The ODE setup implies that the variation for a single subject is described by a single parameter (or vector), namely the variance (covariance) of the residuals. Furthermore the prediction of the states is given as the solution to the ODEs and hence assumed deterministic and can predict the future perfectly. A more realistic approach would be to allow for randomness in the model due to e.g., the model be too simple or errors in input. We describe a modeling and prediction setup which better reflects reality and suggests stochastic differential equations (SDEs) for modeling and forecasting. It is argued that this gives models and predictions which better reflect reality. The SDE approach also offers a more adequate framework for modeling and a number of efficient tools for model building. A software package (CTSM-R) for SDE-based modeling is briefly described.

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Juhl R, Møller JK, Jørgensen JB, Madsen H. Modeling and Prediction Using Stochastic Differential Equations. In Kirchsteiger H, Bagterp Jørgensen J, Renard E, del Re L, editors, Prediction Methods for Blood Glucose Concentration: Design, Use and Evaluation. Springer. 2016. p. 183-209. (Lecture Notes in Bioengineering). https://doi.org/10.1007/978-3-319-25913-0_10