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Estimation for dynamical systems using a population-based Kalman filter - Applications to pharmacokinetics models

Annabelle Collin 1 Mélanie Prague 2 Philippe Moireau 1
1 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine
LMS - Laboratoire de mécanique des solides, Inria Saclay - Ile de France
2 SISTM - Statistics In System biology and Translational Medicine
Inria Bordeaux - Sud-Ouest, BPH - Bordeaux population health
Abstract : Many methods exist to identify parameters of dynamical systems. Unfortunately, in addition to the classical measurement noise and under-sampling drawbacks, mean and variance priors of the estimated parameters can be very vague. These difficulties can lead the estimation procedure to underfitting. In clinical studies, a circumvention consists in using the fact that multiple independent patients are observed as proposed by nonlinear mixed-effect models. However, these very effective approaches can turn to be time-consuming or even intractable when the model complexity increases. Here, we propose an alternative strategy of controlled complexity. We first formulate a population least square estimator and its associated a Kalman based filter, hence defining a robust large population sequential estimator. Then, to reduce and control the computational complexity, we propose a reduced-order version of this population Kalman filter based on a clustering technique applied to the observations. Using simulated pharmacokinetics data and the theophylline pharmacokinetics data, we compare the proposed approach with literature methods. We show that using the population filter improves the estimation performance compared to the classical and fast patient-by-patient Kalman filter and leads to estimation results comparable to state-of-the-art population-based approaches. Then, the reduced-order version allows to drastically reduce the computational time for equivalent estimation and prediction.
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https://hal.inria.fr/hal-02869347
Contributor : Philippe Moireau <>
Submitted on : Monday, June 15, 2020 - 10:22:02 PM
Last modification on : Tuesday, March 23, 2021 - 10:42:04 AM

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  • HAL Id : hal-02869347, version 1

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Annabelle Collin, Mélanie Prague, Philippe Moireau. Estimation for dynamical systems using a population-based Kalman filter - Applications to pharmacokinetics models. 2020. ⟨hal-02869347⟩

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