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

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.