This project aims at developing and implementing a flexible methodology for modelling arbitrary count time series by employing a state space modelling approach and at designing appropriate control strategies based on the modelling results. The focus of the intended applications lies on biomedical time series; in particular, the task of monitoring and controlling the therapy of patients suffering from epilepsy by AED medication will be addressed. This application will serve as a realistic testbed for the developed methodology.
Quantitative methods from system identification and control will be introduced into an important field of clinical therapy planning. We aim at making optimal use of the available data, i.e., of the response of the patient to previously administered medication. This project is based on the hypothesis that the quantitative approach to analysing this data based on time series analysis and state space modelling will provide superior results, as compared to the current standard given by the direct least-squares regression approach or by visual inspection and subjective decision based on the experience of the physician conducting the treatment. As a result, the physician will be provided with a tool for automatic monitoring of ongoing treatment and for suggesting changes and adaptations. The minimum data set size that is required for such tool to function reliably will be investigated, possibly by a suitable simulation approach. We expect that our approach will offer a solution also for cases that are difficult to assess, e.g., given simultaneous administration of several drugs with time-varying dosages.
In future work, also additional data besides the daily counts of seizures may be added to the analysis, such as data on side effects of the medication.
To achieve these goals this project aims at improving and extending the available methodology for nonlinear Kalman Filtering and for estimation of model parameters by maximisation of the likelihood given count time series of limited length, as are common in many biomedical applications. For this purpose, recently proposed algorithms, like square-root Kalman Filtering and Kalman Filtering based on Singular Value Decomposition, will have to be generalised for the nonlinear case. Also available algorithms for numerical optimisation will have to be adapted to the particular situation by employing recent developments, such as square-root versions of the Expectation Maximisation algorithm.