SVD Square-root Iterated Extended Kalman Filter for Modeling of Epileptic Seizure Count Time Series with External Inputs

In this paper a nonlinear filtering algorithm for count time series is developed that takes the non-negativity of the data into account and preserves positive definiteness of the covariance matrices of the model. For this purpose, a recently proposed variant of Kalman Filtering based on Singular Value Decomposition is incorporated into Iterative Extended Kalman Filtering, in order to estimate the states of a nonlinear state space model. The resulting algorithm is applied to the evaluation and design of therapies for patients suffering from Myoclonic Astatic Epilepsy, employing time series of daily seizure rate. The analysis provides a decision whether for a specific patient a particular anti-epileptic drug is increasing or reducing the seizure rate. Through a simulation study the proposed algorithm is validated. Additionally, for clinical data results obtained by the proposed algorithm are compared with the results from a Cox-Stuart trend test as well as with the visual assessment of experienced pediatric epileptologists.