Moontaha Sidratul, Arnrich Bert, Galka Andreas
Digital Health-Connected Healthcare, Hasso Plattner Institute, University of Potsdam, 14482 Potsdam, Germany.
Bundeswehr Technical Centre for Ships and Naval Weapons, Maritime Technology and Research (WTD 71), 24340 Eckernförde, Germany.
Entropy (Basel). 2023 Sep 23;25(10):1372. doi: 10.3390/e25101372.
This paper proposes a class of algorithms for analyzing event count time series, based on state space modeling and Kalman filtering. While the dynamics of the state space model is kept Gaussian and linear, a nonlinear observation function is chosen. In order to estimate the states, an iterated extended Kalman filter is employed. Positive definiteness of covariance matrices is preserved by a square-root filtering approach, based on singular value decomposition. Non-negativity of the count data is ensured, either by an exponential observation function, or by a newly introduced "affinely distorted hyperbolic" observation function. The resulting algorithm is applied to time series of the daily number of seizures of drug-resistant epilepsy patients. This number may depend on dosages of simultaneously administered anti-epileptic drugs, their superposition effects, delay effects, and unknown factors, making the objective analysis of seizure counts time series arduous. For the purpose of validation, a simulation study is performed. The results of the time series analysis by state space modeling, using the dosages of the anti-epileptic drugs as external control inputs, provide a decision on the effect of the drugs in a particular patient, with respect to reducing or increasing the number of seizures.
本文提出了一类基于状态空间建模和卡尔曼滤波的用于分析事件计数时间序列的算法。虽然状态空间模型的动态特性保持为高斯和线性，但选择了一个非线性观测函数。为了估计状态，采用了迭代扩展卡尔曼滤波器。基于奇异值分解的平方根滤波方法可保持协方差矩阵的正定。通过指数观测函数或新引入的“仿射扭曲双曲线”观测函数确保计数数据的非负性。所得算法应用于耐药性癫痫患者每日癫痫发作次数的时间序列。这个次数可能取决于同时服用的抗癫痫药物的剂量、它们的叠加效应、延迟效应以及未知因素，这使得对癫痫发作计数时间序列进行客观分析变得艰巨。为了进行验证，开展了一项模拟研究。以抗癫痫药物的剂量作为外部控制输入，通过状态空间建模进行时间序列分析的结果，为特定患者中药物在减少或增加癫痫发作次数方面的效果提供了决策依据。
