基于密度的蒙特卡罗滤波及其在不可观测变量和药动学参数估计中的应用
Density-based Monte Carlo filter and its applications in estimation of unobservable variables and pharmacokinetic parameters
摘要：
含有不可观测变量的非线性随机微分方程模型目前广泛应用于PK/PD数据分析。对不可观测变量的估计通常采用扩展卡尔曼滤波（EKF），对未知药代动力学参数的估计通常采用极大似然估计。然而，EKF不适用于非线性PK/PD模型，并且已知MLE向下偏倚。本文提出了一种基于密度的蒙特卡罗滤波器（DMF）来估计不可观测变量，并提出了一种基于模拟的估计未知参数的方法，其中设计了一种遗传算法来搜索药代动力学参数的最优值。通过仿真比较了EKF和DMF算法的性能，发现DMF算法在平均绝对误差方面比EKF算法更精确。
英文摘要：
Nonlinear stochastic differential equation models with unobservable variables are now widely used in the analysis of PK/PD data. The unobservable variables are often estimated with extended Kalman filter (EKF), and the unknown pharmacokinetic parameters are usually estimated by maximum likelihood estimator. However, EKF is inadequate for nonlinear PK/PD models, and MLE is known to be biased downwards. A density-based Monte Carlo filter (DMF) is proposed to estimate the unobservable variables, and a simulation-based procedure is proposed to estimate the unknown parameters in this paper, where a genetic algorithm is designed to search the optimal values of pharmacokinetic parameters. The performances of EKF and DMF are compared through simulations, and it is found that the results based on DMF are more accurate than those given by EKF with respect to mean absolute error.
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