Efficient local estimation for time-varying coefficients in deterministic dynamic models with applications to HIV-1 dynamics
Efficient local estimation for time-varying coefficients in deterministic dynamic models with applications to HIV-1 dynamics
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DOI：
10.1198/016214507000001382
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发表时间：
2008-03-01
影响因子：
3.7
通讯作者：
Wu, Hulin
中科院分区：
文献类型：
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作者：
Chen, Jianwei;Wu, Hulin
近年来，确定性动力学模型在生物医学研究和其他科学领域已经变得非常流行，例如人类免疫缺陷病毒（HIV）动力学建模，药代动力学/药效学分析，肿瘤细胞动力学和遗传网络建模。在这篇文章中，我们提出了估计方法的时变系数的确定性动态系统，通常是由一组微分方程描述。提出了三个两阶段局部多项式估计，并证明了它们的渐近正态性。另一种方法，离散化方法，广泛用于随机扩散模型，也进行了研究。我们表明，离散化方法，使用简单的输入离散化方法的确定性动态模型没有达到最佳的收敛速度相比，建议的两阶段估计。我们使用蒙特卡罗模拟研究有限样本的性能，并使用一个真实的数据应用到艾滋病病毒的动力学来说明所提出的方法。
Recently deterministic dynamic models have become very popular in biomedical research and other scientific areas; examples include modeling human immunodeficiency virus (HIV) dynamics, pharmacokinetic/pharmacodynamic analysis, tumor cell kinetics, and genetic network modeling. In this article we propose estimation methods for the time-varying coefficients in deterministic dynamic systems that are usually described by a set of differential equations. Three two-stage local polynomial estimators are proposed, and their asymptotic normality is established. An alternative approach, a discretization method that is widely used in stochastic diffusion models, is also investigated. We show that the discretization method that uses the simple Enter discretization approach for the deterministic dynamic model does not achieve the optimal convergence rate compared with the proposed two-stage estimators. We use Monte Carlo simulations to study the finite-sample performance, and use a real data application to HIV dynamics to illustrate the proposed methods.