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半参数常微分方程模型的参数估计

Parameter Estimation for Semiparametric Ordinary Differential Equation Models.

作者信息

Xue Hongqi, Kumar Arun, Wu Hulin

机构信息

iCardiac Technologies, 150 Allens Creek Rd, Rochester, NY 14618.

Livanova, 100 Cyberonics Blvd, Houston, TX 77058.

出版信息

Commun Stat Theory Methods. 2019;48(24):5985-6004. doi: 10.1080/03610926.2018.1523433. Epub 2018 Dec 29.

DOI:10.1080/03610926.2018.1523433
PMID:32952273
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7500512/
Abstract

We propose a new class of two-stage parameter estimation methods for semiparametric ordinary differential equation (ODE) models. In the first stage, state variables are estimated using a penalized spline approach; In the second stage, form of numerical discretization algorithms for an ODE solver is used to formulate estimating equations. Estimated state variables from the first stage are used to obtain more data points for the second stage. Asymptotic properties for the proposed estimators are established. Simulation studies show that the method performs well, especially for small sample. Real life use of the method is illustrated using Influenza specific cell-trafficking study.

摘要

我们提出了一类用于半参数常微分方程（ODE）模型的新型两阶段参数估计方法。在第一阶段，使用惩罚样条方法估计状态变量；在第二阶段，使用ODE求解器的数值离散算法形式来构建估计方程。第一阶段估计出的状态变量用于为第二阶段获取更多数据点。建立了所提估计量的渐近性质。模拟研究表明该方法表现良好，尤其是对于小样本。通过流感特异性细胞迁移研究说明了该方法在实际中的应用。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/ffec/7500512/fc0f3206da05/nihms-1514797-f0003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/ffec/7500512/0bafe35867ac/nihms-1514797-f0001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/ffec/7500512/9e7f579fde93/nihms-1514797-f0002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/ffec/7500512/fc0f3206da05/nihms-1514797-f0003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/ffec/7500512/0bafe35867ac/nihms-1514797-f0001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/ffec/7500512/9e7f579fde93/nihms-1514797-f0002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/ffec/7500512/fc0f3206da05/nihms-1514797-f0003.jpg

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本文引用的文献

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Penalized Nonlinear Least Squares Estimation of Time-Varying Parameters in Ordinary Differential Equations.常微分方程中时变参数的惩罚非线性最小二乘估计
J Comput Graph Stat. 2012;21(1):42-56. doi: 10.1198/jcgs.2011.10021.
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Numerical discretization-based estimation methods for ordinary differential equation models via penalized spline smoothing with applications in biomedical research.基于数值离散化的常微分方程模型估计方法，通过惩罚样条平滑及其在生物医学研究中的应用
Biometrics. 2012 Jun;68(2):344-52. doi: 10.1111/j.1541-0420.2012.01752.x. Epub 2012 Feb 29.
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Modeling of influenza-specific CD8+ T cells during the primary response indicates that the spleen is a major source of effectors.
在初次反应期间，流感特异性 CD8+ T 细胞的建模表明脾脏是效应器的主要来源。
J Immunol. 2011 Nov 1;187(9):4474-82. doi: 10.4049/jimmunol.1101443. Epub 2011 Sep 23.
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Sieve Estimation of Constant and Time-Varying Coefficients in Nonlinear Ordinary Differential Equation Models by Considering Both Numerical Error and Measurement Error.通过同时考虑数值误差和测量误差对非线性常微分方程模型中的常数和时变系数进行筛估计
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