混合效应的估计 普通微分方程模型在参数中是线性的
Oleksandr Laskorunskyi1, Snigdhansu Chatterjee2, Itai Dattner1
1Department of Statistics, University of Haifa, Abba Khoushy Ave 199, Haifa, IL 3498838, Israel.
Biometrics
|February 28, 2026
概括
我们介绍了直接积分混合效应 (DIME),这是分析动态系统的新框架. DIME 增强了复杂数据结构的统计推理,与现有方法相比,提供了具有竞争力的性能.
科学领域:
- 统计 统计 统计 统计
- 动态系统建模 动态系统建模
- 计算生物学 计算生物学
背景情况:
- 普通微分方程 (ODE) 模型对于分析动态系统至关重要.
- 在具有复杂等级结构的ODE模型中估计固定和随机效应仍然具有挑战性.
- 现有的非线性混合效应模型在处理各种数据结构方面存在局限性.
研究的目的:
- 提出一个一般框架,用于估计ODE模型中的固定和随机效应.
- 将混合效应的ODE建模扩展到单级,嵌套的层次结构和交叉的随机效应结构.
- 增强统计推理对广泛类型的动态系统的可访问性.
主要方法:
- 开发了Direct Integral Mixed-Effects (DIME),这是ODE模型的新框架,其参数是线性的.
- 利用参数-状态分离性,在线性混合效应模型框架内重新构建问题.
- 提供了理论上的保证一致性和非对称的正常性.
主要成果:
- 与nlme和nlmixr2.2相比,DIME显示了竞争偏差和RMSE.
- DIME显示了优越的覆盖概率,特别是在有限数据的方差组件估计中.
- 该方法被证明适用于竞争方法失败的场景.
- 将DIME应用于人口增长和大气动态数据,产生一致和可解释的结果.
结论:
- DIME为混合效果的ODE建模提供了一种灵活和可访问的方法.
- 该框架有效地处理复杂的层次数据结构.
- DIME为动态系统中的统计推理提供了一个强大的替代方案,在各种场景中表现优于现有的方法.
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