Nonparametric Models for Longitudinal Data with Implementation in R
Nonparametric Models for Longitudinal Data with Implementation in R
复制标题
纵向数据的非参数模型及其在 R 中的实现
DOI：
10.1080/10543406.2019.1616155
复制
发表时间：
2019
影响因子：
1.1
通讯作者：
D. Hille
中科院分区：
文献类型：
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作者：
D. Hille
这本书是由美国国立卫生研究院的数理统计学家撰写的，他们与临床合作者有着丰富的经验。这是一本学术参考书。本书分为五个主要部分：介绍和回顾（第1节），非结构化非参数模型（第2节），时变系数模型（第3节），共享参数和混合效应模型（第4节），以及分布的非参数模型（第5节）。作者深入探讨了每个主题的理论推导，然后是例子。每个主题都从前面的主题中逻辑地遵循；然而，每一部分都是如此完整，以至于可以独立研究。第1节提供了纵向数据的全面审查，并对参数和半参数方法进行了高级审查。这些评论提供了纵向数据和标准方法的基础，然后在随后的章节中提出更灵活的非参数方法。第3章介绍了贯穿全书的“遗漏一个主题”交叉验证（LSCV）。第2节介绍核和局部多项式方法，以及基近似光滑方法和惩罚光滑样条方法。作者指出，基本的局部平滑方法的优点是它们在概念上简单，并且估计量的渐近性质不受数据相关结构的影响。第3节介绍了各种平滑方法，首先是对时不变协变量进行平滑，然后是对时变协变量进行一步和两步局部和全局平滑。用同一实例数据集说明了一步平滑法和两步平滑法的实现和结果。第4节继续讨论共享参数和混合效应模型。由于第3节中的模型可能由于其局限性而具有有限的实用价值，因此这些更通用的模型在分析伴随干预措施时可能更有用。第5节介绍了一个统计指标，即秩跟踪概率，用于衡量纵向变量的时间跟踪能力。这可能用于生物医学研究，以确定持续的疾病风险。在整个书中，概念是通过四个现实生活中的例子数据集说明。
This book was written by mathematical statisticians at the National Institutes of Health who have extensive experience with clinical collaborators. The tone is that of an academic reference work. This book is organized in five major sections: Introduction and Review (Section 1), Unstructured Nonparametric Models (Section II), Time-Varying Coefficient Models (Section III), SharedParameter and Mixed-Effects Models (Section IV), and Nonparametric Models for Distribution (Section (V). The authors go into depth on each topic with theoretical derivations followed by examples. Each topic follows logically from the previous ones; however, each section is so complete that it could be studied independently. Section 1 provides a comprehensive review of longitudinal data, and a high-level review of parametric and semi-parametric methods. These reviews provide the groundwork of longitudinal data and standard methods before presenting the more flexible nonparametric methods in the subsequent chapters. Chapter 3 introduces “leave-one-subject-out” cross-validation (LSCV), which is used throughout the book. Section 2 covers kernel and local polynomial methods, along with basis approximation smoothing methods and penalized smoothing spline methods. The authors note that the advantage of the basic local smoothing methods is that they are conceptually simple and that the asymptotic properties of the estimators are not affected by the correlation structures of the data. Section 3 covers various smoothing methods, first for smoothing with time-invariant covariates, followed by oneand two-step local and global smoothing methods for time-dependent covariates. The implementation and results of one-step and two-step smoothing methods are illustrated with the same example dataset. Section 4 continues with shared-parameter and mixed-effects models. Since the models in Section 3 may have limited practical value due to their restrictions, these more general models may be more useful when analyzing concomitant interventions. Section 5 wraps up the text with the introduction of a statistical index, the Rank-Tracking Probability, used to measure the temporal tracking ability of a longitudinal variable. This may be used in biomedical studies to identify persistent disease risk. Throughout the book, the concepts are illustrated via four real-life example datasets.