Nonparametric Estimation and Inference Methods for the Analysis of Longitudinal Data

这个项目的目的是开发一系列统计方法来分析纵向数据。研究者通过一系列的渐近和模拟研究来研究这些方法的理论和实践性质。这种类型的数据包括一组独立受试者在一段时间内的等间隔或不等距重复测量。由于可能存在被试内部的相关性，典型的纵向分析中涉及的两个主要任务是：(1)对感兴趣的反应变量的平均时变协变量效应进行建模和估计；(2)在统计估计和推断过程中量化可能的相关性和个体效应。研究人员通过对四个研究课题的调查，提供了一系列非参数工具来完成上述任务：(A)开发和比较几种局部平滑方法的大样本性质，以估计变系数模型中的系数曲线；(B)开发一类局部和全局推理和模型诊断程序，以评估参数和半参数回归模型的有效性；(C)评估“留一主题”交叉验证和其他选择平滑参数的程序的理论和实际性质；以及(D)通过一类非参数混合效应模型研究全局逼近的理论和实际性质。除了方法学出版物外，该项目的成果还包括允许轻松实施所开发方法的算法。该项目的理论结果为指导纵向分析中新的统计程序的开发提供了有益的见解。这位研究人员和他的合作者通过将他们的方法应用于一些生物医学和流行病学研究，展示了他们的方法的有效性和潜在的影响。计算技术的快速发展使社会科学和自然科学各个领域的科学家能够轻松地获取涉及随时间重复观察的变量的大型数据集。这种类型的数据被称为纵向数据，在生物医学、流行病学、经济学和社会学等领域很常见。统计研究在为从数据中提取有用信息提供理论上合理和实际可行的工具方面发挥着至关重要的作用。在生物医学和流行病学研究中，这类有用的信息可能包括，例如，治疗对疾病随时间发展的影响，母亲吸烟习惯与怀孕期间胎儿生长模式之间的潜在联系，以及其他具有生物医学和公共卫生利益的发现。尽管许多有才华的研究人员取得了长足的进步，但对更可靠、更有效的建模和诊断技术的需求仍然很大，特别是在能够处理重复测量的初始数据探索领域。还需要系统的理论发展，以建立一个坚实的基础，以判断一些现有方法的充分性，并提供导致未来方法论发展的见解。在当前的项目中，研究人员评估了一类灵活而有用的统计模型的理论性质，称为变系数模型，并通过扩展他的理论结果，开发了一类在许多纵向设置下潜在地优于现有建模方法的新的建模方法。由于统计理论、模型和算法可以应用于不存在预先指定的参数模型的情况，它们提供了有价值的工具，能够完全基于数据得出统计推断。这些工具允许科学家、政策制定者和研究人员从他们的数据中得出足够的结论，而不需要依赖于预先指定的假设，这些假设可能对他们的设置过于严格。在与其他统计和生物医学研究人员的合作中，研究人员和他的同事通过将他们的方法应用于一些生物医学和流行病学研究，展示了他们的方法的应用潜力，并讨论了他们的发现的生物学意义。

The aim of this project is to develop a series of statistical methods for the analysis of longitudinal data. The investigator studies the theoretical and practical properties of these methods through a series of asymptotic and simulation studies. This type of data involves either equally or unequally spaced repeated measurements over time from a collection of independent subjects. Because of the possible intra-subject correlations, two major tasks involved in a typical longitudinal analysis are: (1) to model and estimate the mean time-varying covariate effects on the response variables of interest; and (2) to quantify the possible correlations and individual effects in a statistical estimation and inference process. The investigator provides a range of nonparametric tools for accomplishing the above tasks through the investigation of four research topics: (a) developing and comparing the large sample properties of several local smoothing methods for the estimation of coefficient curves in varying coefficient models; (b) developing a class of local and global inference and model diagnostic procedures to assess the validity of parametric and semi-parametric regression models; (c) evaluating the theoretical and practical properties of the "leave-one-subject-out" cross-validation and other procedures for the selection of smoothing parameters; and (d) investigating the theoretical and practical properties of global approximation through a class of nonparametric mixed-effects models. In addition to the methodological publications, results of this project also include algorithms that allow for easy implementations of the developed methods. The theoretical results of this project provide useful insights for guiding the development of new statistical procedures in longitudinal analysis. The investigator and his collaborators demonstrate the usefulness and the potential impacts of their methods by applying them to a number of biomedical and epidemiological studies. The rapid development of computing technology has enabled scientists in various fields of social and natural sciences easy access to large datasets involving variables repeatedly observed over time. This type of data, known as longitudinal data, is common in biomedicine, epidemiology, economics, and sociology, among others. Statistical research plays the crucial role of providing theoretically sound and practically feasible tools for extracting useful information from the data. In biomedical and epidemiological studies, such useful information may include, for example, the effects of treatments on disease progression over time, the potential association between a mother's habit of cigarette smoking and the fetal growth pattern during pregnancy, and other findings that are of biomedical and public health interests. Despite considerable progress made by many talented researchers, there is still a large demand for more reliable and efficient modeling and diagnostic techniques, particularly in the area of initial data exploration, that are capable to handle repeated measurements. Systematic theoretical development is also needed for building a solid foundation to judge the adequacy of some existing methods and providing insights that lead to future methodological development. In the current project, the investigator evaluates the theoretical properties of a class of flexible and useful statistical models known as the varying coefficient models and, by extending his theoretical results, develops a class of new modeling approaches that are potentially superior to the existing ones in many longitudinal settings. Because the statistical theory, models and algorithms can be applied to situations where there does not exist a pre-specified parametric model, they provide valuable tools that are capable to derive statistical inferences entirely based on the data. These tools allow scientists, policy makers and researchers to draw adequate conclusions from their data without depending on pre-specified assumptions that maybe too restrictive to their settings. In a collaborative effort with other statistical and biomedical researchers, the investigator and his colleagues demonstrate the application potential of their methods by applying them to a number of biomedical and epidemiological studies and discuss the biological implications of their findings.