Nonparametric Estimation and Inference Methods for the Analysis of Longitudinal Data

该项目的目的是开发一系列用于纵向数据分析的统计方法。研究者通过一系列的渐近和模拟研究，这些方法的理论和实践性质。这种类型的数据涉及从独立受试者的集合中随时间等间隔或不等间隔地重复测量。由于可能的受试者内相关性，典型纵向分析中涉及的两个主要任务是：（1）建模和估计对感兴趣的响应变量的平均时变协变量效应;（2）量化统计估计和推断过程中可能的相关性和个体效应。研究者提供了一系列的非参数工具来完成上述任务，通过四个研究主题的调查：（a）发展和比较几种局部光滑方法的大样本性质，用于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的有效性。（c）评价“留一主题”交叉验证法和其他选择平滑参数的程序的理论和实际性质;（d）调查通过一类非参数混合效应模型进行的总体近似的理论和实际性质。除了方法学出版物，该项目的结果还包括算法，使开发的方法易于实施。该项目的理论结果为指导纵向分析中新的统计方法的发展提供了有益的见解。研究人员及其合作者通过将其应用于一些生物医学和流行病学研究来证明其方法的有用性和潜在影响。 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访问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。统计研究在提供从数据中提取有用信息的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，这些有用的信息可能包括，例如，治疗对疾病进展的影响，母亲吸烟习惯与怀孕期间胎儿生长模式之间的潜在联系，以及其他生物医学和公共卫生方面的研究结果。尽管许多有才华的研究人员取得了相当大的进展，但仍然需要更可靠，更有效的建模和诊断技术，特别是在初始数据探索领域，能够处理重复测量。系统的理论发展也需要建立一个坚实的基础，以判断一些现有的方法的适当性，并提供见解，导致未来的方法发展。在目前的项目中，研究人员评估的一类灵活和有用的统计模型的理论特性，称为变系数模型，并通过扩展他的理论结果，开发一类新的建模方法，是潜在的上级现有的在许多纵向设置。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，因此它们提供了能够完全基于数据得出统计推断的有价值的工具。这些工具使科学家、政策制定者和研究人员能够从数据中得出充分的结论，而不依赖于可能过于限制其环境的预先设定的假设。在与其他统计和生物医学研究人员的合作努力中，研究人员和他的同事通过将其应用于一些生物医学和流行病学研究来展示其方法的应用潜力，并讨论其研究结果的生物学意义。

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.