带信息观察时间和终止事件的纵向数据联合建模分析

Longitudinal data arise frequently in many fields such as biology, medicine, public health, ecology and environmental science, engineering, finance, economics and social sciences. The statistical modeling and analysis of longitudinal data are hot issues in current statistical research. In this project, we study a number of important semiparametric mean regression models, mixed effects models, single-index regression models, quantile regression models and varying coefficient models for longitudinal data with informative observation and terminal event times, and propose semiparametric joint modeling and analysis of such data, including the joint distribution modeling approach, the used-latent modeling approach, the conditional modeling approach and the variable selection problem. Furthermore, we make the statistical inference on the proposed models when the data are measured with error or missing. Finally, we apply the proposed methods to biology, medicine, public health, ecology and environmental science, engineering, finance, economics and social sciences, and solve some statistical problems. This project belongs to the research on fundamental theories and new methods, which has practical background and application prospect. It is one of the current topics of the basic research in statistical application, and has important theoretical significance and practical application value.

纵向数据经常出现在生物学、医学、公共卫生学、生态与环境科学、工程学、金融学、经济学和社会科学等领域，其统计建模和分析是当前统计学研究领域的热点问题。本项目主要是在带信息观察时间和终止事件的纵向数据下，针对一些重要的半参数均值回归模型、混合效应模型、单指标回归模型、分位点回归模型以及变系数模型等，进行半参数联合建模分析，包括联合分布建模、基于潜变量建模和条件建模以及变量选择等，并在测量具有误差或数据缺失的情况下进行各种半参数联合模型的统计推断。最后把所获得的统计方法用于生物学、医学、公共卫生学、生态与环境科学、工程学、金融学、经济学和社会学等实际中，解决相关的统计问题。本项目属于具有实际背景和应用前景的基础理论和新方法研究，是统计应用基础研究前沿的课题之一，具有重要的理论意义和实际应用价值。

纵向数据和复发事件数据等经常出现在生物学、医学、公共卫生学、生态与环境科学、工程学、金融学、经济学和社会科学等领域，其统计建模和分析是当前统计学研究领域的热点问题。本项目主要是在带信息观察时间和终止事件的纵向数据下，针对一些重要的半参数均值回归模型、混合效应模型、单指标回归模型、分位点回归模型以及变系数模型等，进行了半参数联合建模分析，包括联合分布建模、基于潜变量建模和条件建模以及变量选择等。同时也对相关的复发事件数据和删失数据以及其它复杂数据进行了统计建模分析，并用所得的统计方法分析了相关的实际数据。所获得的成果具有重要的理论意义和实际应用价值，其研究成果会对统计学及其交叉学科特别是生物统计领域的研究具有推动作用。本项目在J. Mach. Learn. Res., Statist. Sci., Biometrics, Stat. Methods Med. Res., Stat. Med., Statist. Sinica等国内外核心期刊已发表学术论文31篇。