New methodology for the analysis of correlated data arising from longitudinal studies

纵向研究在许多研究领域越来越普遍，其定义特征是在一段时间内对每个人进行重复测量。在纵向研究中，当涉及多变量或聚类纵向数据时，往往会出现更复杂类型的相关结构。例子包括纵向收集健康指标变量向量的医学研究以及基于社区或学校的干预研究。 该提案提出了纵向研究相关数据的分析方法。一个挑战是从多变量/聚类纵向数据中解决复杂的关联结构。开发的方法是基于混合过渡模型，其中的集群内和横截面的相关性被纳入随机效应和序列纵向相关性被纳入一个过渡（马尔可夫）模型。 设计标准是根据随机效应公式制定的。另一个挑战出现时，空间聚类是明显的人口混合物的位置和他们的演变随着时间的推移。激励的例子是一个研究复发象鼻虫感染白松在不列颠哥伦比亚省。空间分析的方法，可以同时提供推断的过渡率和处理多余的零的数据。通常，从研究中收集的数据不仅包括一个或多个纵向过程的重复测量，而且还包括感兴趣的事件时间的信息。该建议还考虑了相关纵向过程和生存数据的联合分析方法，重点是空间相关性和事件时间间隔删失的复杂情况。上述项目在关节损伤的关节炎研究、眼睛视力状况进展的眼科学研究以及松树甲虫攻击和树木生长与死亡率之间关系的林业研究中具有实质性应用。

Longitudinal studies are increasingly common in many areas of research with the defining characteristic of repeated measurements from each individual over a period of time. Frequently, more complex types of correlation structure arise in the longitudinal studies when multivariate or clustered longitudinal data are involved. Examples include medical studies where a vector of health indicator variables are collected longitudinally and community or school based intervention studies. This proposal develops methods for the analysis of correlated data arising from longitudinal studies. One challenge is to address the complex association structure from the mutlivariate/clustered longitudinal data. The methods developed are based on mixed transitional models, where the intra-cluster and cross-sectional correlations are incorporated by random effects and serial longitudinal correlation is incorporated by a transition (Markov) model. Design criteria are developed based on random effect formulations. Another challenge arises when the spatial clustering is evident both in the placement of the population mixtures and their evolution over time. The motivating example is a study of recurrent weevil infection in white pine in British Columbia. Methods for spatial analysis which can simultaneously provide inference for transition rates and handle the excess zeros in the data are developed. Often, data collected from studies include not only repeated measurements of one or more longitudinal processes, but also include information for an event time of interest. This proposal also considers methods for the joint analysis of correlated longitudinal processes and survival data, with focus on the complicate situations where there are spatial correlations and event times are interval censored. The above projects find substantive applications in arthritis studies of joint damage, in ophthalmology studies of progression of eye vision condition and, in forestry studies of pine beetle attacks and relationship between growth and mortality of trees.