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

纵向研究在许多研究领域中越来越常见，其决定性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，当涉及多变量或聚集的纵向数据时，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和基于社区或学校的干预研究。 这项建议开发了分析纵向研究产生的相关数据的方法。一个挑战是解决来自多变量/聚集的纵向数据的复杂的关联结构。所开发的方法基于混合过渡模型，其中簇内关联和截面关联由随机效应合并，而序列纵向关联则由过渡(马尔可夫)模型合并。设计标准是基于随机效应公式制定的。当空间集聚在种群混合的位置及其随时间的演变中都明显时，另一个挑战就出现了。一个鼓舞人心的例子是不列颠哥伦比亚省白松树反复感染象甲的研究。开发了一种空间分析方法，可以同时提供转换率的推断和处理数据中的多余零点。通常，从研究中收集的数据不仅包括对一个或多个纵向过程的重复测量，还包括感兴趣的事件时间的信息。这一建议还考虑了相关纵向过程和生存数据的联合分析方法，重点关注存在空间相关性和事件时间被间隔删失的复杂情况。上述项目在关节损害的关节炎研究、眼睛视力状况进展的眼科研究以及松毛虫侵袭和树木生长与死亡之间的关系的林业研究中得到了实质性的应用。

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.