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

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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.