Challenges in transitional analysis of longitudinal data

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Longitudinal studies frequently involve monitoring dynamic processes, and transitional models are most appropriate when scientific interest lies in characterizing the rates of transitions between states in the processes. Examples include the progression of a chronic disease, the onset and resolution of episodic conditions and behavior change in health promotion studies. This proposal develops efficient methods for the transitional analysis of longitudinal data with more complex types of association structures. Situations considered include clustered longitudinal data and spatially correlated longitudinal data. Statistical challenges in transitional analysis of these kinds of data lie in accommodating both longitudinal and cross-sectional associations for valid inferences. The methods are developed based on random-effects models where the association structure of the observed data is controlled by the form of the multivariate distribution for the random effects. Design criteria are developed based random effect formulations that are suitable for testing treatment effects. Unique challenges arise with transitional analysis of longitudinal data when missing values exist. This proposal also considers methods to handle both monotone and intermittent missing data patterns in the multivariate and clustered longitudinal data setting. In addition, given that the primary assumption in most transitional methods is that the process follows a Markov chain with a certain order, this proposal derives score-based tests for the order of the Markov chain based on the robust approach of using estimating functions.   These projects find substantive applications in school-based prevention studies on changes in smoking behaviors, in ophthalmology studies of the progression of vision conditions for two eyes and, in BC Forestry studies of the attacks of mountain pine beetle.