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Abstract:
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Longitudinal studies have long been recognized as important for understanding growth and aging processes. It has been suggested that the progression of Alzheimer's Disease results from an interplay between brain damage and cognitive function decline. However, brain damage is more difficult to measure directly due to physical constraints, timing of introduction of new technology or cost, and thus observations of brain damage may be limited. We are interested in analyzing the correlated processes, where the cognitive process is well observed but the pathology process is systematically missing. We consider three cases of missingness. First, pathology measure is only available post-mortem. Second, two measures of pathology are available at the beginning and the end of the process. Last, pathology measures are only given at a few chances to the end. Under each setting of pathology measure, we propose a family of mixed effects models with constraints. Simulation results and asymptotic properties are used to assess the models and estimation procedures developed. Model performances and the criteria in model selection are discussed in real data applications.
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