Distribution-free Models for Longitudinal Count Data

Thesis (Ph.D.)--University of Rochester. School of Medicine and Dentistry. Dept. of Biostatistics and Computational Biology, 2009.Count response is common in behavioral, biomedical, psychosocial, and healthcare related research. The Poisson distribution is commonly used to model such responses. However, in practice, count data often exhibit variability exceeding that predicted by Poisson, a concept known as overdispersion. Data clustering is one of the primary factors responsible for this typical phenomenon. Also, in biomedical and psychosocial research, distributions of outcome often exhibit a preponderance of zeros. Again, the Poisson model is not appropriate for modeling such excess, or structural zeros. Like data clustering, the presence of structural zeros has been acknowledged as a serious problem for data analysis. In this thesis, we rst review existing approaches for modeling count response under overdispersion and in the presence of structural zeros and discuss their relative strengths and weaknesses, especially with respect to their limitations for longitudinal data analysis. We then propose a new class of distribution-free models for second- and higher-order moments and utilize this new class of models as a unifying framework to simultaneously address overdispersion and structural zeros when modeling count response within a longitudinal data setting. We discuss inference under complete data as well as under missing data for the two most popular missing data mechanisms. The approach is illustrated with real as well as simulated study data