Models for Serially Correlated Over or Underdispersed Unequally Spaced Longitudinal Count Data with Applications to Asthma Inhaler Use

摘要

This research focuses on longitudinal count data methods that do not conform to the well-behaved properties of normality. Potential complications that can arise with longitudinal count data are serial correlation, subject heterogeneity, underdispersion (or overdispersion), and unequally spaced or missing data. Many of the current models in the literature address one or two of the potential complications, but currently there is not a model that addresses all of the complications listed previously, so our goal, given enough data, was to develop a model capable of accommodating all the listed complications. We applied this model to a National Jewish Medical and Research Center study of asthma inhaler use in asthmatic children during school. Using a likelihood based approach, the data were clearly underdispersed relative to the Poisson distribution so a generalized Poisson process was used. Physical activity was the most influential independent variable resulting in a decrease of inhaler usage when the children did not participate in gym class.