A Likelihood Model for Dispersion in Longitudinal Count Data

• Activity Number: 178
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Stephanie Bruce*+ and Gary K. Grunwald and Luohua Jiang and Matthew Strand and Nathan Rabinovitch
• Companies: U.S. Air Force Academy and University of Colorado Denver and University of Colorado Denver and National Jewish Health and National Jewish Health
• Keywords: Generalized linear mixed models ; Multi-level count models ; Underdispersion

Abstract

Longitudinal data with count outcomes are common in health care. In addition to the typical challenges of subject heterogeneity, serial correlation, and missing or unequally spaced observations, longitudinally observed count outcomes are subject to probability distributions that are not easily specified. Underdispersion may occur in longitudinal data due to repetitive, habitual, or prescribed behaviours. We were motivated by data from a study of the association of air pollution with daily counts of asthma inhaler use by children during a school year. We developed a likelihood-based model for correlated count data that display under- or overdispersion within units. The model is based on a Generalized Linear Mixed Model with log link function and has a continuous time process that allows for missing or unequally spaced observations. A family of observation distributions based on birth event processes due to Faddy (1997) is used to model dispersion. We developed a Markov Chain Monte Carlo (MCMC) approach and use a tabling technique to overcome the parameterization difficulties encountered. This approach allows use of common MCMC software for estimation.