A statistical model for under- or overdispersed clustered and longitudinal count data

• Published in: Biometrical journal Vol. 53; no. 4; pp. 578 - 594
• Main Authors: Grunwald, Gary K., Bruce, Stephanie L., Jiang, Luohua, Strand, Matthew, Rabinovitch, Nathan
• Format: Journal Article
• Language: English
• Published: Weinheim WILEY-VCH Verlag 01.07.2011; WILEY‐VCH Verlag; Wiley-VCH
• Subjects: Air Pollution - adverse effects; Applications; Asthma - therapy; Biology, psychology, social sciences; Child; Cluster Analysis; Distribution theory; Exact sciences and technology; General topics; Generalized linear mixed models; Humans; Longitudinal Studies - statistics & numerical data; Markov Chains; Mathematics; Models, Statistical; Monte Carlo Method; Multi-level count models; Multivariate analysis; Nebulizers and Vaporizers - statistics & numerical data; Negative binomial longitudinal data; Poisson longitudinal data; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Software; Statistics; Underdispersion; Biometrics; Generalized linear model; Generalized linear mixed models; Statistical distribution; Overdispersion; Cluster analysis (statistics); Negative binomial longitudinal data; Underdispersion; Daily variation; Serial correlation; Multivariate analysis; Stochastic method; Parameterization; Negative binomial distribution; Markov chain; Heterogeneity; Distribution function; Approximation theory; Multi-level count models; Child; Human; Monte Carlo method; Discriminant analysis; Poisson longitudinal data; Estimation; Life science; Statistical association; Birth process; Statistical method; Missing data; Numerical analysis; Correlation analysis; Statistical model; Software
• ISSN: 0323-3847; 1521-4036; 1521-4036
• DOI: 10.1002/bimj.201000076

We propose a likelihood‐based model for correlated count data that display under‐ or overdispersion within units (e.g. subjects). The model is capable of handling correlation due to clustering and/or serial correlation, in the presence of unbalanced, missing or unequally spaced data. A family of distributions based on birth‐event processes is used to model within‐subject underdispersion. A computational approach is given to overcome a parameterization difficulty with this family, and this allows use of common Markov Chain Monte Carlo software (e.g. WinBUGS) for estimation. Application of the model to daily counts of asthma inhaler use by children shows substantial within‐subject underdispersion, between‐subject heterogeneity and correlation due to both clustering of measurements within subjects and serial correlation of longitudinal measurements. The model provides a major improvement over Poisson longitudinal models, and diagnostics show that the model fits well.