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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/7840

Title: An extended random-effects approach to modeling repeated, overdispersed count data
Authors: Molenberghs, Geert
Verbeke, Geert
Demetrio, Clarice G. B.
Issue Date: 2007
Publisher: SPRINGER
Citation: LIFETIME DATA ANALYSIS, 13(4). p. 513-531
Abstract: Non-Gaussian outcomes are often modeled using members of the so-called exponential family. The Poisson model for count data falls within this tradition. The family in general, and the Poisson model in particular, are at the same time convenient since mathematically elegant, but in need of extension since often somewhat restrictive. Two of the main rationales for existing extensions are (1) the occurrence of overdispersion, in the sense that the variability in the data is not adequately captured by the model's prescribed mean-variance link, and (2) the accommodation of data hierarchies owing to, for example, repeatedly measuring the outcome on the same subject, recording information from various members of the same family, etc. There is a variety of overdispersion models for count data, such as, for example, the negative-binomial model. Hierarchies are often accommodated through the inclusion of subject-specific, random effects. Though not always, one conventionally assumes such random effects to be normally distributed. While both of these issues may occur simultaneously, models accommodating them at once are less than common. This paper proposes a generalized linear model, accommodating overdispersion and clustering through two separate sets of random effects, of gamma and normal type, respectively. This is in line with the proposal by Booth et al. (Stat Model 3:179-181, 2003). The model extends both classical overdispersion models for count data (Breslow, Appl Stat 33:38-44, 1984), in particular the negative binomial model, as well as the generalized linear mixed model (Breslow and Clayton, J Am Stat Assoc 88:9-25, 1993). Apart from model formulation, we briefly discuss several estimation options, and then settle for maximum likelihood estimation with both fully analytic integration as well as hybrid between analytic and numerical integration. The latter is implemented in the SAS procedure NLMIXED. The methodology is applied to data from a study in epileptic seizures.
Notes: Hasselt Univ, Ctr Stat, Diepenbeek, Belgium. Katholieke Univ Leuven, Ctr Biostat, Louvain, Belgium. ESALQ, Piracicaba, SP, Brazil.Molenberghs, G, Hasselt Univ, Ctr Stat, Diepenbeek, Belgium.geert.molenberghs@uhasselt.be geert.verbeke@med.kuleuven.be clarice@carpa.ciagri.usp.br
URI: http://hdl.handle.net/1942/7840
DOI: 10.1007/s10985-007-9064-y
ISI #: 000251970800011
ISSN: 1380-7870
Category: A1
Type: Journal Contribution
Validation: ecoom, 2009
Appears in Collections: Research publications

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