A Generalized Poisson-Gamma Model for Spatially Overdispersed Data When Modeling Counts Multivariately

• Activity Number: 137
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Thomas Neyens*+ and Christel Faes and Geert Molenberghs
• Companies: I-Biostat and I-Biostat and I-BioStat/Universiteit Hasselt/Katholieke Universiteit Leuven
• Keywords: Multivariate Modeling ; Disease Mapping ; Overdispersion ; Poisson-Gamma ; Spatially Structured Prior ; Conditional Autoregressive Model

Abstract

When modeling count data with spatially structured and unstructured extra-Poisson variance, a number of bayesian methods exist to model relative risks within areas. The conditional autoregressive (CAR) convolution model is popular. Recently, an alternative model was proposed, combining the Poisson-gamma model with a CAR prior. The latter model was shown to have interesting conjugacy characteristics, but also to behave superiorly to the CAR convolution model in certain settings. Less solutions exist for the bi- or multivariate case (on the county level). Furthermore, all proposed models are based on the CAR convolution model. Here we make multivariate extensions of the combined model in accordance to existing multivariate models. Both traditional and newly proposed models were applied to the Limburg cancer data and fits were compared, while different estimation methods were investigated too. The combined model constitutes an interesting model when the data have a large amount of spatially unstructured overdispersion, mostly seen when diseases are abundant. This model can operate as an efficient alternative to the popular CAR convolution model in both uni- and multivariate settings.