Comparison Of Negative-Binomial And Extra-Poisson Models For Over-Dispersed Count Data: A Simulation-Based Study

• Activity Number: 78
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Yaming Chen and Xiaochun Zhu*+ and John Connett
• Companies: Center for International Blood & Marrow Transplant Research and University of Minnesota at Twin Cities and University of Minnesota at Twin Cities
• Keywords: Extra-Poisson ; over-dispersion ; count data ; Negative-Binomial

Abstract

Modeling count data is a hot topic in clinical trials and epidemiological studies. In reality, over-dispersion is often observed and the Negative-binomial (Neg-bin) model is often used in such situation. However, the performance of the Neg-bin model varies in existence of different underlying data distributions. Breslow (1984) proposed the Extra-Poisson (Ext-Poi) variation model, which has no pre-assumed distribution for the heterogeneity term. In this study, we simulated homogeneous Poisson processes under two distributions, one with the heterogeneity term following a normal distribution, and the other with the heterogeneity term following a gamma distribution. The simulated data under these two distributions were analyzed by both Neg-bin and Ext-Poi regressions. Based on our study, the Ext-Poi method is almost as powerful as Neg-bin model when the true distribution is Neg-bin. The Ext-Poi method yields appropriate Type I error rates for both situations. However, the Neg-Bin method can have excessively high Type I error rates when the data have Poisson-log-normal distribution. That is, the Ext-Poi method appears to be more robust than the Neg-bin method.