Zero-Inflated Poisson and Negative Binomial Models Applied to the Analysis of Colorectal Polyp Prevention Trial Data

• Activity Number: 522
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Christopher Davidson*+ and Chiu-Hsieh Hsu
• Companies: University of Arizona and University of Arizona
• Keywords: Poisson ; Negative-Binomial ; Zero-inflated ; ZIP ; ZINB ; GLM

Abstract

Colorectal polyp prevention trials (PPTs) are conducted to evaluate some chemo-preventive agent in reducing the recurrence rate of adenomas where participants are followed for at least 3 years. A large proportion of zero counts will likely be observed at the end of observation. Poisson regression models are usually fitted to the number of recurrent adenoma data to estimate the recurrence rate. In a situation with excessive zeros, Poisson regression models could produce inconsistent recurrence rate estimates. To seek alternative models, we applied a class of models, including negative binomial GLM, zero-inflated Poisson (ZIP) and negative binomial (ZINB) models, to a large PPT dataset previously studied using a Poisson regression model. Overdispersion was evaluated using dispersion statistics and fit was assessed using AIC and BIC. Models were compared using likelihood ratio tests or the Vuong test. Zero-inflation in the ZIP model was assessed using tests proposed by Ridout et al (2001). The negative binomial GLM and ZIP models provided superior fit to the data compared with the Poisson GLM, thus providing a compelling reason to utilize these methods for the analysis of PPTs.