Application of the Zero-Inflated Negative Binomial Distribution

• Activity Number: 538
• Type: Contributed
• Date/Time: Thursday, August 2, 2007 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Arlene Swern*+ and Hongwei Wang and Qian Dong and Eric C. Kleerup
• Companies: Merck & Co., Inc. and Merck & Co., Inc. and Merck & Co., Inc. and David Geffen School of Medicine at UCLA
• Keywords: distribution ; zero inflated Poisson ; count data ; overdispersion ; negative binomial ; zero modified

Abstract

Count data is typically modeled with a Poisson distribution. In real life settings however, the assumptions of this distribution are often violated because of too many or too few zero events or because of overdispersion. The zero-inflated negative binomial (ZINB) model and an extension, the zero-modified negative binomial (ZMNB) are proposed as a robust family of distributions for summarizing count data. These models are generalizations of the Poisson and negative binomial distributions, with parameters to handle the excess or deficit of zeroes and overdispersion. The amount of daily albuterol used as inhaled rescue medication is an important clinical measure of both the efficacy of asthma treatment and the extent of asthma control, but the Poisson distribution is not always appropriate. The application of the ZINB and ZMNB models to summarize this measure will be explored.