Zero-Modified Negative Binomial Distribution as a Robust Family for Modeling Count Data

• Activity Number: 233
• Type: Contributed
• Date/Time: Monday, August 3, 2009 : 2:00 PM to 3:50 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Qian Dong*+ and Hongwei Wang and Arlene Swern and Eric C. Kleerup
• Companies: Merck & Co., Inc. and Merck & Co., Inc. and Merck & Co., Inc. and University of California, Los Angeles
• Keywords: count data ; overdisperstion ; zero-modification ; Poisson distribution ; negative binomial

Abstract

Count data is very common in many disciplines and the Poisson regression model is often used to analyze such data. However, a limitation of the Poisson model is that it assumes the equality of the mean and the variance. In real life, this assumption may be violated because of too many or too few zeroes or due to increased variability. The zero-modified negative binomial (ZMNB) is proposed as a robust distribution with parameters to handle both the excess/deficit of zeros and overdispersion, which by definition includes Poisson, negative binomial, zero-modified Poisson and zero-inflated negative binomial as its special cases. To evaluate its performance, extensive simulation studies were conducted under a wide range of parameter settings. The proposed approach was also applied to data from two clinical trials to model the amount of daily albuterol used as rescue medication for asthma.