Analysis of overdispersed count data by mixtures of Poisson variables and
Poisson processes.
Philip Hougaard
Novo Nordisk
Bagsvaerd, Denmark
|
Mei-Ling Ting Lee
Harvard Medical School
Boston, U.S.A.
|
G. A. Whitmore
McGill University
Montreal, Canada
|
Abstract
Count data often show overdispersion compared to the Poisson distribution.
Overdispersion is typically modeled by a random effect for the mean, based on
the gamma distribution, leading to the negative binomial distribution for the
count. This paper considers a larger family of mixture distributions,
including
the inverse Gaussian mixture distribution. It is demonstrated that it gives a
significantly better fit for a data set on the frequency of epileptic
seizures.
The same approach can be used to generate counting processes from Poisson
processes, where the rate or the time is random. A random rate corresponds to
variation between patients, whereas a random time corresponds to variation
within patients.
Key words: Frailty; Inverse Gaussian; Mixture; Negative binomial; Power
variance
function
Mailing address: Philip Hougaard, Novo Nordisk, Bldg 9ES, Novo Alle, DK-2880
Bagsvaerd, Denmark. e-mail: pho@novo.dk, phone +45 4442 3595.