title: Analysis of overdispersed count data by mixtures of Poisson variables and Poisson processes.
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.
authors.affiliation: Novo Nordisk, Bagsvaerd, Denmark.
authors.forename: P
authors.initials: P
authors.lastname: Hougaard
authors.forename: M L
authors.initials: ML
authors.lastname: Lee
authors.forename: G A
authors.initials: GA
authors.lastname: Whitmore
mesh_terms: D000927:Anticonvulsants / Q000627:therapeutic use; D001699:Biometry / Q000379:methods*; D004827:Epilepsy / Q000188:drug therapy / Q000503:physiopathology; D006801:Humans; D016013:Likelihood Functions; D016011:Normal Distribution; D016012:Poisson Distribution; D011336:Probability; D012640:Seizures / Q000188:drug therapy / Q000503:physiopathology; D016008:Statistical Distributions; D005680:gamma-Aminobutyric Acid / Q000031:analogs & derivatives / Q000627:therapeutic use
chemical_list: D000927:Anticonvulsants; C017985:progabide; D005680:gamma-Aminobutyric Acid