Maximum Likelihood Estimation of the Negative Binomial Dispersion Parameter for Highly Overdispersed Data, with Applications to Infectious Diseases

The negative binomial distribution is used commonly throughout biology as a model for overdispersed count data, with attention focused on the negative binomial dispersion parameter, k. A substantial literature exists on the estimation of k, but most attention has focused on datasets that are not hig...

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Vydáno v:PloS one Ročník 2; číslo 2; s. e180
Hlavní autor: Lloyd-Smith, James O.
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States Public Library of Science 14.02.2007
Public Library of Science (PLoS)
Témata:
Accuracy
Bias
Binomial Distribution
Biometrics
Communicable diseases
Computer Simulation
Confidence Intervals
Counting
Data analysis
Data collection
Datasets
Development and progression
Disease Outbreaks
Disease transmission
Disease Transmission, Infectious - statistics & numerical data
Dispersion
Ecology/Population Ecology
Ecology/Theoretical Ecology
Epidemics
Epidemiology
Humans
Infectious Disease Medicine - statistics & numerical data
Infectious diseases
Likelihood Functions
Mathematics/Statistics
Maximum likelihood estimates
Maximum likelihood estimation
Outbreaks
Parameter estimation
Parasites
Population Surveillance
Public Health and Epidemiology/Epidemiology
Public Health and Epidemiology/Infectious Diseases
Sample variance
Selection Bias
Simulation
Studies
Surveillance
ISSN:1932-6203, 1932-6203
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Shrnutí:The negative binomial distribution is used commonly throughout biology as a model for overdispersed count data, with attention focused on the negative binomial dispersion parameter, k. A substantial literature exists on the estimation of k, but most attention has focused on datasets that are not highly overdispersed (i.e., those with k>or=1), and the accuracy of confidence intervals estimated for k is typically not explored. This article presents a simulation study exploring the bias, precision, and confidence interval coverage of maximum-likelihood estimates of k from highly overdispersed distributions. In addition to exploring small-sample bias on negative binomial estimates, the study addresses estimation from datasets influenced by two types of event under-counting, and from disease transmission data subject to selection bias for successful outbreaks. Results show that maximum likelihood estimates of k can be biased upward by small sample size or under-reporting of zero-class events, but are not biased downward by any of the factors considered. Confidence intervals estimated from the asymptotic sampling variance tend to exhibit coverage below the nominal level, with overestimates of k comprising the great majority of coverage errors. Estimation from outbreak datasets does not increase the bias of k estimates, but can add significant upward bias to estimates of the mean. Because k varies inversely with the degree of overdispersion, these findings show that overestimation of the degree of overdispersion is very rare for these datasets.
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Conceived and designed the experiments: JL. Performed the experiments: JL. Analyzed the data: JL. Contributed reagents/materials/analysis tools: JL. Wrote the paper: JL.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0000180