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Modeling and simulation of count data.

Plan EL - CPT Pharmacometrics Syst Pharmacol (2014)

Bottom Line: Count data, or number of events per time interval, are discrete data arising from repeated time to event observations.Their mean count, or piecewise constant event rate, can be evaluated by discrete probability distributions from the Poisson model family.Consideration is given to overdispersion, underdispersion, autocorrelation, and inhomogeneity.

View Article: PubMed Central - PubMed

Affiliation: 1] Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden [2] Pharmetheus, Uppsala, Sweden.

ABSTRACT
Count data, or number of events per time interval, are discrete data arising from repeated time to event observations. Their mean count, or piecewise constant event rate, can be evaluated by discrete probability distributions from the Poisson model family. Clinical trial data characterization often involves population count analysis. This tutorial presents the basics and diagnostics of count modeling and simulation in the context of pharmacometrics. Consideration is given to overdispersion, underdispersion, autocorrelation, and inhomogeneity.

No MeSH data available.


Nonequidispersed distributions. The same distribution density issued from a Poisson model (λ = 3) is plotted on both panels, together with two models for underdispersion (narrower distributions) on the left panel and two models displaying overdispersion (wider distributions) on the right panel. The explored models are double Poisson (DP) (υ = 3), generalized Poisson (GP) (δ = −0.75 and 0.50), and negative binomial (NB) ( = 0.75).
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fig4: Nonequidispersed distributions. The same distribution density issued from a Poisson model (λ = 3) is plotted on both panels, together with two models for underdispersion (narrower distributions) on the left panel and two models displaying overdispersion (wider distributions) on the right panel. The explored models are double Poisson (DP) (υ = 3), generalized Poisson (GP) (δ = −0.75 and 0.50), and negative binomial (NB) ( = 0.75).

Mentions: Negative binomial model. The negative binomial (NB) model,22,23 also sometimes referred to as the inverse binomial model, is the main alternative to the Poisson model in case of overdispersion (Figure 4, right panel). It uses a supplementary parameter, (omicron), responsible for an increased variability compared with the mean counts. This overdispersion parameter belongs to the range ∈ (0,∞), but values below 1 are generally sufficient. The discrete probability distribution (Eq. 9) still has a mean of E(Yij) = λ, while the variance is now Var(Yij) = λi(1+ i·λi).


Modeling and simulation of count data.

Plan EL - CPT Pharmacometrics Syst Pharmacol (2014)

Nonequidispersed distributions. The same distribution density issued from a Poisson model (λ = 3) is plotted on both panels, together with two models for underdispersion (narrower distributions) on the left panel and two models displaying overdispersion (wider distributions) on the right panel. The explored models are double Poisson (DP) (υ = 3), generalized Poisson (GP) (δ = −0.75 and 0.50), and negative binomial (NB) ( = 0.75).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4150925&req=5

fig4: Nonequidispersed distributions. The same distribution density issued from a Poisson model (λ = 3) is plotted on both panels, together with two models for underdispersion (narrower distributions) on the left panel and two models displaying overdispersion (wider distributions) on the right panel. The explored models are double Poisson (DP) (υ = 3), generalized Poisson (GP) (δ = −0.75 and 0.50), and negative binomial (NB) ( = 0.75).
Mentions: Negative binomial model. The negative binomial (NB) model,22,23 also sometimes referred to as the inverse binomial model, is the main alternative to the Poisson model in case of overdispersion (Figure 4, right panel). It uses a supplementary parameter, (omicron), responsible for an increased variability compared with the mean counts. This overdispersion parameter belongs to the range ∈ (0,∞), but values below 1 are generally sufficient. The discrete probability distribution (Eq. 9) still has a mean of E(Yij) = λ, while the variance is now Var(Yij) = λi(1+ i·λi).

Bottom Line: Count data, or number of events per time interval, are discrete data arising from repeated time to event observations.Their mean count, or piecewise constant event rate, can be evaluated by discrete probability distributions from the Poisson model family.Consideration is given to overdispersion, underdispersion, autocorrelation, and inhomogeneity.

View Article: PubMed Central - PubMed

Affiliation: 1] Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden [2] Pharmetheus, Uppsala, Sweden.

ABSTRACT
Count data, or number of events per time interval, are discrete data arising from repeated time to event observations. Their mean count, or piecewise constant event rate, can be evaluated by discrete probability distributions from the Poisson model family. Clinical trial data characterization often involves population count analysis. This tutorial presents the basics and diagnostics of count modeling and simulation in the context of pharmacometrics. Consideration is given to overdispersion, underdispersion, autocorrelation, and inhomogeneity.

No MeSH data available.