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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.


Related in: MedlinePlus

Serial correlated counts. A population displaying correlation between consecutive observations (Markov Poisson) is represented in comparison with a simulation from a Poisson model (assuming independence between counts). The left panel investigates the correlation between neighboring counts with the dots representing the counts and the solid lines the linear regressions (dash line is identity line). In the right panel four individuals are exhibited, with slowly varying profiles in the Markov population and highly fluctuating curves in the vanilla Poisson simulations.
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fig5: Serial correlated counts. A population displaying correlation between consecutive observations (Markov Poisson) is represented in comparison with a simulation from a Poisson model (assuming independence between counts). The left panel investigates the correlation between neighboring counts with the dots representing the counts and the solid lines the linear regressions (dash line is identity line). In the right panel four individuals are exhibited, with slowly varying profiles in the Markov population and highly fluctuating curves in the vanilla Poisson simulations.

Mentions: Dependence between events can be diagnosed by scrutinizing the data. A simple way to visualize dependence is to plot consecutive observations against each other (Figure 5, left panel). A linear regression line can indicate in which fashion their dependence occurs. Individual profiles (Figure 5, right panel) may also support independence invalidation, since within-individual dependence in biomedical observations is likely to be expressed as trains of similar values. Correlations may be involved if the displayed time courses are smoother than when generated under an independence assumption.


Modeling and simulation of count data.

Plan EL - CPT Pharmacometrics Syst Pharmacol (2014)

Serial correlated counts. A population displaying correlation between consecutive observations (Markov Poisson) is represented in comparison with a simulation from a Poisson model (assuming independence between counts). The left panel investigates the correlation between neighboring counts with the dots representing the counts and the solid lines the linear regressions (dash line is identity line). In the right panel four individuals are exhibited, with slowly varying profiles in the Markov population and highly fluctuating curves in the vanilla Poisson simulations.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig5: Serial correlated counts. A population displaying correlation between consecutive observations (Markov Poisson) is represented in comparison with a simulation from a Poisson model (assuming independence between counts). The left panel investigates the correlation between neighboring counts with the dots representing the counts and the solid lines the linear regressions (dash line is identity line). In the right panel four individuals are exhibited, with slowly varying profiles in the Markov population and highly fluctuating curves in the vanilla Poisson simulations.
Mentions: Dependence between events can be diagnosed by scrutinizing the data. A simple way to visualize dependence is to plot consecutive observations against each other (Figure 5, left panel). A linear regression line can indicate in which fashion their dependence occurs. Individual profiles (Figure 5, right panel) may also support independence invalidation, since within-individual dependence in biomedical observations is likely to be expressed as trains of similar values. Correlations may be involved if the displayed time courses are smoother than when generated under an independence assumption.

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.


Related in: MedlinePlus