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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

Dispersion plots. The left panel is a mean–variance plot and the right panel is a Poissonness plot. Each dot represents metrics of all counts for one individual on the left, and a metric for each possible count of one individual on the right. Each line consists in a linear regression of the dots belonging to the same model on the left and to the same individual on the right, and the additional dashed line on the left panel displays the identity. The dots on the right panel also have their 95% confidence interval represented and are colored black if the linear regression did not include this interval. The plots were produced from simulations with different models: Poisson, negative binomial (NB), generalized Poisson with a positive dispersion parameter (GP (δ >0)), and double Poisson (DP).
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fig3: Dispersion plots. The left panel is a mean–variance plot and the right panel is a Poissonness plot. Each dot represents metrics of all counts for one individual on the left, and a metric for each possible count of one individual on the right. Each line consists in a linear regression of the dots belonging to the same model on the left and to the same individual on the right, and the additional dashed line on the left panel displays the identity. The dots on the right panel also have their 95% confidence interval represented and are colored black if the linear regression did not include this interval. The plots were produced from simulations with different models: Poisson, negative binomial (NB), generalized Poisson with a positive dispersion parameter (GP (δ >0)), and double Poisson (DP).

Mentions: Graphically, when individual means and variances are plotted against each other, a linear relationship suggests that the condition is respected. Violations of the equidispersion assumption can be of two kinds: overdispersion or underdispersion. Overdispersion corresponds to cases of a variance greater than the mean for most of the population, and underdispersion to the opposite, a variance lower than the mean. In the mean–variance plot (Figure 3, left panel), these types of profiles are respectively situated above and below the identity line. Again, this may be impacted by a nonconstant λ, and thus, a stratification on time (e.g., by week in this daily record example) should be considered.


Modeling and simulation of count data.

Plan EL - CPT Pharmacometrics Syst Pharmacol (2014)

Dispersion plots. The left panel is a mean–variance plot and the right panel is a Poissonness plot. Each dot represents metrics of all counts for one individual on the left, and a metric for each possible count of one individual on the right. Each line consists in a linear regression of the dots belonging to the same model on the left and to the same individual on the right, and the additional dashed line on the left panel displays the identity. The dots on the right panel also have their 95% confidence interval represented and are colored black if the linear regression did not include this interval. The plots were produced from simulations with different models: Poisson, negative binomial (NB), generalized Poisson with a positive dispersion parameter (GP (δ >0)), and double Poisson (DP).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig3: Dispersion plots. The left panel is a mean–variance plot and the right panel is a Poissonness plot. Each dot represents metrics of all counts for one individual on the left, and a metric for each possible count of one individual on the right. Each line consists in a linear regression of the dots belonging to the same model on the left and to the same individual on the right, and the additional dashed line on the left panel displays the identity. The dots on the right panel also have their 95% confidence interval represented and are colored black if the linear regression did not include this interval. The plots were produced from simulations with different models: Poisson, negative binomial (NB), generalized Poisson with a positive dispersion parameter (GP (δ >0)), and double Poisson (DP).
Mentions: Graphically, when individual means and variances are plotted against each other, a linear relationship suggests that the condition is respected. Violations of the equidispersion assumption can be of two kinds: overdispersion or underdispersion. Overdispersion corresponds to cases of a variance greater than the mean for most of the population, and underdispersion to the opposite, a variance lower than the mean. In the mean–variance plot (Figure 3, left panel), these types of profiles are respectively situated above and below the identity line. Again, this may be impacted by a nonconstant λ, and thus, a stratification on time (e.g., by week in this daily record example) should be considered.

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