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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.


Inhomogeneous model variables. The plot displays variables for two individuals. The “count” variable corresponds to observed data and the “hazard” to the function λ. The “cumulative hazard” and the “survival” function are quantities involved in the estimation, and scaled here to share the same y-axis.
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fig6: Inhomogeneous model variables. The plot displays variables for two individuals. The “count” variable corresponds to observed data and the “hazard” to the function λ. The “cumulative hazard” and the “survival” function are quantities involved in the estimation, and scaled here to share the same y-axis.

Mentions: Ordinary differential equations are, therefore, required most of the time in this family of models. Nevertheless, analytical solutions may be employed in some cases (e.g., the Weibull distribution). The parameter/function λ acts as hazard which accumulates over time. The likelihood of positive counts is set to the chosen pmf, while the likelihood of zero count is equal to the survivor function. The hazard, cumulative hazard, and survival were represented in Figure 6.


Modeling and simulation of count data.

Plan EL - CPT Pharmacometrics Syst Pharmacol (2014)

Inhomogeneous model variables. The plot displays variables for two individuals. The “count” variable corresponds to observed data and the “hazard” to the function λ. The “cumulative hazard” and the “survival” function are quantities involved in the estimation, and scaled here to share the same y-axis.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig6: Inhomogeneous model variables. The plot displays variables for two individuals. The “count” variable corresponds to observed data and the “hazard” to the function λ. The “cumulative hazard” and the “survival” function are quantities involved in the estimation, and scaled here to share the same y-axis.
Mentions: Ordinary differential equations are, therefore, required most of the time in this family of models. Nevertheless, analytical solutions may be employed in some cases (e.g., the Weibull distribution). The parameter/function λ acts as hazard which accumulates over time. The likelihood of positive counts is set to the chosen pmf, while the likelihood of zero count is equal to the survivor function. The hazard, cumulative hazard, and survival were represented in Figure 6.

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.