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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.


Properties of the parameter λ. The plots represent how varying λ values between individuals or groups of individuals result in shifted probability mass functions (left panel, with three distributions) and shifted mean counts (right panel, stratified on treatment). Varying λ within individuals can also be revealed in the right panel with fluctuating means over time, here represented with their 95% prediction intervals.
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fig2: Properties of the parameter λ. The plots represent how varying λ values between individuals or groups of individuals result in shifted probability mass functions (left panel, with three distributions) and shifted mean counts (right panel, stratified on treatment). Varying λ within individuals can also be revealed in the right panel with fluctuating means over time, here represented with their 95% prediction intervals.

Mentions: This feature of the Poisson distribution is illustrated in Figure 2 (left panel) with three pmfs corresponding to three λ values. It can be observed that as λ increases: (i) the mean of the distribution shifts and the probability of zeros decreases, (ii) the function is less skewed and approximates a normal distribution, and (iii) the variance increases and higher counts are encountered.


Modeling and simulation of count data.

Plan EL - CPT Pharmacometrics Syst Pharmacol (2014)

Properties of the parameter λ. The plots represent how varying λ values between individuals or groups of individuals result in shifted probability mass functions (left panel, with three distributions) and shifted mean counts (right panel, stratified on treatment). Varying λ within individuals can also be revealed in the right panel with fluctuating means over time, here represented with their 95% prediction intervals.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig2: Properties of the parameter λ. The plots represent how varying λ values between individuals or groups of individuals result in shifted probability mass functions (left panel, with three distributions) and shifted mean counts (right panel, stratified on treatment). Varying λ within individuals can also be revealed in the right panel with fluctuating means over time, here represented with their 95% prediction intervals.
Mentions: This feature of the Poisson distribution is illustrated in Figure 2 (left panel) with three pmfs corresponding to three λ values. It can be observed that as λ increases: (i) the mean of the distribution shifts and the probability of zeros decreases, (ii) the function is less skewed and approximates a normal distribution, and (iii) the variance increases and higher counts are encountered.

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.