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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.


Visual predictive check for count data. Each panel represents the probability of observing a range of counts against time  The solid line is the median of the observed data and the ribbon the 95% confidence interval around the median (dotted line) of 500 simulations from a count model fitted to count data.
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fig7: Visual predictive check for count data. Each panel represents the probability of observing a range of counts against time The solid line is the median of the observed data and the ribbon the 95% confidence interval around the median (dotted line) of 500 simulations from a count model fitted to count data.

Mentions: Simulation-based evaluation remains nonetheless the gold-standard due to its ability to reliably depict several aspects—variability and structure—of the model efficiently. Based on a preferably high number of simulations potentially including uncertainty, a visual predictive check can, for instance, be produced. A visual predictive check typically displays percentiles of a dependent variable plotted against an independent variable both for observations and simulations, overlap of fitted data and simulated data is the goal. In the case of count data, the ordinate can be the number of events although its integer nature may alter the plot. A favored representation consists in plotting the proportions of counts within certain ranges. In Figure 7, these proportions are featured with regard to time. Other graphs to consider to complete the assessment include: a stratification on treatment and other important categorical covariates, a switch to dose on the x-axis if enough dose levels and to important continuous covariates, an adjustment of the count proportions to proportions of transition values between consecutive counts, and a replacement of the y-axis by the variance-to-mean ratio. Some software, like PsN,54 feature an automation tool generating the visual predictive check with simulations, autobinning, and percentile calculation being done with one command.55


Modeling and simulation of count data.

Plan EL - CPT Pharmacometrics Syst Pharmacol (2014)

Visual predictive check for count data. Each panel represents the probability of observing a range of counts against time  The solid line is the median of the observed data and the ribbon the 95% confidence interval around the median (dotted line) of 500 simulations from a count model fitted to count data.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig7: Visual predictive check for count data. Each panel represents the probability of observing a range of counts against time The solid line is the median of the observed data and the ribbon the 95% confidence interval around the median (dotted line) of 500 simulations from a count model fitted to count data.
Mentions: Simulation-based evaluation remains nonetheless the gold-standard due to its ability to reliably depict several aspects—variability and structure—of the model efficiently. Based on a preferably high number of simulations potentially including uncertainty, a visual predictive check can, for instance, be produced. A visual predictive check typically displays percentiles of a dependent variable plotted against an independent variable both for observations and simulations, overlap of fitted data and simulated data is the goal. In the case of count data, the ordinate can be the number of events although its integer nature may alter the plot. A favored representation consists in plotting the proportions of counts within certain ranges. In Figure 7, these proportions are featured with regard to time. Other graphs to consider to complete the assessment include: a stratification on treatment and other important categorical covariates, a switch to dose on the x-axis if enough dose levels and to important continuous covariates, an adjustment of the count proportions to proportions of transition values between consecutive counts, and a replacement of the y-axis by the variance-to-mean ratio. Some software, like PsN,54 feature an automation tool generating the visual predictive check with simulations, autobinning, and percentile calculation being done with one command.55

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.