Math. Model. Nat. Phenom.
Volume 11, Number 6, 2016Pharmacokinetics-Pharmacodynamics
|Page(s)||9 - 27|
|Published online||04 January 2017|
Parameter Estimation Using Unidentified Individual Data in Individual Based Models
Center for Research in Scientific Computation, North Carolina State University Raleigh, NC 27695-8212 USA
* Corresponding author. E-mail: firstname.lastname@example.org
In physiological experiments, it is common for measurements to be collected from multiple subjects. Often it is the case that a subject cannot be measured or identified at multiple time points (referred to as unidentified individual data in this work but often referred to as aggregate population data [5, Chapter 5]). Due to a lack of alternative methods, this form of data is typically treated as if it is collected from a single individual. This assumption leads to an overconfidence in model parameter values and model based predictions. We propose a novel method which accounts for inter-individual variability in experiments where only unidentified individual data is available. Both parametric and nonparametric methods for estimating the distribution of parameters which vary among individuals are developed. These methods are illustrated using both simulated data, and data taken from a physiological experiment. Taking the approach outlined in this paper results in more accurate quantification of the uncertainty attributed to inter-individual variability.
Mathematics Subject Classification: 92C45 / 34F05 / 49N45
Key words: pharmacokinetics / pharmacodynamics / physiological based pharmacokinetic modeling / inter-individual parameter variability / uncertainty quantification / random differential equations / distribution estimation / Prohorov metric framework / aggregate population data
© EDP Sciences, 2016
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