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Incorporation of stochastic variability in mechanistic population pharmacokinetic models: handling the physiological constraints using normal transformations

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Abstract

The utilisation of physiologically-based pharmacokinetic models for the analysis of population data is an approach with progressively increasing impact. However, as we move from empirical to complex mechanistic model structures, incorporation of stochastic variability in model parameters can be challenging due to the physiological constraints that may arise. Here, we investigated the most common types of constraints faced in mechanistic pharmacokinetic modelling and explored techniques for handling them during a population data analysis. An efficient way to impose stochastic variability on the parameters of interest without neglecting the underlying physiological constraints is through the assumption that they follow a distribution with support and properties matching the underlying physiology. It was found that two distributions that arise through transformations of the normal, the logit-normal generalisation and the logistic-normal, are excellent for such an application as not only they can satisfy the physiological constraints but also offer high flexibility during characterisation of the parameters’ distribution. The statistical properties and practical advantages/disadvantages of these distributions for such an application were clearly displayed in the context of different modelling examples. Finally, a simulation study clearly illustrated the practical gains of the utilisation of the described techniques, as omission of population variability in physiological systems parameters leads to a biased/misplaced stochastic model with mechanistically incorrect variance structure. The current methodological work aims to facilitate the use of mechanistic/physiologically-based models for the analysis of population pharmacokinetic clinical data.

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Acknowledgments

N.T. was the recipient of a PhD grant jointly awarded by the University of Manchester and Eli Lilly and Company. A.R-H. is an employee of the University of Manchester and parttime secondee to Simcyp Limited (a Certara Company). The authors would like to acknowledge the discussions and fruitful comments made by Dr Alison Margolskee and by the members of the Centre for Applied Pharmacokinetic Research at the University of Manchester.

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Authors and Affiliations

  1. Centre for Applied Pharmacokinetic Research, Manchester Pharmacy School, University of Manchester, Stopford Building, Oxford Road, Manchester, M13 9PT, UK

    Nikolaos Tsamandouras, Thierry Wendling, Amin Rostami-Hodjegan, Aleksandra Galetin & Leon Aarons

  2. Simcyp Limited, Blades Enterprise Centre, Sheffield, UK

    Amin Rostami-Hodjegan

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  1. Nikolaos Tsamandouras
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  2. Thierry Wendling
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  5. Leon Aarons
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Correspondence to Nikolaos Tsamandouras.

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Tsamandouras, N., Wendling, T., Rostami-Hodjegan, A. et al. Incorporation of stochastic variability in mechanistic population pharmacokinetic models: handling the physiological constraints using normal transformations. J Pharmacokinet Pharmacodyn 42, 349–373 (2015). https://doi.org/10.1007/s10928-015-9418-0

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  • DOI: https://doi.org/10.1007/s10928-015-9418-0

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