Helen Barnett

Pharmacokinetic (PK) studies (e.g. Kallen, 2008) are vital in drug development as they aim to understand how externally administered compounds are absorbed, distributed, metabolised and excreted. PK behaviour is typically assessed by measuring the substance’s concentration in the blood or plasma at a number of time points after administration. Based on these data a variety of PK parameters such as the area under the concentration versus time curve (AUC) are considered. To obtain accurate estimates of these parameters a large number of time points are sampled and complete sets of samples per subject are ideal. Non-linear mixed effects models (NMLE, Davidian & Giltinan, 2003) are then typically used to estimate the parameters of interest. Limitations in blood volume as well as ethical considerations, however, often prevent such rich sampling strategies. As an alternative, sparse sampling designs which sample subjects at some, but not all time points and are utilized.

Recent advances in technology have led to the development of micro-sampling techniques (e.g. capillary microsampling) which allow a more frequent sampling of patients due to the burden of each sample being smaller. The objective of this project is to develop designs for PK studies utilizing micro-sampling and specifically to:

  1. develop a structured approach to compare the accuracy and variability of rich sampling versus sparse sampling techniques;

  2. develop an adaptive design that allows the sampling times to be updated based on accumulating data;

  1. construct optimal designs for repeated dose toxicity studies.

The first aim of this project will develop a statistical framework that allows a formal comparison of PK estimates originating from different sampling strategies. When traditional sampling is used it is often appropriate to assume constant variability across all measured time points. For Micro-sampling techniques such an assumption is unlikely to hold as increased variability for low concentration values is expected. Flexible NLME models that allow for non-constant variability will therefore be developed. Subsequently we will investigate how to compare the accuracy and variability of the resulting PK estimates to those based on traditional sampling.

One of the main drawbacks of current PK designs is that optimal sampling times depend on the true, but unknown, concentration versus time curve. The second aim seeks to address this shortcoming by re-evaluating the sampling time points based on accumulating data in an adaptive fashion. Particular attention will be given to goodness of fit criteria for determining optimal time points and the potential bias in estimates that may be introduced by such an approach.

The final aim of this project will investigate the potential of micro-sampling in the context of studies in which the compound is given repeatedly over the period for a few weeks. Typically such studies only obtain concentration measures at the first and last day of the study despite the trajectory of the concentration level of the compound over time being of interest. The reduced burden of micro-sampling techniques opens the door to the assessment of the time course through sampling additional days. As in aim 2 we will explore an adaptive strategy that allows for the selection of the optimal days to be sampled to obtain the most accurate profile.


Davidian M, Giltinan MD. (2003) Nonlinear Models for Repeated Measurement Data. CRC.

Kallen A. (2007) Computational pharmacokinetics. CRC Press.

Helen Barnett
The MPS Research Unit
Department of Mathematics and Statistics
Fylde College; Lancaster University Lancaster, Lancashire LA1 4YF

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Research Interests

  • Pharmacokinetic studies
  • Modelling