Optimal Population Designs for Pk Models With Serial Sampling

Abstract

In various pharmaceutical applications, repeated measurements are taken from each subject, and model parameters are estimated from the collected data. Examples include dose response modeling and PK/PD studies with serial blood sampling, among others. The quality of the information in an experiment is reflected in the precision of estimates of model parameters, which is traditionally measured by their variance-covariance matrix. In this article, we concentrate on the example of a clinical PK study where multiple blood samples are taken for each enrolled patient, which leads to nonlinear mixed effects regression models with multiple responses. The sampling scheme for each patient is considered a multidimensional point in the space of admissible sampling sequences. We demonstrate how to optimize the precision of parameter estimates by finding the best number and allocation of sampling times. It is shown that a reduced number of samples may be taken without significant loss of precision of parameter estimates. Moreover, our approach allows for taking experimental costs into account, which leads to a more meaningful comparison of sampling schemes and to potential cost savings.

Design Optimization in Nonlinear Mixed Effects Models Using Cost Functions: Application to a Joint Model of Infliximab and Methotrexate Pharmacokinetics

“…Assuming the individual parameters θ are normally distributed, this expansion is equivalent to the one around β as in Gagnon and Leonov (2005). The statistical model can then be written as:…”

“…We now assume, following Mentré et al (1997) and Gagnon and Leonov (2005), that there is a cost incurred by each elementary design, which we denote ( ) …”

“…It is a block matrix depending on the approximated marginal expectation E and variance V of the observations: (Gagnon and Leonov (2005)). This matrix represents the average information matrix for one individual in design Ξ.…”

“…This expression has been extended for more complex models including fixed effects for the influence of covariates on the response and for an additional variability of the parameters of a given individual between several periods of treatment (Retout and Mentré (2003a)). Evaluation of M F using a first order expansion is also performed in Fedorov et al (2002) and Gagnon and Leonov (2005). Recently, an approximate M F has been proposed for multiple response models by Hooker and Vicini (2005) and Gueorguieva et al (2006) using the same first order linearisation of the model.…”

“…This problem has been introduced for single response models through the use of cost functions by Mentré et al (1997); Gagnon and Leonov (2005) illustrate and highlight the benefits of such an approach on a clinical PK study.…”