Pharmacokinetic parameters estimation using adaptive Bayesian P-splines models

In preclinical and clinical experiments, pharmacokinetic (PK) studies are designed to analyse the
evolution of drug concentration in plasma over time i.e. the PK profile. Some PK parameters are
estimated in order to summarize the complete drug’s kinetic profile: area under the curve (AUC),
maximal concentration (Cmax), time at which the maximal concentration occurs (tmax) and half-life
time (t1/2).
Several methods have been proposed to estimate these PK parameters. A first method relies on
interpolating between observed concentrations. The interpolation method is often chosen linear. This
method is simple and fast. Another method relies on compartmental modelling. In this case, nonlinear
methods are used to estimate parameters of a chosen compartmental model. This method provides
generally good results. However, if the data are sparse and noisy, two difficulties can arise with this
method. The first one is related to the choice of the suitable compartmental model given the small
number of data available in preclinical experiment for instance. Second, nonlinear methods can fail to
converge. Much work has been done recently to circumvent these problems (J. Pharmacokinet.
Pharmacodyn. 2007; 34:229–249, Stat. Comput., to appear, Biometrical J., to appear, ESAIM P&S
2004; 8:115–131).
In this paper, we propose a Bayesian nonparametric model based on P-splines. This method
provides good PK parameters estimation, whatever be the number of available observations and the
level of noise in the data. Simulations show that the proposed method provides better PK parameters
estimations than the interpolation method, both in terms of bias and precision. The Bayesian nonparametric method provides also better AUC and t1/2 estimations than a correctly specified
compartmental model, whereas this last method performs better in tmax and Cmax estimations.
We extend the basic model to a hierarchical one that treats the case where we have concentrations
from different subjects. We are then able to get individual PK parameter estimations. Finally, with
Bayesian methods, we can get easily some uncertainty measures by obtaining credibility sets for each
PK parameter.