Section of Pharmacokinetics,
Department of Pharmacology,
Martin Luther University Halle-Wittenberg, 06097 Halle, Germany
Although the analysis of PK/PD data by mathematical models is now common practice, the design of the studies (including the collection of data) may be far from optimal. Is there a rational basis for design optimisation? In principle, we can obtain information from any observation; in practice, however, nobody performs experiments without having a model in mind (albeit not necessarily an explicit mathematical one). This is in accordance with information theory: the amount of information obtained from an experiment would vanish without having expectations about its outcome (Rescigno and Beck, 1987). Consequently, the question of how to design experiments cannot be answered without discussing the problem of model selection, the latter being dictated by the objectives and goals of the study. Experiment design and model selection are therefore closely interrelated. This implies that, in contrast to its common use in pharmacokinetics, the term ‘optimal experimental design’ should not be reduced to the application of optimal sampling theory, where both the structural and variance model as well as parameter values must be known (e.g., Kimko and Duffull, 2003). Since this condition is hardly fulfilled in most cases (where the goal of experiments is just to validate a model and to estimate parameters), one objective of this review is to demonstrate that optimal sampling is the last rather than the first step of an iterative procedure. Since the basic goal is identification of the PK/PD system, i.e., the unique estimation of model parameters, the conditions of a priori and a posteriori identifiability will determine the design of experiments. A poor experimental design can lead to model misspecification and inaccurate parameter estimates. In other words, we have to distinguish between a statistical and a PK/PD (or physiological) approach to study design optimisation. The latter is not only about when but also what and where to measure. In addition, the choice of the drug input schedule (single or multiple doses, infusion rate, route of administration) may play a critical role. One important point of the statistical approach to experiment design is the decision between a population and individual PK/PD study. Population analysis can provide important PK and PD information from sparse data.
Thus, the design of experiment involves the following factors:
- Choice of drug input function
- Choice of route of administration
- Choice of sampling site
- Choice of sampling scheme
- Choice of surrogate effects in PK/PD studies
-
Examples that demonstrate the importance of these factors include: (A) Estimation of the basic pharmacokinetic parameters clearance (CL) and steady-state volume of distribution (Vss). (B) Minimal sampling design to estimate CL. (C) Kinetics of metabolite formation. (D) Input rate dependency of amiodarone PK and digoxin PD (Weiss and Kang, 2004). (E) Arterial vs. peripheral venous sampling, where arterial sampling may have the paradoxical consequence of biased CL estimation when conventional PK models are applied (Weiss, 1997).
Both sensitivity analysis and model simulation have emerged as powerful tools for study design optimisation. Bayesian methods are very useful to incorporate a priory knowledge when the PK/PD system is not uniquely identifiable on the basis of available data. Finally, when the role of the other factors mentioned above has been clarified, optimal sampling schedules can be constructed using the D-or C-optimality criterion. The utility of these techniques will be demonstrated for the analysis of initial distribution PK (according to its central role in intravenous anaesthesia) using the ADAPT software (D’Argenio and Schumitzky, 1997). While frequent sampling within the first minutes after bolus injection is a prerequisite for the identification of recirculatory models including lung uptake kinetics (e.g., Boer, 2003), knowledge of cardiac output and/or the simultaneous administration of vascular markers may allow the analysis of minimal recirculatory models/initial distribution PK using more conventional sampling schedules (Weiss et al, 1996, Avram et al., 1990).
In conclusion, the results of many studies suggest that the use of optimised sampling schedules is both feasible and practical (e.g, Drusano et al., 1988). However, this statistically based strategy may be misleading if the underlying PK/PD model is not appropriate (i.e., design optimisation based on a non-optimal model). One extremely important factor is the choice of the sampling duration which depends on prior knowledge of the drug’s disposition characteristics.
Boer F. Drug handling by the lungs. Br J Anaesth 91:50-60 (2003)
D’Argenio DZ and Schumitzky A. ADAPT II User’s guide: Pharmacokinetic/ Pharmacodynamic Systems Analysis Software. Biomedical Simulations Resource, Los Angeles, 1997
Drusano GL, Forrest A, Snyder MJ, Reed MD, Blumer JL. An evaluation of optimal sampling strategy and adaptive study design. Clin Pharmacol Ther 44:232-238 (1988)
Henthorn TK, Avram MJ, Krejcie TC. Intravascular mixing and drug distribution: the concurrent disposition of thiopental and indocyanine green. Clin Pharmacol Ther 45: 56-65 (1989)
Kimko HC, Duffull,
SB (eds.). Simulation for designing clinical trials. A
pharmacokinetic-pharmacodynamic modeling perspective. Dekker, New York, 2003.
Rescigno A, Beck JS.
The use and abuse of models. J Pharmacokinet Biopharm 15: 327-344 (1987)
Weiss M, Hübner GH, Hübner GI, Teichmann W. Effects of cardiac output on disposition kinetics of sorbitol: recirculatory modelling. Br J Clin Pharmacol 41: 261-268 (1996)
Weiss M. Errors in clearance estimation after bolus injection and arterial sampling: Non-existence of a central compartment. J Pharmacokin Biopharm 25: 255-260 (1997)
Weiss M, Kang W. Inotropic effect of digoxin in humans: mechanistic pharmacokinetic-pharmacodynamic model based on slow receptor binding. Pharm Res 21: 231-236 (2004)