2001
   Basel, Switzerland

Bayesian Optimal Design Applied to Mixed Effect Pharmacokinetic Models

Gordon Graham and Leon Aarons

Centre for Applied Pharmacokinetic Research, School of Pharmacy and Pharmaceutical Sciences, University of Manchester, Oxford Road, Manchester, M13 9PL, UK.

Research into design issues associated with experiments resulting in data analysed using mixed effect models have become prominent in recent years. Clinical trial simulation (Holford et al. 1999) has attempted to incorporate complex models into the design of clinical trials by simulating different design scenarios and considering the effect in fulfilling multi-objective criteria. From an alternative perspective, Mentré et al (1997) have attacked the problem by applying the D-optimal design criterion to random effects models. Both these methods have extended design techniques for complex modelling situations with clinical trial simulation being the more readily accepted.

A new approach to Bayesian optimal design has been described by Muller and Parmigiani (1995) in which a (Markov Chain) Monte Carlo sampling algorithm was implemented. This approach is used here in the context of nonlinear mixed effect pharmacokinetic models. Although not considered, such an approach could be used for non-normal likelihoods and population distributions resulting in a general framework for the optimal design of mixed effects model. Countering this generality is the main problem with any such simulation technique, computational burden which means that the detection of optimal decisions can be time consuming.

The examples presented here are simple pharmacokinetic models for which there are known results (at least in terms of fixed effect models). The utility function considered is the Kullback-Leibler distance (Lindley 1956). This has been shown to be asymptotically equivalent to the D-optimal design for a linear model with vague prior parameter information and the Bayesian D-optimal design for a nonlinear model. This is just one possible function that could be considered amongst many clinically relevant utility functions.

References:
N.H.G. Holford, M. Hale, H.C. Ko, J.-L. Steimer, L.B. Sheiner, C.C. Peck (Editors). Simulation in drug development: Good practices. Publication of CDDS, http://www.dml.georgetown.edu/cdds/sddgp723.html (1999).
D.V. Lindley. On a measure of the information provided by an experiment. Ann. Math. Statist., 27: 986-1005 (1956).
F. Mentré, A. Mallet, D. Baccar. Optimal design in random-effects regression models. Biometrika, 84: 429-442 (1997).
P. Muller, G. Parmigiani. Optimal design via curve fitting of Monte Carlo experiments. J. Am. Stat. Ass., 90: 1322-1330 (1995).