Compound Optimum Designs in Pharmacokinetics
by
A.C. Atkinson
London School of Economics

Optimum designs for features of a model often have very poor properties for estimation of the parameters in the chosen model. A nonlinear example from pharmacokinetics is the three-parameter compartmental model, often used to model the time trace of the concentration of a drug in the blood of an animal, human or not. Possible features of interest include the area under the curve and the time to maximum concentration, for both of which the c-optimum designs have two support points. These designs both therefore have zero efficiency for estimation of the parameters of the model. The talk will describe the use of a weighted product of D-efficiency for parameter estimation and c-efficiency for feature estimation to define a compound design criterion which satisfies the convexity conditions of optimum experimental design. This criterion is called CD-optimality. The adjustable weighting parameter is chosen to give designs with good efficiencies both for parameter estimation and for estimation of the features of interest.

An equivalence theorem for CD-optimality will be presented that can be used in the construction of designs and in checking their optimality. Numerical examples of designs will be given and the properties of simple approximate hybrid designs explored.

Date received: June 29, 2006