Robustness Properties of Multiple-Objective Optimal Designs for a Bi-Exponential Model
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David Huang, DrPH Senior Statistician, Neuropsychiatric Institute, Integrated Substance Abuse Programs Weng Kee Wong, PhD Professor, Department of Biostatistics University of California, Los Angeles, Los Angeles, California
Key Words Approximate design; Compartmental model; Information matrix; D-optimality; Design efficiency; Locally optimal design Correspondence Address Weng Kee Wong. PhD, Professor, Department ofliostatistics, University of California, Los Angeles, 1640 S. Sepulveda Blvd., Suite 200, Los Angeles, CA 90095 (e-mail: wAwong9ucla.edu).
Robustness Properties of Multiple-Objective Optimal Designs for a Bi-Exponential Model
I N T R O D U CTI 0 N Modelling in pharmacokinetic studies usually assumes a nonlinear model with one independent variable. A simple example is the one exponential term model which describes how plasma concentration falls exponentially with time after a bolus dose is administered. Typically, the aim of these studies is to estimate the model parameters or some function of the model parameters, see, for example, Landaw (l),Silvey ( 2 ) and Wu (3). Designs for accomplishing such a task are motivated from practical experience with a similar drug or previous experiments from the same drug. Because drug studies are costly, it is important to choose a design carefully. Ideally, the design provides maximal information with minimal cost. Optimal designs are useful because they serve as a benchmark for comparing competing designs. Applications of optimal designs to pharmacokinetics are at least two decades old, but it appears that, to date, few designs used in pharmacokinetics are constructed partly or wholly based on statistical considerations. Examples of doctoral theses in optimal designs for pharmacokinetics applications using statistical ideas include Landaw (l),Huang (4), and Han (5). Landaw (1) designed optimal experiments for biologic compartmental systems and Han (5) found D- and c-optimal designs for exponential
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We first discuss a design strategy for constructing locally optimal designs when there are several competing objectives in the study Using a bi-exponential Compartmental model as an ilbtrative example, we investigate robu~tness properties of the multiple-objective optimal designs to mis-specification of the nominal values of the parameters. It is shown that misspecijlcations in the nominal values can influence the model profile, with some pammeters having a strong& influence than others. Our numm'd results also show that locally multiple-objective optimal designs have differentlevd of skitivities under different optimality criteria.
regression models used for studying pharmacokinetics and viral dynamics in AIDS patients. Because of the complexity of the problem, optimal designs are frequently constructed under a single optimality criterion. A popular design criterion for estimating parameters is D-optimality. Under normal error assumption, a D-optimal design minimizes the volume of the confidence ellipsoid of the parameters and so provides the most accurate estimate
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