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 illustrative example, we investigate robustness properties of the multiple-objective optimal designs to mis-specification of the nominal values of the parameters. It is shown that misspecifications in the nominal values can influence the model profile, with some parameters having a stronger influence than others. Our numerical results also show that locally multiple-objective optimal designs have different level of sensitivities under different optimality criteria.
LandawEMOptimal Experimental Design for Biologic Compartmental Systems with Applications of Pharmacokinetics. Doctorate dissertation. Los Angeles, CA: University of California, Los Angeles; 1980.
2.
SilveySDOptimal Design.London: Chapman and Hall; 1980.
3.
WuG.Sensitivity Analysis of Pharmacokinetic Parameters in One Compartment models. Pharmacolog Res.2000;41(4):445–453.
4.
HuangYCMultiple-Objective Optimal Designs. Doctorate Dissertation in Public Health, Los Angeles, CA: University of California, Los Angeles, Department of Prostatitis; 1996.
5.
HanC.Optimal Designs for Nonlinear Regression Models with Applications to HIV Dynamic Studies. Doctorate Dissertation. Minneapolis, MN: University of Minnesota; 2002.
6.
CookRDWongWKOn the equivalence of constrained and compound optimal designs. J Am Stat Assoc.1994;89:687–692.
7.
HuangYCWongWKSequential construction of multiple-objective optimal designs. Biometrics.1998;54:1388–1397.
8.
ZengQZhuWWongWKDual-objective Bayesian optimal designs for a dose-ranging study. Drug Inf J.2000;34:421–428.
9.
WongWKRecent advances in constrained optimal design strategies. Stat Neerlandica.1999;53: 257–276.
10.
ChernoffH.Locally optimal designs for estimating parameters. Ann Math Stat.1953;24: 586–602.
MetzlerCMUsefulness of the two-compartment open model in pharmacokinetics. IJ Am Stat Assoc.1971;66:49–54.
13.
NotariRE“Introduction,” in Biopharmaceutics and Clinical Pharmacokinetics.New York and Basel: Marcel Dekker, Inc.; 1980.
14.
KieferJ.Optimum experimental designs. J Royal Stat Soc, Series B.1959;21:272–319.
15.
PukelsheimFRiederS.Efficient rounding of approximate designs. Biometrika.1992;79:763–770.
16.
ImhofLWongWKA graphical method for finding maximin designs. Biometrics.2000;56: 113–117.
17.
RowlandMTozerTNClinical Pharmacokinetics: Concepts and Applications.2nd edition. Philadelphia, PA: Lea and Febiger; 1989.
18.
WagnerJGFundamentals of Clinical Pharmacokinetics.Hamilton, ILL: Drug Intelligence Publications, Inc.; 1975.
19.
DetteHWongWKOptimal designs when the variance is a function of the mean. Biometrics.1999;55:925–929.
20.
MerleYMentreFMalletAAurengoAHDesigning an optimal experiment for bayesian estimation: Application to the kinetics of iodine thyroid uptake. Stat Med.1994;13:185–196.
