We discuss optimal experimental design issues for nonlinear models arising in dose response studies. The optimization is performed with respect to various criteria which depend on the Fisher information matrix. Special attention is given to models with a variance component that depends on unknown parameters.
WuCFJOptimal design for percentile estimation of a quantal-response curve. In: DodgeYFedorovVVWynnHP, eds. Optimal Design and Analysis of Experiments.Elsevier, North Holland; 1988: 213–223.
6.
SitterRRRobust designs for binary data. Biometrics.1992;48:1145–1155.
7.
WhiteLVThe Optimal Design of Experiments for Estimation in Nonlinear Model. Ph.D. Thesis, University of London; 1975.
8.
AbdelbasitKMPlackettRLExperimental design for binary data. J Am Stat Assoc.1983;40:90–98.
9.
MinkinS.Optimal designs for binary data. J Am Stat Assoc.1987;82:1098–1103.
10.
TorsneyBMusratiAKOn the construction of optimal designs with applications to binary response and to weighted regression models. In: MüllerWGWynnHPZhigljavskyAA, eds. Model-Oriented Data Analysis.Heidelberg, Germany: Physica-Verlag; 1993: 37–52.
11.
BeggCBKalishLATreatment allocation for nonlinear models in clinical trials: The logistic model. Biometrics.1984;40:409–420.
12.
KalishLAEfficient design for estimation of median lethal dose and quantal dose-response curves. Biometrics.1990;46:737–748.
13.
MinkinSKundhalK.Likelihood-based experimental design for estimation of ED50. Biometrics.1999;55:1030–1037.
14.
ChernoffH.Locally optimal designs for estimating parameters. Ann Math Stat.1953;24:586–602.
15.
BoxGEPHunterWGSequential design of experiments for nonlinear models. In: KorthJJ, ed. Proceedings of IBM Scientific Computing Symposium. White Plains, NY: IBM; 1965: 113–137.
16.
FedorovVVHacklP.Model-Oriented Design of Experiments.New York, NY: Springer-Verlag; 1997.
17.
ChalonerKVerdinelliI.Bayesian experimental design: A review. Stat Sci.1995;10:273–304.
18.
WongWKLachenbruchPATutorial in biostatistics. Designing studies for dose response. Stat Med.1996;15:343–359.
KarpinskiKFOptimality assessment in the enzyme-linked immunosorbent assay (ELISA). Biometrics.1990;46:381–390.
21.
HedayatASYanBPezuttoJMModeling and identifying optimum designs for fitting dose response curves based on raw optical data. J Am Stat Assoc.1997;92:1132–1140.
22.
KällénALarssonP.Dose response studies: How do we make them conclusive?Stat Med.1999;18:629–641.
23.
LindseyJKWangJByromWDJonesB.Modeling the covariance structure in pharmacokinetic crossover trials. J Biopharm Stat.1999;9(3):439–450.
VoneshEFChinchilliVMLinear and Nonlinear Models for the Analysis of Repeated Measurements.New York, NY: Marcel Dekker; 1997.
29.
BezeauMEndrenyiL.Design of experiments for the precise estimation of dose-response parameters: The Hill equation. J Theoretical Biology.1986;123:415–430.
30.
KieferJWolfowitzJ.The equivalence of two extremum problems. Canadian J Math.1960;12:363–366.
31.
GaffkeNMatharR.On a class of algorithms from experimental design. Optimization.1992;24:91–126.
32.
AtkinsonACCookRDD-optimum designs for heteroscedastic linear models. J Am Stat Assoc.1995;90(429):204–212.
33.
DowningDJFedorovVVLeonovSLExtracting information from the variance function: optimal design. In: AtkinsonACHacklPMüllerWG, eds. Proceedings of MODA-6 (Advances in Model-Oriented Design and Analysis) Conference. Heidelberg: Physica-Verlag; 2001: 45–52.
34.
CookDFedorovVVConstrained optimization of experimental design. Statistics.1995;26:129–178.
35.
SahmMSchwabeR.A note on optimal bounded designs. In: AtkinsonACBogackaBZhigljavskyA, eds. Optimum Design 2000.Dordrecht, The Netherlands: Kluwer; 2001: 131–140.
36.
TorsneyBMandaiS.Construction of constrained optimal designs. In: AtkinsonACBogackaBZhigljavskyA, eds. Optimum Design 2000.Dordrecht, The Netherlands: Kluwer; 2001: 141–152.
37.
HeiseMAMyersRHOptimal designs for bivariate logistic regression. Biometrics.1996;52:613–624.