Locally D-optimal designs based on a class of composed models resulted from blending Emax and one-compartment models
X. Fang and A. S. Hedayat
Source: Ann. Statist. Volume 36, Number 1 (2008), 428-444.
Abstract
A class of nonlinear models combining a pharmacokinetic compartmental model and a pharmacodynamic Emax model is introduced. The locally D-optimal (LD) design for a four-parameter composed model is found to be a saturated four-point uniform LD design with the two boundary points of the design space in the LD design support. For a five-parameter composed model, a sufficient condition for the LD design to require the minimum number of sampling time points is derived. Robust LD designs are also investigated for both models. It is found that an LD design with k parameters is equivalent to an LD design with k−1 parameters if the linear parameter in the two composed models is a nuisance parameter. Assorted examples of LD designs are presented.
Primary Subjects: 62K05
Keywords: D-optimal design; pharmacokinetic compartmental model; pharmacodynamic Emax model; nonlinear model
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aos/1201877308
Digital Object Identifier: doi:10.1214/009053607000000776
Mathematical Reviews number (MathSciNet):
MR2387978
Zentralblatt MATH identifier:
1132.62056
References
Angus, B. J., Thaiaporn, I., Chanthapadith, K., Suputtamongkol, Y. and White, N. J. (2002). Oral artesunate dose-response relationship in acute falciparum malaria. Antimicrobial Agents and Chemotherapy 46 778–782.
Atkinson, A. C., Chaloner, K., Herzberg, A. M. and Juritz, J. (1993). Optimal experimental designs for properties of a compartmental model. Biometrics 49 325–337.
Davidian, M. and Gallant, A. (1992). Smooth nonparametric maximum likelihood estimation for population pharmacokinetics, with application to Quinidine. J. Pharmacokinetics and Biopharmaceutics 20 529–556.
Demana, P., Smith, E., Walker, R., Haigh, J. and Kanfer, I. (1997). Evaluation of the proposed FDA pilot dose-response methodology for topical corticosteroid bioequivalence testing. Pharmaceutical Research 14 303–308.
Dette, H. and Neugebauer, H.-M. (1997). Bayesian D-optimal designs for exponential regression models. J. Statist. Plann. Inference 60 331–349.
Mathematical Reviews (MathSciNet):
MR1456635
Digital Object Identifier: doi:10.1016/S0378-3758(96)00131-0
Fedorov, V. V. (1972). Theory of Optimal Experiments. Academic Press, New York.
Mathematical Reviews (MathSciNet):
MR403103
Graves, D., Muir, K., Richards, W., Steiger, B., Chang, I. and Patel, B. (1990). Hydralazine dose-response curve analysis. J. Pharmacokinetics and Biopharmaceutics 18 279–291.
Han, C. and Chaloner, K. (2003). D- and c-optimal designs for exponential regression models used in viral dynamics and other applications. J. Statist. Plann. Inference 115 585–601.
Mathematical Reviews (MathSciNet):
MR1985885
Digital Object Identifier: doi:10.1016/S0378-3758(02)00175-1
Han, C. and Chaloner, K. (2004). Bayesian experimental design for nonlinear mixed-effects models with application to HIV dynamics. Biometrics 60 25–33.
Mathematical Reviews (MathSciNet):
MR2043615
Digital Object Identifier: doi:10.1111/j.0006-341X.2004.00148.x
Hedayat, A. S., Zhong, J. and Nie, L. (2004). Optimal and efficient designs for 2-parameter nonlinear models. J. Statist. Plann. Inference 124 205–217.
Mathematical Reviews (MathSciNet):
MR2066235
Digital Object Identifier: doi:10.1016/S0378-3758(03)00196-4
Hedayat, A. S., Yan, B. and Pezzuto, J. M. (2002). Optimum designs for estimating EDp based on raw optical density data. J. Statist. Plann. Inference 104 161–174.
Mathematical Reviews (MathSciNet):
MR1900524
Digital Object Identifier: doi:10.1016/S0378-3758(01)00120-3
Hedayat, A. S., Yan, B. and Pezzuto, J. M. (1997). Modeling and identifying optimum designs for fitting dose-response curves based on raw optical density data. J. Amer. Statist. Assoc. 92 1132–1140.
Mathematical Reviews (MathSciNet):
MR1482144
Digital Object Identifier: doi:10.2307/2965578
JSTOR: links.jstor.org
Hedayat, A. (1981). Study of optimality criteria in design of experiments. In Statistics and Related Topics (M. Csorgo, D. A. Dawson, J. N. K. Rao and A. K. M. E. Saleh, eds.) 39–56. North-Holland, Amsterdam.
Mathematical Reviews (MathSciNet):
MR665266
Zentralblatt MATH:
0485.62072
Karlin, S. and Studden, W. J. (1966). Tchebyscheff Systems: With Applications in Analysis and Statistics. Wiley, New York.
Mathematical Reviews (MathSciNet):
MR204922
Zentralblatt MATH:
0153.38902
Kiefer, J. and Wolfowitz, J. (1960). The equivalence of two extremum problems. Cannid. J. Math. 12 363–366.
Mathematical Reviews (MathSciNet):
MR117842
Landaw, E. M. (1980). Optimal experimental design for biological compartmental systems with applications to pharmacokinetics. Ph.D. dissertation, UCLA, University Microfilms International.
Lindsey, J. K., Byrom, W. D., Wang, J., Jarvis, P. and Jones, B. (2000). Generalized nonlinear models for pharmacokinetic data. Biometrics 56 81–88.
Mallet, A. (1992). A nonparametric method for population pharmacokinetics: A case study. Amer. Statist. Assoc. Proceedings of the Biopharmaceutical Section 11–20.
Mandema, J. W., Verotta, D. and Sheiner, L. (1992). Building population pharmacokinetic pharmacodynamic models. I. Models for covariate effects. J. Pharmacokinetics and Biopharmaceutics 20 511–528.
Mentre, F., Mallet, A. and Baccar, D. (1997). Optimal design in random-effect regression models. Biometrika 84 429–442.
Mathematical Reviews (MathSciNet):
MR1467058
Zentralblatt MATH:
0882.62069
Digital Object Identifier: doi:10.1093/biomet/84.2.429
JSTOR: links.jstor.org
Palmer, J. L. and Muller, P. (1998). Bayesian optimal design in population models for haematologic data. Statistics in Medicine 17 1613–1622.
Ritschel, W. A. (1992). Handbook of Basic Pharmacokinetics, 4th ed. Drug Intelligence Publications, Inc.
Rodda, B. E., Sampson, C. B. and Smith, D. W. (1975). The one-compartment open model: Some statistical aspects of parameter estimation. Appl. Statist. 24 309–318.
Rowland, M. and Tozer, T. N. (1995). Clinical Pharmacokinetics—Concepts and Applications, 3rd ed. Philadelphia Lea and Febiger.
Silvey, S. D. (1980). Optimal Design. Chapman and Hall, New York.
Mathematical Reviews (MathSciNet):
MR606742
Zentralblatt MATH:
0468.62070
Staab, A., Tillmann, C., Forgue, S., Macie, A., Allerheiligen, S., Rapado, J. and Troconiz, I. (2004). Population dose-response model for tadalafil in the treatment of male erectile dysfunction. Pharmaceutical Research 21 1463–1470.
Verme, C. N., Ludden, T. M., Clementi, W. A. and Harris, S. C. (1992). Pharmacokinetics of quinidine in male patients. Clinical Pharmacokinetics 22 468–480.
Wakefield, J. (1996). The Bayesian analysis of population pharmacokinetic models. J. Amer. Statist. Assoc. 91 62–75.
White, L. (1973). An extension of the general equivalence theorem to nonlinear models. Biometrika 60 345–348.
Mathematical Reviews (MathSciNet):
MR326948
Zentralblatt MATH:
0262.62037
Digital Object Identifier: doi:10.1093/biomet/60.2.345
JSTOR: links.jstor.org
The Annals of Statistics
