Locally D-optimal designs based on a class of composed models resulted from blending Emax and one-compartment models. (English) Zbl 1132.62056

Fang, X.; Hedayat, A. S.

Ann. Stat. 36, No. 1, 428-444 (2008).

Summary: 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.

MSC:

62K05	Optimal statistical designs
62P10	Applications of statistics to biology and medical sciences; meta analysis
92C45	Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)

Keywords:

pharmacokinetic compartmental model; pharmacodynamic Emax model; nonlinear model

References:

[1]	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.
[2]	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. · Zbl 0780.62056 · doi:10.2307/2532547
[3]	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.
[4]	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.
[5]	Dette, H. and Neugebauer, H.-M. (1997). Bayesian D-optimal designs for exponential regression models. J. Statist. Plann. Inference 60 331-349. · Zbl 0900.62408 · doi:10.1016/S0378-3758(96)00131-0
[6]	Fedorov, V. V. (1972). Theory of Optimal Experiments . Academic Press, New York. · Zbl 0258.62044
[7]	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.
[8]	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. · Zbl 1016.62088 · doi:10.1016/S0378-3758(02)00175-1
[9]	Han, C. and Chaloner, K. (2004). Bayesian experimental design for nonlinear mixed-effects models with application to HIV dynamics. Biometrics 60 25-33. · Zbl 1130.62316 · doi:10.1111/j.0006-341X.2004.00148.x
[10]	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. · Zbl 1095.62087 · doi:10.1016/S0378-3758(03)00196-4
[11]	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. · Zbl 0988.62046 · doi:10.1016/S0378-3758(01)00120-3
[12]	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. JSTOR: · Zbl 0889.62064 · doi:10.2307/2965578
[13]	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. · Zbl 0485.62072
[14]	Karlin, S. and Studden, W. J. (1966). Tchebyscheff Systems: With Applications in Analysis and Statistics . Wiley, New York. · Zbl 0153.38902
[15]	Kiefer, J. and Wolfowitz, J. (1960). The equivalence of two extremum problems. Cannid. J. Math. 12 363-366. · Zbl 0093.15602 · doi:10.4153/CJM-1960-030-4
[16]	Landaw, E. M. (1980). Optimal experimental design for biological compartmental systems with applications to pharmacokinetics. Ph.D. dissertation, UCLA, University Microfilms International.
[17]	Lindsey, J. K., Byrom, W. D., Wang, J., Jarvis, P. and Jones, B. (2000). Generalized nonlinear models for pharmacokinetic data. Biometrics 56 81-88. · Zbl 1060.62637 · doi:10.1111/j.0006-341X.2000.00081.x
[18]	Mallet, A. (1992). A nonparametric method for population pharmacokinetics: A case study. Amer. Statist. Assoc. Proceedings of the Biopharmaceutical Section 11-20.
[19]	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.
[20]	Mentre, F., Mallet, A. and Baccar, D. (1997). Optimal design in random-effect regression models. Biometrika 84 429-442. JSTOR: · Zbl 0882.62069 · doi:10.1093/biomet/84.2.429
[21]	Palmer, J. L. and Muller, P. (1998). Bayesian optimal design in population models for haematologic data. Statistics in Medicine 17 1613-1622.
[22]	Ritschel, W. A. (1992). Handbook of Basic Pharmacokinetics , 4th ed. Drug Intelligence Publications, Inc.
[23]	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.
[24]	Rowland, M. and Tozer, T. N. (1995). Clinical Pharmacokinetics-Concepts and Applications , 3rd ed. Philadelphia Lea and Febiger.
[25]	Silvey, S. D. (1980). Optimal Design . Chapman and Hall, New York. · Zbl 0468.62070
[26]	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.
[27]	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.
[28]	Wakefield, J. (1996). The Bayesian analysis of population pharmacokinetic models. J. Amer. Statist. Assoc. 91 62-75. · Zbl 0925.62474 · doi:10.2307/2291383
[29]	White, L. (1973). An extension of the general equivalence theorem to nonlinear models. Biometrika 60 345-348. JSTOR: · Zbl 0262.62037 · doi:10.1093/biomet/60.2.345