TY - JOUR
T1 - Optimal design for goodness-of-fit of the Michaelis-Menten enzyme kinetic function
AU - Dette, Holger
AU - Melas, Viatcheslav B.
AU - Wong, Weng Kee
N1 - Funding Information:
Holger Dette is Professor, Fakultät für Mathematik, Ruhr-Universität Bochum, Bochum, Germany (E-mail: [email protected]). Viatcheslav B. Melas is Professor, Department of Mathematics, St. Petersburg State University, St. Petersburg, Russia (E-mail: [email protected]). Weng Kee Wong is Professor, Department of Biostatistics, School of Public Health, University of California, Los Angeles, CA 90095 (E-mail: wkwong@ ucla.edu). The authors would like to thank A. Pepelyshev for computational assistance and Isolde Gottschlich, who typed most parts of this article with considerable technical expertise. Parts of this article were written during a visit of the first author at Purdue University and this author would like to thank the Department of Statistics for their hospitality. The support of the Deutsche Forschungsgemeinschaft (DE 502/14-1 and SFB 475, Komplexitätsreduktion in multivariaten Datenstrukturen, Teilprojekt A2) is gratefully acknowledged. We also want to thank all referees for a very careful review of the manuscript.
PY - 2005/12
Y1 - 2005/12
N2 - We construct efficient designs for the Michaelis-Menten enzyme kinetic model capable of checking model assumptions. An extended model called EMAX is also considered for this purpose. This model is widely used in pharmacokinetics and reduces to the Michaelis-Menten model for a specific choice of parameter settings. Our strategy is to find efficient designs for estimating the parameters in the EMAX model and at the same time test the validity of the Michaelis-Menten model against the EMAX model by maximizing a minimum of the D or D 1 efficiencies taken over a range of values for the nonlinear parameters. In particular, we show that such designs are (a) efficient for estimating parameters in the EMAX model, (b) about 70% efficient for estimating parameters in the Michaelis-Menten model, (c) efficient for testing the Michaelis-Menten model against the EMAX model, and (d) robust with respect to misspecification of the unknown parameters in the nonlinear model.
AB - We construct efficient designs for the Michaelis-Menten enzyme kinetic model capable of checking model assumptions. An extended model called EMAX is also considered for this purpose. This model is widely used in pharmacokinetics and reduces to the Michaelis-Menten model for a specific choice of parameter settings. Our strategy is to find efficient designs for estimating the parameters in the EMAX model and at the same time test the validity of the Michaelis-Menten model against the EMAX model by maximizing a minimum of the D or D 1 efficiencies taken over a range of values for the nonlinear parameters. In particular, we show that such designs are (a) efficient for estimating parameters in the EMAX model, (b) about 70% efficient for estimating parameters in the Michaelis-Menten model, (c) efficient for testing the Michaelis-Menten model against the EMAX model, and (d) robust with respect to misspecification of the unknown parameters in the nonlinear model.
UR - https://www.scopus.com/pages/publications/29144435295
UR - https://www.scopus.com/pages/publications/29144435295#tab=citedBy
U2 - 10.1198/016214505000000600
DO - 10.1198/016214505000000600
M3 - Article
AN - SCOPUS:29144435295
SN - 0162-1459
VL - 100
SP - 1370
EP - 1381
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 472
ER -