H. T. Abebe, F. E. Tan, G. J. Breukelen, and M. P. Berger, Bayesian <mml:math altimg="si67.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mi>D</mml:mi></mml:math>-optimal designs for the two parameter logistic mixed effects model, Computational Statistics & Data Analysis, vol.71, pp.1066-1076, 2014.
DOI : 10.1016/j.csda.2013.07.040

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 1964.

M. K. Al-banna, A. W. Kelman, and B. Whiting, Experimental design and efficient parameter estimation in population pharmacokinetics, Journal of Pharmacokinetics and Biopharmaceutics, vol.46, issue.4, pp.347-360, 1990.
DOI : 10.1007/BF01062273

A. C. Atkinson, A. N. Donev, and R. D. Tobias, Optimum Experimental Designs, with SAS, 2007.

A. C. Atkinson, V. V. Fedorov, A. M. Herzberg, and R. Zhang, Elemental information matrices and optimal experimental design for generalized regression models, Journal of Statistical Planning and Inference, vol.144, pp.81-91, 2014.
DOI : 10.1016/j.jspi.2012.09.012

D. M. Bates and D. G. Watts, Relative curvature measures of nonlinearity, Journal of the Royal Statistical Society: Series B, vol.42, pp.1-25, 1980.

C. Bazzoli, S. Retout, and F. Mentré, Fisher information matrix for nonlinear mixed effects multiple response models: Evaluation of the appropriateness of the first order linearization using a pharmacokinetic/pharmacodynamic model, Statistics in Medicine, vol.60, issue.14, pp.1940-1956, 2009.
DOI : 10.1111/j.0006-341X.2004.00148.x

URL : https://hal.archives-ouvertes.fr/inserm-00371363

C. Bazzoli, S. Retout, and F. Mentré, Design evaluation and optimisation in multiple response nonlinear mixed effect models: PFIM 3.0, Computer Methods and Programs in Biomedicine, vol.98, issue.1, pp.55-65, 2010.
DOI : 10.1016/j.cmpb.2009.09.012

URL : https://hal.archives-ouvertes.fr/inserm-00431457

G. E. Box and H. L. Lucas, DESIGN OF EXPERIMENTS IN NON-LINEAR SITUATIONS, Biometrika, vol.46, issue.1-2, pp.77-90, 1959.
DOI : 10.1093/biomet/46.1-2.77

F. Bretz, H. Dette, and J. C. Pinheiro, Practical considerations for optimal designs in clinical dose finding studies, Statistics in Medicine, vol.27, issue.6, pp.7-8, 2010.
DOI : 10.1002/sim.3802

H. Chernoff, Locally Optimal Designs for Estimating Parameters, The Annals of Mathematical Statistics, vol.24, issue.4, pp.586-602, 1953.
DOI : 10.1214/aoms/1177728915

D. Clarkson and Y. Zhan, Using Spherical???Radial Quadrature to Fit Generalized Linear Mixed Effects Models, Journal of Computational and Graphical Statistics, vol.11, issue.3, pp.639-659, 2002.
DOI : 10.1198/106186002439

R. D. Cook and M. L. Goldberg, Curvatures for Parameter Subsets in Nonlinear Regression, The Annals of Statistics, vol.14, issue.4, pp.1399-1418, 1986.
DOI : 10.1214/aos/1176350166

D. 'argenio and D. Z. , Optimal sampling times for pharmacokinetic experiments, Journal of Pharmacokinetics and Biopharmaceutics, vol.10, issue.6, pp.739-756, 1981.
DOI : 10.1007/BF01070904

C. Dartois, K. Brendel, E. Comets, C. M. Laffont, C. Laveille et al., Overview of model-building strategies in population PK/PD analyses: 2002???2004 literature survey, British Journal of Clinical Pharmacology, vol.4, issue.5, pp.603-612, 2007.
DOI : 10.1007/s10928-006-9046-9

URL : https://hal.archives-ouvertes.fr/inserm-00159122

H. Dette and A. Pepelyshev, Efficient experimental designs for sigmoidal growth models, Journal of Statistical Planning and Inference, vol.138, issue.1, pp.2-17, 2008.
DOI : 10.1016/j.jspi.2007.05.027

URL : http://dx.doi.org/10.17877/DE290R-6731

C. Dumont, M. Chenel, and F. Mentré, Influence of Covariance Between Random Effects in Design for Nonlinear Mixed-Effect Models with an Illustration in Pediatric Pharmacokinetics, Journal of Biopharmaceutical Statistics, vol.7, issue.4, pp.471-492, 2014.
DOI : 10.2165/00003088-200847040-00002

URL : https://hal.archives-ouvertes.fr/inserm-00769812

V. V. Fedorov, Theory of Optimal Experiments, 1972.

V. V. Fedorov, S. Leonov, and L. , Optimal Design for Nonlinear Response Models, 2014.

R. Fletcher and M. J. Powell, A Rapidly Convergent Descent Method for Minimization, The Computer Journal, vol.6, issue.2, pp.163-168, 1963.
DOI : 10.1093/comjnl/6.2.163

L. K. Foo and S. Duffull, Adaptive Optimal Design for Bridging Studies with an Application to Population Pharmacokinetic Studies, Pharmaceutical Research, vol.34, issue.6, pp.1530-1543, 2012.
DOI : 10.1007/s11095-011-0659-3

J. Gabrielson and D. Weiner, Pharmacokinetic and Pharmacodynamic Data Analysis: Concepts and Applications, 2006.

G. H. Golub, Some Modified Matrix Eigenvalue Problems, SIAM Review, vol.15, issue.2, pp.318-334, 1973.
DOI : 10.1137/1015032

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

G. H. Golub and J. H. Welsh, Calculation of Gauss quadrature rules, Mathematics of Computation, vol.23, issue.106, pp.221-230, 1969.
DOI : 10.1090/S0025-5718-69-99647-1

C. M. Gotwalt, B. A. Jones, and D. M. Steinberg, Fast Computation of Designs Robust to Parameter Uncertainty for Nonlinear Settings, Technometrics, vol.51, issue.1, pp.88-95, 2009.
DOI : 10.1198/TECH.2009.0009

J. Guedj, C. Bazzoli, A. U. Neumann, and F. Mentré, Design evaluation and optimization for models of hepatitis C viral dynamics, Statistics in Medicine, vol.38, issue.18, pp.1045-1056, 2011.
DOI : 10.1002/sim.4191

URL : https://hal.archives-ouvertes.fr/inserm-00615142

J. Guedj, R. Thiébaut, and D. Commenges, Practical Identifiability of HIV Dynamics Models, Bulletin of Mathematical Biology, vol.48, issue.8, pp.2493-2513, 2007.
DOI : 10.1007/s11538-007-9228-7

URL : https://hal.archives-ouvertes.fr/inserm-00204273

I. Gueorguieva, K. Ogungbenro, G. Graham, S. Glatt, and L. Aarons, A program for individual and population optimal design for univariate and multivariate response pharmacokinetic???pharmacodynamic models, Computer Methods and Programs in Biomedicine, vol.86, issue.1, pp.51-61, 2007.
DOI : 10.1016/j.cmpb.2007.01.004

C. Han and K. Chaloner, Bayesian Experimental Design for Nonlinear Mixed-Effects Models with Application to HIV Dynamics, Biometrics, vol.50, issue.1, pp.25-33, 2004.
DOI : 10.1038/373117a0

C. Han and K. Chaloner, Design of population studies of HIV dynamics Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention, pp.525-548, 2005.

Y. Hashimoto and L. B. Sheiner, Designs for population pharmacodynamics: Value of pharmacokinetic data and population analysis, Journal of Pharmacokinetics and Biopharmaceutics, vol.76, issue.3, pp.333-353, 1991.
DOI : 10.1007/BF03036255

B. Jones and J. Wang, Constructing optimal designs for fitting pharmacokinetic models, Statistics and Computing, vol.9, issue.3, pp.209-218, 1999.
DOI : 10.1023/A:1008922030873

B. Jones, J. Wang, P. Jarvis, and W. Byrom, Design of cross-over trials for pharmacokinetic studies, Journal of Statistical Planning and Inference, vol.78, issue.1-2, pp.307-316, 1999.
DOI : 10.1016/S0378-3758(98)00221-3

E. N. Jonsson, J. R. Wade, and M. O. Karlsson, Comparison of some practical sampling strategies for population pharmacokinetic studies, Journal of Pharmacokinetics and Biopharmaceutics, vol.19, issue.2, pp.245-263, 1996.
DOI : 10.1007/BF02353491

J. Kiefer and J. Wolfowitz, The equivalence of two extremum problems, Journal canadien de math??matiques, vol.12, issue.0, pp.363-366, 1960.
DOI : 10.4153/CJM-1960-030-4

E. Kuhn and M. Lavielle, Maximum likelihood estimation in nonlinear mixed effects models, Computational Statistics & Data Analysis, vol.49, issue.4, pp.1020-1038, 2005.
DOI : 10.1016/j.csda.2004.07.002

R. L. Lalonde, K. G. Kowalski, M. M. Hutmacher, W. Ewy, D. J. Nichols et al., Model-based Drug Development, Clinical Pharmacology & Therapeutics, vol.33, issue.1, pp.21-32, 2007.
DOI : 10.1038/sj.clpt.6100235

S. Leonov and A. Aliev, Optimal design for population pk/pd models, Tatra Mountains Mathematical Publications, vol.51, issue.1, pp.115-130, 2012.
DOI : 10.2478/v10127-012-0012-1

S. Leonov and S. Miller, Model and Its Application in Clinical Trials, Journal of Biopharmaceutical Statistics, vol.19, issue.2, pp.360-385, 2009.
DOI : 10.1002/sim.2213

M. L. Lindstrom and D. M. Bates, Nonlinear Mixed Effects Models for Repeated Measures Data, Biometrics, vol.46, issue.3, pp.673-687, 1990.
DOI : 10.2307/2532087

T. Louis, Finding the observed information matrix when using the EM algorithm, Journal of the Royal Statistical Society Series B, vol.44, pp.226-233, 1982.

J. Mcgree, C. Drovandi, M. Thompson, J. Eccleston, S. Duffull et al., Adaptive Bayesian compound designs for dose finding studies, Journal of Statistical Planning and Inference, vol.142, issue.6, pp.1480-1492, 2012.
DOI : 10.1016/j.jspi.2011.12.029

F. Mentré, M. Chenel, E. Comets, J. Grevel, A. C. Hooker et al., Current Use and Developments Needed for Optimal Design in Pharmacometrics: A Study Performed Among DDMoRe???s European Federation of Pharmaceutical Industries and Associations Members, CPT: Pharmacometrics and Systems Pharmacology 2, p.46, 2013.
DOI : 10.1007/s11095-011-0659-3

F. Mentré, A. Mallet, and D. Baccar, Optimal design in random-effects regression models, Biometrika, vol.84, issue.2, pp.429-442, 1997.
DOI : 10.1093/biomet/84.2.429

T. Mielke, Approximations of the Fisher information for the construction of efficient experimental designs in nonlinear mixed effects models, 2012.

T. Mielke and R. Schwabe, Some Considerations on the Fisher Information in Nonlinear Mixed Effects Models, Proceedings of the 9th International Workshop in Model-Oriented Design and Analysis. Physica Verlag, pp.129-136, 2010.
DOI : 10.1007/978-3-7908-2410-0_17

J. Monahan and A. Genz, Spherical-Radial Integration Rules for Bayesian Computation, Journal of the American Statistical Association, vol.38, issue.438, pp.664-674, 1997.
DOI : 10.1080/01621459.1997.10474018

T. T. Nguyen, C. Bazzoli, and F. Mentré, Design evaluation and optimisation in crossover pharmacokinetic studies analysed by nonlinear mixed effects models, Statistics in Medicine, vol.30, issue.11-12, pp.11-12, 2012.
DOI : 10.1002/sim.4191

URL : https://hal.archives-ouvertes.fr/inserm-00629594

E. I. Nielsen, A. Viberg, E. Lowdin, O. Cars, M. O. Karlsson et al., Semimechanistic Pharmacokinetic/Pharmacodynamic Model for Assessment of Activity of Antibacterial Agents from Time-Kill Curve Experiments, Antimicrobial Agents and Chemotherapy, vol.51, issue.1, pp.128-136, 2007.
DOI : 10.1128/AAC.00604-06

J. Nyberg, C. Bazzoli, K. Ogungbenro, A. Aliev, S. Leonov et al., Methods and software tools for design evaluation for population pharmacokineticspharmacodynamics studies, British Journal of Clinical Pharmacology, 2014.
URL : https://hal.archives-ouvertes.fr/inserm-00978789

D. Oakes, Direct calculation of the information matrix via the EM, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.61, issue.2, pp.479-482, 1999.
DOI : 10.1111/1467-9868.00188

A. S. Perelson and R. M. Ribeiro, Estimating drug efficacy and viral dynamic parameters: HIV and HCV, Statistics in Medicine, vol.43, issue.23, pp.4647-4657, 2008.
DOI : 10.1002/sim.3116

G. Pillai, F. Mentré, and J. L. Steimer, Non-Linear Mixed Effects Modeling ??? From Methodology and Software Development to Driving Implementation in Drug Development Science, Journal of Pharmacokinetics and Pharmacodynamics, vol.72, issue.6, pp.161-183, 2005.
DOI : 10.1007/s10928-005-0062-y

J. C. Pinheiro and D. M. Bates, Approximations to the log-likelihood function in the nonlinear mixed-effects model, Journal of Computational and Graphical Statistics, vol.4, pp.12-35, 1995.

E. L. Plan, A. Maloney, F. Mentré, M. O. Karlsson, and J. Bertrand, Performance Comparison of Various Maximum Likelihood Nonlinear Mixed-Effects Estimation Methods for Dose???Response Models, The AAPS Journal, vol.14, issue.3, pp.420-432, 2012.
DOI : 10.1208/s12248-012-9349-2

URL : https://hal.archives-ouvertes.fr/inserm-00709829

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, The Art of Scientific Computing, 1992.

L. Pronzato, Penalized optimal designs for dose-finding, Journal of Statistical Planning and Inference, vol.140, issue.1, pp.283-296, 2010.
DOI : 10.1016/j.jspi.2009.07.012

URL : https://hal.archives-ouvertes.fr/hal-00416014

S. Retout, E. Comets, A. Samson, and F. Mentré, Design in nonlinear mixed effects models: Optimization using the Fedorov???Wynn algorithm and power of the Wald test for binary covariates, Statistics in Medicine, vol.39, issue.28, pp.5162-5179, 2007.
DOI : 10.1002/sim.2910

URL : https://hal.archives-ouvertes.fr/hal-00263513

S. Retout and F. Mentré, Further Developments of the Fisher Information Matrix in Nonlinear Mixed Effects Models with Evaluation in Population Pharmacokinetics, Journal of Biopharmaceutical Statistics, vol.13, issue.2, pp.209-227, 2003.
DOI : 10.1081/BIP-100101009

S. Retout, F. Mentré, and R. Bruno, Fisher information matrix for non-linear mixed-effects models: evaluation and application for optimal design of enoxaparin population pharmacokinetics, Statistics in Medicine, vol.26, issue.6, pp.2623-2639, 2002.
DOI : 10.1002/sim.1041

R. M. Savic, F. Mentré, and M. Lavielle, Implementation and Evaluation of the SAEM Algorithm for Longitudinal Ordered Categorical Data with an Illustration in Pharmacokinetics???Pharmacodynamics, The AAPS Journal, vol.13, issue.1, pp.44-53, 2011.
DOI : 10.1208/s12248-010-9238-5

URL : https://hal.archives-ouvertes.fr/hal-00637400

L. B. Sheiner, B. Rosenberg, and V. V. Marathe, Estimation of population characteristics of pharmacokinetic parameters from routine clinical data, Journal of Pharmacokinetics and Biopharmaceutics, vol.15, issue.5, pp.445-479, 1977.
DOI : 10.1007/BF01061728

L. B. Sheiner, B. Rosenberg, and K. L. Melmon, Modelling of individual pharmacokinetics for computer-aided drug dosage, Computers and Biomedical Research, vol.5, issue.5, pp.411-459, 1972.
DOI : 10.1016/0010-4809(72)90051-1

B. P. Smith and J. Vincent, Biostatistics and Pharmacometrics: Quantitative Sciences to Propel Drug Development Forward, Clinical Pharmacology & Therapeutics, vol.46, issue.2, pp.141-144, 2010.
DOI : 10.2307/749110

G. Smyth, Nonlinear regression Encyclopedia of Environmetrics 3, pp.1405-1411, 2002.

S. Ueckert, J. Nyberg, and A. C. Hooker, Application of Quasi-Newton algorithms in optimal design. Workshop of Population Optimum Design of Experiments, 2010.

P. H. Van-der-graaf, CPT: Pharmacometrics and Systems Pharmacology, CPT: Pharmacometrics & Systems Pharmacology, vol.1, issue.9, p.8, 2012.
DOI : 10.1038/psp.2012.8

M. Vigan, J. Stirnemann, and F. Mentré, Evaluation of estimation methods for repeated time to event models: application to analysis of bone events during treatment of Gaucher Disease, 2012.

C. Vong, S. Ueckert, J. Nyberg, and A. C. Hooker, Handling below limit of quantification data in optimal trial design, 2012.

E. Walter and L. Pronzato, Identifiabilities and nonlinearities, Nonlinear Systems 1, pp.111-143, 1995.
DOI : 10.1007/978-1-4615-2047-4_4

E. Walter and L. Pronzato, Identification of Parametric Models from Experimental Data, 2007.

R. Wolfinger, Laplace's approximation for nonlinear mixed models, Biometrika, vol.80, issue.4, pp.791-795, 1993.
DOI : 10.1093/biomet/80.4.791

H. P. Wynn, Results in the theory and construction of D-optimum designs, Journal of the Royal Statistical Society Series B, vol.34, pp.133-147, 1972.