Approximate testing in two-stage nonlinear mixed models

References

• Beal SL, Sheiner LB. Estimating population kinetics. Crit Rev Biomed Eng. 1981;8:195–222.
   Web of Science ®Google Scholar
• Lindstrom MJ, Bates DM. Nonlinear mixed effects models for repeated measures data. Biometrics. 1990;46:673–687. doi: 10.2307/2532087
   PubMed Web of Science ®Google Scholar
• Vonesh E, Chinchilli V. Linear and nonlinear models for the analysis of repeated measurements. New York, NY: Marcel Dekker, Inc.; 1997.
   Google Scholar
• Wolfinger R. Laplace's approximation for nonlinear mixed models. Biometrika. 1993;80:791–795. doi: 10.1093/biomet/80.4.791
   Web of Science ®Google Scholar
• Dubois A, Lavielle M, Gsteiger S, Pigeoletc E, Mentré F. Model-based analyses of bioequivalence crossover trials using the stochastic approximation expectation maximisation algorithm. Stat Med. 2010;30:2582–2600.
   Web of Science ®Google Scholar
• Bertrand J, Comets E, Mentré F. Comparison of model-based tests and selection strategies to detect genetic polymorphisms influencing pharmacokinetic parameters. J Biopharm Stat. 2008;18:1084–1102. doi: 10.1080/10543400802369012
   PubMed Web of Science ®Google Scholar
• Bertrand J, Comets E, Chenel M, Mentré F. Some alternatives to asymptotic tests for the analysis of pharmacogenetic data using nonlinear mixed effects models. Biometrics. 2012;68:146–155. doi: 10.1111/j.1541-0420.2011.01665.x
   PubMed Web of Science ®Google Scholar
• Volaufova J. Approximate small sample tests in nonlinear mixed models. Commun Stat – Simul C. 2014; 43(9):2117–2137. doi: 10.1080/03610918.2013.835407
   Web of Science ®Google Scholar
• Volaufova J, LaMotte L. Comparison of approximate tests of fixed effects in linear repeated measures design models with covariates. Tatra Mountains. 2008;39:17–25.
   Google Scholar
• Volaufova J, LaMotte LR. A simulation comparison of approximate tests for fixed effects in random coefficients growth curve models. Commun Stat – Simul C. 2013;42(2):344–359. doi: 10.1080/03610918.2011.635254
   Web of Science ®Google Scholar
• Harville DA. Matrix algebra from a statistician's perspective. New York, NY: Springer; 1997.
   Google Scholar
• Davidian M, Giltinan D. Nonlinear models for repeated measurement data: An overview and update. J Agr Biol Environ Stud. 2003;8(4):387–419. doi: 10.1198/1085711032697
   Web of Science ®Google Scholar
• Jennrich R. Asymptotic properties of non-linear least squares estimators. Ann Math Stat. 1969;40(2):633–643. doi: 10.1214/aoms/1177697731
   Google Scholar
• Wu C. Asymptotic theory of nonlinear least squares estimation. Ann Stat. 1981;9(3):501–513. doi: 10.1214/aos/1176345455
   Web of Science ®Google Scholar
• Amemiya T. Handbook of econometrics. In: Grilichest Z, Intriligator MD, editors. Chapter 6, Non-linear regression models. 1st ed. Amsterdam, The Netherlands: Elsevier Science; 1983; p. 333–389.
   Google Scholar
• Vonesh E, Carter R. Efficient inference for random-coefficient growth curve models with unbalanced data. Biometrics. 1987;43(3):617–628. doi: 10.2307/2531999
   PubMed Web of Science ®Google Scholar
• Burton JH. Improved hypothesis tests of linear combinations of fixed effects parameters in nonlinear random coefficients models [dissertation]. New Orleans (LA): Louisiana State University Health Sciences Center; 2013.
   Google Scholar
• Kenward M, Roger J. Small sample inference for fixed effects from restricted maximum likelihood. Biometrics. 1997;53(3):983–997. doi: 10.2307/2533558
   PubMed Web of Science ®Google Scholar
• Retout S, Mentré F, Bruno R. Fisher information matrix for nonlinear mixed effects models: evaluation and application for optimal design of Enoxaparin population pharmacokinetics. Stat Med. 2002;21:2623–2639. doi: 10.1002/sim.1041
   PubMed Web of Science ®Google Scholar
• Retout S, Mentré F. Further developments of the fisher information matrix in nonlinear mixed effects models with evaluation in population pharmacokinetics. J Biopharm Stat. 2003;13:209–227. doi: 10.1081/BIP-120019267
   PubMedGoogle Scholar
• Volaufova J, Burton JH. Note on hypothesis testing in mixed models. Paper presentation at: LINSTAT 2012/21st IWMS; 2012; Bedlewo, Poland.
   Google Scholar
• Mielke T, Schwabe R. Some considerations on the fisher information in nonlinear mixed effects models. In: Giovagnoli A, Atkinson AC, Torsney B, May C, editors. mODa 9 – Advances in Model-Oriented Design and Analysis. Proceedings of the 9th International Workshop in Model-Oriented Design and Analysis; 2010 June 14–18; Bertinoro, Italy. Heidelberg: Springer, Physica Verlag; 2010;129–136.
   Google Scholar
• Mielke T. Approximation of the fisher information and design in nonlinear mixed effects models [unpublished preprint]. Available from: http://www.math.uni-magdeburg.de/institute/imst/ag_schwabe/preprints/2011_22.pdf.
   Google Scholar
• Fai A, Cornelius P. Approximate F-tests of multiple degree of freedom hypotheses in generalized least squares analyses of unbalanced split-plot experiments. J Stat Comput Simul. 1996;54:363–378. doi: 10.1080/00949659608811740
   Web of Science ®Google Scholar
• Wolfinger RD. Fitting nonlinear mixed models with the new NLMIXED procedure [technical report 287]. Cary (NC): SAS Institute; 2000.
   Google Scholar
• Hartford A, Davidian M. Consequences of misspecifying assumptions in nonlinear mixed effects models. Comput Stat and Data Anal. 2000;34:139–164. doi: 10.1016/S0167-9473(99)00076-6
   Web of Science ®Google Scholar
• Casella G., Berger RL. Statistical inference. 2nd ed. Pacific Grove, CA: Duxbury; 2002.
   Google Scholar
• Pinheiro J, Bates D. Approximations to the log-likelihood function in the non-linear mixed-effects model. J Comput Graph Stat. 1995;4(1):12–35.
   Google Scholar