IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v53y2009i3p642-656.html
   My bibliography  Save this article

Comparison of nonparametric methods in nonlinear mixed effects models

Author

Listed:
  • Antic, J.
  • Laffont, C.M.
  • Chafaï, D.
  • Concordet, D.

Abstract

During the drug development, nonlinear mixed effects models are routinely used to study the drug's pharmacokinetics and pharmacodynamics. The distribution of random effects is of special interest because it allows to describe the heterogeneity of the drug's kinetics or dynamics in the population of individuals studied. Parametric models are widely used, but they rely on a normality assumption which may be too restrictive. In practice, this assumption is often checked using the empirical distribution of random effects' empirical Bayes estimates. Unfortunately, when data are sparse (like in patients phase III clinical trials), this method is unreliable. In this context, nonparametric estimators of the random effects distribution are attractive. Several nonparametric methods (estimators and their associated computation algorithms) have been proposed but their use is limited. Indeed, their practical and theoretical properties are unclear and they have a reputation for being computationally expensive. Four nonparametric methods in comparison with the usual parametric method are evaluated. Statistical and computational features are reviewed and practical performances are compared in simulation studies mimicking real pharmacokinetic analyses. The nonparametric methods seemed very useful when data are sparse. On a simple pharmacokinetic model, all the nonparametric methods performed roughly equivalently. On a more challenging pharmacokinetic model, differences between the methods were clearer.

Suggested Citation

  • Antic, J. & Laffont, C.M. & Chafaï, D. & Concordet, D., 2009. "Comparison of nonparametric methods in nonlinear mixed effects models," Computational Statistics & Data Analysis, Elsevier, vol. 53(3), pages 642-656, January.
  • Handle: RePEc:eee:csdana:v:53:y:2009:i:3:p:642-656
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00421-0
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wang, Xiaoning & Schumitzky, Alan & D'Argenio, David Z., 2007. "Nonlinear random effects mixture models: Maximum likelihood estimation via the EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6614-6623, August.
    2. Fenton, Victor M & Gallant, A Ronald, 1996. "Convergence Rates of SNP Density Estimators," Econometrica, Econometric Society, vol. 64(3), pages 719-727, May.
    3. ChafaI¨, Djalil & Loubes, Jean-Michel, 2006. "On nonparametric maximum likelihood for a class of stochastic inverse problems," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1225-1237, July.
    4. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    5. Wang, Ji-Ping, 2007. "A linearization procedure and a VDM/ECM algorithm for penalized and constrained nonparametric maximum likelihood estimation for mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2946-2957, March.
    6. Fenton, Victor M & Gallant, A Ronald, 1996. "Erratum [Convergence Rates of SNP Density Estimators]," Econometrica, Econometric Society, vol. 64(6), pages 1493-1493, November.
    7. Tze Leung Lai, 2003. "Nonparametric estimation in nonlinear mixed effects models," Biometrika, Biometrika Trust, vol. 90(1), pages 1-13, March.
    8. Vaart,A. W. van der, 1998. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521496032.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Comte, F. & Genon-Catalot, V. & Samson, A., 2013. "Nonparametric estimation for stochastic differential equations with random effects," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2522-2551.
    2. Leonardo Grilli & Carla Rampichini, 2015. "Specification of random effects in multilevel models: a review," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 967-976, May.
    3. Fabienne Comte & Adeline Samson, 2012. "Nonparametric estimation of random-effects densities in linear mixed-effects model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 951-975, December.
    4. B. L. S. Prakasa Rao, 2021. "Nonparametric Estimation for Stochastic Differential Equations Driven by Mixed Fractional Brownian Motion with Random Effects," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 554-568, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liesenfeld, Roman & Breitung, Jörg, 1998. "Simulation based methods of moments in empirical finance," Tübinger Diskussionsbeiträge 136, University of Tübingen, School of Business and Economics.
    2. Pieter J. Van Der Sluis, 1998. "Computationally attractive stability tests for the efficient method of moments," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages 203-227.
    3. Foster, Joshua, 2022. "Semi-nonparametric estimation of secret reserve prices in auctions," Economics Letters, Elsevier, vol. 220(C).
    4. Andersen, Torben G. & Chung, Hyung-Jin & Sorensen, Bent E., 1999. "Efficient method of moments estimation of a stochastic volatility model: A Monte Carlo study," Journal of Econometrics, Elsevier, vol. 91(1), pages 61-87, July.
    5. Neha Gupta, 2013. "Government Intervention In Grain Markets In India--Rethinking The Procurement Policy," Working papers 231, Centre for Development Economics, Delhi School of Economics.
    6. Brendstrup, Bjarne & Paarsch, Harry J., 2006. "Identification and estimation in sequential, asymmetric, English auctions," Journal of Econometrics, Elsevier, vol. 134(1), pages 69-94, September.
    7. Kristensen, Dennis & Shin, Yongseok, 2012. "Estimation of dynamic models with nonparametric simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 167(1), pages 76-94.
    8. Yangxin Huang & Xiaosun Lu & Jiaqing Chen & Juan Liang & Miriam Zangmeister, 2018. "Joint model-based clustering of nonlinear longitudinal trajectories and associated time-to-event data analysis, linked by latent class membership: with application to AIDS clinical studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(4), pages 699-718, October.
    9. Ming Liu & Harold H. Zhang, "undated". "Specification Tests in the Efficient Method of Moments Framework with Application to the Stochastic Volatility Models," Computing in Economics and Finance 1997 93, Society for Computational Economics.
    10. repec:wyi:journl:002117 is not listed on IDEAS
    11. Ignacio Mauleon, 2006. "Modelling multivariate moments in European Stock Markets," The European Journal of Finance, Taylor & Francis Journals, vol. 12(3), pages 241-263.
    12. Dennis Kristensen, 2009. "Semiparametric modelling and estimation (in Russian)," Quantile, Quantile, issue 7, pages 53-83, September.
    13. Dias, Ronaldo & Garcia, Nancy L., 2007. "Consistent estimator for basis selection based on a proxy of the Kullback-Leibler distance," Journal of Econometrics, Elsevier, vol. 141(1), pages 167-178, November.
    14. Coppejans, Mark, 2004. "On Kolmogorov's representation of functions of several variables by functions of one variable," Journal of Econometrics, Elsevier, vol. 123(1), pages 1-31, November.
    15. Ignacio Mauleon & Javier Perote, 2000. "Testing densities with financial data: an empirical comparison of the Edgeworth-Sargan density to the Student's t," The European Journal of Finance, Taylor & Francis Journals, vol. 6(2), pages 225-239.
    16. Fenton, Victor M. & Gallant, A. Ronald, 1996. "Qualitative and asymptotic performance of SNP density estimators," Journal of Econometrics, Elsevier, vol. 74(1), pages 77-118, September.
    17. repec:wyi:journl:002142 is not listed on IDEAS
    18. Gallant, A. Ronald & Hsieh, David & Tauchen, George, 1997. "Estimation of stochastic volatility models with diagnostics," Journal of Econometrics, Elsevier, vol. 81(1), pages 159-192, November.
    19. Kevin Hasker & Robin Sickles, 2010. "eBay in the Economic Literature: Analysis of an Auction Marketplace," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 37(1), pages 3-42, August.
    20. Teruko Takada, 2001. "Nonparametric density estimation: A comparative study," Economics Bulletin, AccessEcon, vol. 3(16), pages 1-10.
    21. Fu, Liyong & Wang, Mingliang & Lei, Yuancai & Tang, Shouzheng, 2014. "Parameter estimation of two-level nonlinear mixed effects models using first order conditional linearization and the EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 173-183.
    22. Mauleon, Ignacio, 2003. "Financial densities in emerging markets: an application of the multivariate ES density," Emerging Markets Review, Elsevier, vol. 4(2), pages 197-223, June.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:53:y:2009:i:3:p:642-656. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.