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Simulation-based fully Bayesian experimental design for mixed effects models

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  • Ryan, Elizabeth G.
  • Drovandi, Christopher C.
  • Pettitt, Anthony N.

Abstract

Bayesian inference has commonly been performed on nonlinear mixed effects models. However, there is a lack of research into performing Bayesian optimal design for nonlinear mixed effects models, especially those that require searches to be performed over several design variables. This is likely due to the fact that it is much more computationally intensive to perform optimal experimental design for nonlinear mixed effects models than it is to perform inference in the Bayesian framework. Fully Bayesian experimental designs for nonlinear mixed effects models are presented, which involve the use of simulation-based optimal design methods to search over both continuous and discrete design spaces. The design problem is to determine the optimal number of subjects and samples per subject, as well as the (near) optimal urine sampling times for a population pharmacokinetic study in horses, so that the population pharmacokinetic parameters can be precisely estimated, subject to cost constraints. The optimal sampling strategies, in terms of the number of subjects and the number of samples per subject, were found to be substantially different between the examples considered in this work, which highlights the fact that the designs are rather problem-dependent and can be addressed using the methods presented.

Suggested Citation

  • Ryan, Elizabeth G. & Drovandi, Christopher C. & Pettitt, Anthony N., 2015. "Simulation-based fully Bayesian experimental design for mixed effects models," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 26-39.
    • Handle: RePEc:eee:csdana:v:92:y:2015:i:c:p:26-39
    DOI: 10.1016/j.csda.2015.06.007
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    References listed on IDEAS

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    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Ryan, Elizabeth G. & Drovandi, Christopher C. & Thompson, M. Helen & Pettitt, Anthony N., 2014. "Towards Bayesian experimental design for nonlinear models that require a large number of sampling times," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 45-60.
    3. Alex R. Cook & Gavin J. Gibson & Christopher A. Gilligan, 2008. "Optimal Observation Times in Experimental Epidemic Processes," Biometrics, The International Biometric Society, vol. 64(3), pages 860-868, September.
    4. Jonathan R. Stroud & Peter Müller & Gary L. Rosner, 2001. "Optimal sampling times in population pharmacokinetic studies," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(3), pages 345-359.
    5. Cong Han & Kathryn Chaloner, 2004. "Bayesian Experimental Design for Nonlinear Mixed-Effects Models with Application to HIV Dynamics," Biometrics, The International Biometric Society, vol. 60(1), pages 25-33, March.
    6. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2004. "Generalized multilevel structural equation modeling," Psychometrika, Springer;The Psychometric Society, vol. 69(2), pages 167-190, June.
    7. Christopher C. Drovandi & Anthony N. Pettitt, 2013. "Bayesian Experimental Design for Models with Intractable Likelihoods," Biometrics, The International Biometric Society, vol. 69(4), pages 937-948, December.
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    3. Morgan, Joshua C. & Chinen, Anderson Soares & Anderson-Cook, Christine & Tong, Charles & Carroll, John & Saha, Chiranjib & Omell, Benjamin & Bhattacharyya, Debangsu & Matuszewski, Michael & Bhat, K. S, 2020. "Development of a framework for sequential Bayesian design of experiments: Application to a pilot-scale solvent-based CO2 capture process," Applied Energy, Elsevier, vol. 262(C).
    4. Walker, Stephen G., 2016. "Bayesian information in an experiment and the Fisher information distance," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 5-9.
    5. Xiao-Dong Zhou & Yun-Juan Wang & Rong-Xian Yue, 2018. "Robust population designs for longitudinal linear regression model with a random intercept," Computational Statistics, Springer, vol. 33(2), pages 903-931, June.
    6. McGree, J.M., 2017. "Developments of the total entropy utility function for the dual purpose of model discrimination and parameter estimation in Bayesian design," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 207-225.

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