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Robustifying a Non-Linear Model using Wavelets: A Bayesian Approach with an Application to Pharmacokinetics Modeling.

Zou, Yuanshu
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1378197606

Abstract Details

, PhD, University of Cincinnati, Arts and Sciences: Mathematical Sciences.
Parametric models are easy to fit and easy to interpret, however, they may not be sufficient for modeling data arising from complex phenomenon. Nonparametric models allow flexible modeling but have the difficulties in interpreting and dealing with very few observations. In my dissertation, we propose a nonparametric extension to robustify parametric nonlinear regression models. We consider in particular pharmacokinetic models that define the nonlinear regression function indirectly as solution of an ordinary differential equation (ODE) system. We begin with a tentative parametric model, e.g., a compartment model, and define a a nonparametric neighborhood of the tentative model using wavelet decomposition. We do this by defining a suitable prior for the wavelet coefficients, centered around that of the parametric model, with the wavelet based nonparametric neighborhood as the support. We use Bayesian approach to fit the model, implementing wavelet thresholding proposed by Muller and Vidakovic [26]. We also extend our method to population pharmacokinetics. Our method is flexible enough to adapt to deviations from a standard nonlinear drug concentration profile allowing robust modeling and predictions. We illustrate the proposed approach using simulated and real data sets.
Siva Sivaganesan, Ph.D. (Committee Chair)
Seongho Song, Ph.D. (Committee Member)
Xia Wang, Ph.D. (Committee Member)
134 p.
Statistics
robustify; wavelet; bayesian; pharmacokinetics

Recommended Citations

Citations

  • Zou, Y. (n.d.). Robustifying a Non-Linear Model using Wavelets: A Bayesian Approach with an Application to Pharmacokinetics Modeling. [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1378197606

    APA Style (7th edition)

  • Zou, Yuanshu. Robustifying a Non-Linear Model using Wavelets: A Bayesian Approach with an Application to Pharmacokinetics Modeling. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1378197606.

    MLA Style (8th edition)

  • Zou, Yuanshu. "Robustifying a Non-Linear Model using Wavelets: A Bayesian Approach with an Application to Pharmacokinetics Modeling." Doctoral dissertation, University of Cincinnati. Accessed APRIL 19, 2024. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1378197606

    Chicago Manual of Style (17th edition)

ucin1378197606
376
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This open access ETD is published by University of Cincinnati and OhioLINK.