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Activity Number: 497
Type: Topic Contributed
Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #305836
Title: Robustifying a Nonlinear Model Using Wavelets with an Application to PK Modeling
Author(s): Siva Sivaganesan*+ and Yuanshu Zou and Peter Mueller
Companies: University of Cincinnati and University of Cincinnati and The University of Texas at Austin
Address: 4304 French Hall, University of Cincinnati, Cincinnati, OH, 45220-0025, United States
Keywords: Bayesian nonparametrics ; Robust ; Non-linear Model ; PK ; wavelet

We propose a non-parametric extension to robustify parametric non-linear regression models. We consider in particular pharmacokinetic models that define the non-linear regression function indirectly as solution of an ODE system. We begin with a tentative parametric model, e.g., a compartment model, and define a a non-parametric 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 non-parametric neighborhood as the support. We use Bayesian approach to fit the model, implementing wavelet thresholding proposed by Muller and Vidakovic (1998). Our method is flexible enough to adapt to deviations from a standard non-linear drug concentration profile allowing robust modeling and predictions. We illustrate the proposed approach using simulated data and a real dataset.

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