Robustifying a Nonlinear Model Using Wavelets with an Application to PK Modeling

• Activity Number: 497
• Type: Topic Contributed
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• 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
• Keywords: Bayesian nonparametrics ; Robust ; Non-linear Model ; PK ; wavelet

Abstract

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.