Statistical Inference for Dynamic Systems Governed by Differential Equations with Applications to Toxicology

• Activity Number: 351
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Siddhartha Mandal*+ and Pranab K. Sen and Shyamal D. Peddada
• Companies: The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill and National Institute of Environmental Health Sciences
• Keywords: Differential equations ; physiologically based pharmacokinetic ; basis expansions

Abstract

Stochastic and deterministic differential equations are used to describe a wide variety of biological and physiological phenomena. For example, in Physiologically based pharmacokinetic(PBPK) models, differential equations explain the absorption, distribution, metabolism and excretion (ADME) of a compound in the human or animal body. Usual approaches for parameter estimation in such situations include non-linear least squares and Bayesian hierarchical modeling. However, a common challenge with these problems is the lack of explicit equations/models that relate response variable to the explanatory variables. Recent functional data analysis methods indicate the use of basis functions to bypass this problem. This talk focuses on estimation and inference of the model parameters, taking into account the variability within and between multiple subjects, while exploiting the structure implied by the system of differential equations. Large sample behavior of the parameter estimates are also explored. Application of the methods are shown using simulated and real life data on compartmental and state space models.