Random-effects Selection in a Nonlinear Mixed Model with Many Parameters

• Activity Number: 69
• Type: Contributed
• Date/Time: Sunday, August 7, 2005 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Karen Chiswell*+ and John F. Monahan
• Companies: North Carolina State University and North Carolina State University
• Keywords: nonlinear mixed model ; PBPK model ; smoothing splines ; random effects ; parameter sensitivity

Abstract

When fitting a nonlinear model to longitudinal data, a two-stage approach often is adopted. At the first stage, a nonlinear model describes the expected trajectory for each subject. Parameters in the first stage model are subject-specific. At the second stage, these subject-specific parameters are modeled as random variables from a probability distribution. Although in reality all parameters in the model may vary randomly among subjects, for practical and computational purposes, only some of the parameters are allowed to vary randomly; the other parameters are modeled as being fixed across subjects. We look at the problem of selecting which parameters are to be modeled as random effects in the case where the first-stage nonlinear model has many parameters. We estimate a low-rank approximation of the residual covariance matrix using cubic smoothing splines. In order to select the random effects, we explore the associations between the fitted splines and the parameter sensitivities of the model (partial derivatives of the nonlinear model with respect to the parameters).