Thresholds in Nonlinear Models for Repeated Measurements
M. J. Bartholomew1 and C. Gennings2, 1CVM, FDA, Rockville, MD 20855, 2Department of Biostatistics, Medical College of Virginia, VCU
The literature contains numerous applications of threshold models in the linear or generalized linear model context for the analysis of cross-sectional data. Thresholds in nonlinear models for cross-sectional data are less prevalent in the literature. We extend nonlinear models with thresholds to the analysis of repeated measurement data. We obtain estimates for parameters for these new models using the Nelder-Mead simplex algorithm, an efficient searching algorithm. This method does not require the evaluation of derivatives of the nonlinear function in order to obtain the estimates for the mean model parameters themselves, although derivatives are required to estimate the variances of the parameters. An application of the procedure to fit a population-averaged model to a toxicological study in mice and an application of the procedure to fit a subject-specific model to specific activity of a labelled compound in test subjects are provided.