Davidian, M. and Giltinan, D.M., 1993. Analysis of repeated measurement data using the nonlinear mixed effects model. Chemometrics and Intelligent Laboratory Systems, 20: 1–24. Situations in which repeated measurements are taken on each of several individual items arise in many areas. These include assay development, where concentration—response data are available for each assay run in a series of assay experiments; pharmacokinetic analysis, where repeated blood concentration measurements are obtained from each of several subjects; and growth or decay studies, where growth or decay are measured over time for each plant, animal, or some other experimental unit. In these situations the model describing the response is often nonlinear in the parameters to be estimated, as is the case for the four-parameter logistic model, which is frequently used to characterize concentration—response relationships for radioimmunoassay enzyme-linked immunosorbent assay. Furthermore, response variability typically increases with level of response. The objectives of an analysis vary according to the application: for assay analysis, calibration of unknowns for the most recent run may be of interest; in pharmacokinetics, characterization of drug disposition for a patient population may be the focus. The nonlinear mixed effects (NME) model has been used to describe repeated measurement data for which the mean response function is nonlinear. In this tutorial, the NME model is motivated and described, and several methods are given for estimation and inference in the context of the model. The methods are illustrated by application to examples from the fields of water transport kinetics, assay development, and pharmacokinetics.
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