David M. Giltinan

Nonlinear Models for Repeated Measurement Data: An Overview and Update

Nonlinear mixed effects models for data in the form of continuous, repeated measurements on each of a number of individuals, also known as hierarchical nonlinear models, are a popular platform for analysis when interest focuses on individual-specific characteristics. This framework first enjoyed widespread attention within the statistical research community in the late 1980s, and the 1990s saw vigorous development of new methodological and computational techniques for these models, the emergence of general-purpose software, and broad application of the models in numerous substantive fields. This article presentsan overview of the formulation, interpretation, and implementation of nonlinear mixed effects models and surveys recent advances and applications.

Some general estimation methods for nonlinear mixed-effects model

A nonlinear mixed-effects model suitable for characterizing repeated measurement data is described. The model allows dependence of random coefficients on covariate information and accommodates general specifications of a common intraindividual covariance structure, such as models for variance within individuals that depend on individual mean response and autocorrelation. Two classes of procedures for estimation in this model are described, which incorporate estimation of unknown parameters in the assumed intraindividual covariance structure. The procedures are straightforward to implement using standard statistical software. The techniques are illustrated by examples in growth analysis and assay development.

A Two-Step Approach to Measurement Error in Time-Dependent Covariates in Nonlinear Mixed-Effects Models, with Application to IGF-I Pharmacokinetics

Abstract The usual approach to the analysis of population pharmacokinetic studies is to represent the concentration-time data by a nonlinear mixed-effects model. Primary objectives are to characterize the pattern of drug disposition in the population and to identify individual-specific covariates associated with pharmacokinetic behavior. We consider data from a study of insulin-like growth factor I (IGF-I) administered by intravenous infusion to patients with severe head trauma. Failure to maintain steady-state levels of IGF-I was thought to be related to the temporal pattern of several covariates measured in the study, and an analysis investigating this issue was of interest. Observations on these potentially relevant covariates for each subject were made at time points different from those at which IGF-I concentrations were determined; moreover, the covariates themselves were likely subject to measurement error. The usual approach to time-dependent covariates in population analysis is to invoke a simple...

Some simple methods for estimating intraindividual variability in nonlinear mixed effects models

Methods are proposed to improve both population and individual inference within the nonlinear random coefficient regression framework by incorporating possible heterogeneity in the intraindividual variance structure. These methods extend existing variance function estimation techniques by pooling information across individuals. The methods are appropriate when it is reasonable to assume that there exists a common intraindividual variance structure.

The Effect of Variance Function Estimation on Nonlinear Calibration Inference in Immunoassay Data

Often with data from immunoassays, the concentration-response relationship is nonlinear and intra-assay response variance is heterogeneous. Estimation of the standard curve is usually based on a nonlinear heteroscedastic regression model for concentration-response, where variance is modeled as a function of mean response and additional variance parameters. This paper discusses calibration inference for immunoassay data which exhibit this nonlinear heteroscedastic mean-variance relationship. An assessment of the effect of variance function estimation in three types of approximate large-sample confidence intervals for unknown concentrations is given by theoretical and empirical investigation and application to two examples. A major finding is that the accuracy of such calibration intervals depends critically on the nature of response variance and the quality with which variance parameters are estimated.

Analysis of repeated measurement data using the nonlinear mixed effects model

Abstract 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.

Statistical Issues in Assay Development and Use

Technical advances in assay methods over the past decades have made reliable measurement of analytes at extremely low concentrations a reality. The potential utility of this enhancement in assay resolution for clinical and laboratory studies, particularly those focusing on pharmacokinetics and metabolism, is obvious. However, any potential gains may be lost by failure of the investigator to appreciate the nuances and limitations of the specific assay being used. In particular, if the study design does not incorporate appropriate measures to minimize any potential confounding effects of assay limitations, the resulting ambiguity in interpreting the data may be great enough to preclude reaching definitive conclusions. To avoid this particular type of experimental failure, scientists should be sufficiently aware of assay-related issues to be able to function as intelligent ‘assay consumers.’