Nonlinear random-effects mixture models for repeated measures

A mixture model for repeated measures based on nonlinear functions with random effects is reviewed. The model can include individual schedules of measurement, data missing at random, nonlinear functions of the random effects, of covariates and of residuals. Individual group membership probabilities and individual random effects are obtained as empirical Bayes predictions. Although this is a complicated model that combines a mixture of populations, nonlinear regression, and hierarchical models, it is straightforward to estimate by maximum likelihood using SAS PROC NLMIXED. Many different models can be studied with this procedure. The model is more general than those that can be estimated with most special purpose computer programs currently available because the response function is essentially any form of nonlinear regression. Examples and sample code are included to illustrate the method.