Fitting nonlinear and constrained generalized estimating equations with optimization software.

In this article, we present an estimation approach for solving nonlinear constrained generalized estimating equations that can be implemented using object-oriented software for nonlinear programming, such as nlminb in Splus or fmincon and lsqnonlin in Matlab. We show how standard estimating equation theory includes this method as a special case so that our estimates, when unconstrained, will remain consistent and asymptotically normal. To illustrate this method, we fit a nonlinear dose-response model with nonnegative mixed bound constraints to clustered binary data from a developmental toxicity study. Satisfactory confidence intervals are found using a nonparametric bootstrap method when a common correlation coefficient is assumed for all the dose groups and for some of the dose-specific groups.