Contreras M, Ryan L M
Department of Biometry, Cornell University, 435 Warren Hall, Ithaca, New York 14853, USA.
Biometrics. 2000 Dec;56(4):1268-71. doi: 10.1111/j.0006-341x.2000.01268.x.
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.
