title: Fitting nonlinear and constrained generalized estimating equations with optimization software.
abstract: 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.
authors: Department of Biometry, Cornell University, 435 Warren Hall, Ithaca, New York 14853, USA. mpc14@cornell.edu
authors: M
authors: M
authors: Contreras
authors: L M
authors: LM
authors: Ryan
mesh_terms: D000818:Animals; D001699:Biometry / Q000379:methods*; D016001:Confidence Intervals; D004051:Diethylhexyl Phthalate / Q000633:toxicity; D005260:Female; D015233:Models, Statistical; D011247:Pregnancy; D012984:Software; D018709:Statistics, Nonparametric; D013723:Teratogens / Q000633:toxicity; D018675:Toxicity Tests
chemical_list: D013723:Teratogens; D004051:Diethylhexyl Phthalate