  Deriving optimal designs for nonlinear models is in general challenging. One
crucial step is to determine the number of support points needed. Current tools
handle this on a case-by-case basis. Each combination of model, optimality
criterion and objective requires its own proof. The celebrated de la Garza
Phenomenon states that under a (p-1)th-degree polynomial regression model, any
optimal design can be based on at most p design points, the minimum number of
support points such that all parameters are estimable. Does this conclusion
also hold for nonlinear models? If the answer is yes, it would be relatively
easy to derive any optimal design, analytically or numerically. In this paper,
a novel approach is developed to address this question. Using this new
approach, it can be easily shown that the de la Garza phenomenon exists for
many commonly studied nonlinear models, such as the Emax model, exponential
model, three- and four-parameter log-linear models, Emax-PK1 model, as well as
many classical polynomial regression models. The proposed approach unifies and
extends many well-known results in the optimal design literature. It has four
advantages over current tools: (i) it can be applied to many forms of nonlinear
models; to continuous or discrete data; to data with homogeneous or
non-homogeneous errors; (ii) it can be applied to any design region; (iii) it
can be applied to multiple-stage optimal design; and (iv) it can be easily
implemented.
