An asymptotic confidence interval for the response at the stationary point of a quadratic response surface

The delta method is utilized to construct an asymptotic 100(1 - a)% confidence interval for the response at the stationary point of a quadratic response surface. The end-points of the interval can be found directly compared to other more computationally intense procedures that result in a conservative interval. The coverage probability associated with intervals constructed in this manner from studies with relatively small numbers of observations is investigated via a simulation study. Finally the methodology is illustrated with an example involving the evaluation of a combination of cytotoxic agents in the treatment of murine LI210 leukemia.