Optimal and efficient designs for Gompertz regression models

Gompertz functions have been widely used in characterizing biological growth curves. In this paper we consider D-optimal designs for Gompertz regression models. For homoscedastic Gompertz regression models with two or three parameters, we prove that D-optimal designs are minimally supported. Considering that minimally supported designs might not be applicable in practice, alternative designs are proposed. Using the D-optimal designs as benchmark designs, these alternative designs are found to be efficient in general. Copyright The Institute of Statistical Mathematics, Tokyo 2012