Optimal discrimination designs for exponential regression models

Abstract

We investigate optimal designs for discriminating between exponential regression models of different complexity, which are widely used in the biological sciences; see, e.g., Landaw (1995) or Gibaldi and Perrier (1982). We discuss different approaches for the construction of appropriate optimality criteria, and find sharper upper bounds on the number of support points of locally optimal discrimination designs than those given by Caratheodory's Theorem. These results greatly facilitate the numerical construction of optimal designs. Various examples of optimal designs are then presented and compared to different other designs. Moreover, to protect the experiment against misspecifications of the nonlinear model parameters, we adapt the design criteria such that the resulting designs are robust with respect to such misspecifications and, again, provide several examples, which demonstrate the advantages of our approach.

Optimal discrimination designs

“…where the explanatory variable varies in the interval X = [−1, 1]. These models have numerous applications in pharmacokinetics (see, e.g., Shargel and Yu [31] or Rowland [29]) and optimal designs have been discussed extensively in the recent literature (see, Dette, Melas and Pepelysheff [15] or Biedermann, Dette and Pepelysheff [6]). It follows by similar arguments as given in Example 4.3 that a T -optimal design has at most three support points.…”