D-Optimal designs for poisson regression models

We consider the problem of finding an optimal design under a Poisson regression model with a log link, any number of independent variables, and an additive linear predictor. Local D-optimality of a class of designs is established through use of a canonical form of the problem and a general equivalence theorem. The results are applied in conjunction with clustering techniques to obtain a fast method of finding designs that are robust to wide ranges of model parameter values. The methods are illustrated through examples.