Resumen
Most of the current research on optimal experimental designs for generalized linear models focuses on logistic regression models. In this paper, D-optimal designs for Poisson regression models are discussed. For the one-variable first-order Poisson regression model, it has been found that the D-optimal design, in terms of effective dose levels, is independent of the model parameters. However, it is not the case for more complicated models. We investigate how the D-optimal designs depend on the model parameters for the one-variable second-order model and two-variable interaction model. The performance of some “standard” designs that appeal to practitioners is also studied.

Resumen
The locally D-optimal design for the two-variable interaction Poisson regression model is not robust to parameter misspecification. To deal with this issue, a sequential design approach is investigated. Simulation is used to evaluate the sequential design. It is found that the sequential design is very efficient and quite robust to parameter misspecification on both unrestricted and restricted design regions.