Optimal Designs for 2^k Factorial Experiments with Binary Response

We consider the problem of obtaining D-optimal designs for factorial experiments with a binary response and $k$ qualitative factors each at two levels. We obtain a characterization for a design to be locally D-optimal. Based on this characterization, we develop efficient numerical techniques to search for locally D-optimal designs. Using prior distributions on the parameters, we investigate EW D-optimal designs, which are designs that maximize the determinant of the expected information matrix. It turns out that these designs can be obtained very easily using our proposed algorithm for locally D-optimal designs and are very good surrogates for the Bayes D-optimal designs. We also investigate the properties of fractional factorial designs and study the robustness with respect to the assumed parameter values of locally D-optimal designs.