Abstract: In typical binary response models, the information matrix depends both on the design and the unknown parameters of interest. Thus to obtain optimal designs, one must have `good' initial parameter estimates. Often this is not the case. One solution which may be applicable in some settings is to perform the experiment in two (or more) stages, that is, use an initial design to get parameter estimates and then treating these as the true parameter values choose a second stage design so that the combined first and second stage design is optimal in some sense. In this article, we consider a class of symmetric binary response models which includes the common logit and probit models, and show that for any of the main optimality criteria in the literature (eg. A-, D-, E-, F-, G- and c-optimality) the optimal second stage design will consist of two points symmetrically placed about the ED50 (the 50% response dose) with possibly different weights at each point. We go on to give examples where one can further reduce the resulting optimization to a one variable maximization. In the process some insight is gained into how the second stage design corrects skewness in the first stage design.
Key words and phrases: Binary data, confidence interval, Fieller's theorem, logit, probit.