Optimal Bayesian Design Applied to Logistic Regression Experiments

A traditional way to design a binary response experiment is to design the experiment to be most efficient for a best guess of the parameter values. A design which is optimal for a best guess however may not be efficient for parameter values close to that best guess. We propose designs which formally account for the prior uncertainty in the parameter values. A design for a situation where the best guess has substantial uncertainty attached to it is very different from a design for a situation where approximate values of the parameters are known. We derive a general theory for concave design critria for non-linear models and then apply the theory to logistic regression. Designs found by numerical optimization are examined for a range of prior distributions and a range of criteria. The theoretical results are used to verify that the designs are indeed optimal. AMS Subject Classification: Primary 62KO5; Secondary 62F15.