Binary reponse data is often modeled using the logistic regression model, a
well known nonlinear model. Designing an optimal experiment for this nonlinear
situation poses some problems not encountered with a linear model. The
application of several optimality design criteria to the logistic regression model is
explored, and many resulting optimal designs are given. The implementation of
these optimal designs requires the parameters of the model to be known.
However, the model parameters are not known. If they were, there would be no
need to design an experiment. Consequently the parameters must be estimated
prior to implementing a design.
Standard one-stage optimal designs are quite sensitive to parameter
misspecification and are therefore unsatisfactory in practice. A two-stage
Bayesian design procedure is developed which effectively deals with poor
parameter knowledge while maintaining high efficiency. The first stage makes use
of Bayesian design as well as Bayesian estimation in order to cope with parameter
misspecification. Using the parameter estimates from the first stage, the second
stage conditionally optimizes a chosen design optimality criterion.
Asymptotically, the two-stage design procedure is considerably more efficient than
the one-stage design when the parameters are misspecified and only slightly less
efficient when the parameters are known. The superiority of the two-stage
procedure over the one-stage is even more evident for small samples.
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