Designing the future: A simple algorithm for sequential design of a generalized linear model

Abstract In bioassay it is common to design an experiment for the purpose of estimating the quantiles of a response function. For example if an experimental subject is administered a log dose z of a potentially toxic agent, and we either observe an effect Y=1 or no effect Y=0, we might wish to estimate the dose at which only a small fraction, say 1% of the experimental subjects are effected. Designing such an experiment is typically not easy, since an optimal design requires initial estimators of the underlying parameters. In this paper, we suggest a simple sequential method for constructing a design in a generalized linear model based on information collected so far. Geometric tools for evaluating the success of the design are suggested.