The methods of optimum experimental design are particularly important in non-standard problems. One important class is that of models nonlinear in the parameters. As an example we find an optimum design for the parameters in the model for competitive inhibition in enzyme kinetics, an extension of the Michaelis-Menten model. With each experimental run yielding a single observation, an equivalence theorem can be used to demonstrate he optimality of the design.
We introduce an extension of the equivalence theorem for experiments in which each run produces several observations, for example a series of points over time. We use this extension to find optimum experiments for the parameters of a linear model in an experiment in deep brain stimulation with sets of treatment combinations per experimental run limited by restrictions on the amount of radiation.
Further topics develop the designs for both these problems. There are several models for inhibition in enzyme kinetics and experiments are required to choose which model is appropriate. In the experiment in deep brain stimulation, patients arrive sequentially and should be randomized to selected sets of treatment combinations to provide balance over prognostic factors. Both problems are solved through the use of optimum design theory.
Anthony Atkinson obtained his Ph.D. from Imperial College, where his supervisor was David Cox. He remained at IC for 20 years becoming a Professor of Statistics. In 1989 he moved to the London School of Economics. As well as optimum experimental design, his current research interests include robust statistical methods using the forward search and randomization methods in clinical trials.