Sequential experimental designs for generalized linear models

We consider the problem of experimental design when the response is modeled by a generalized linear model (GLM) and the experimental plan can be determined sequentially. Most previous research on this problem has been limited either to one-factor, binary response experiments or to augmenting the design when there are already sufficient data to compute parameter estimates. We suggest a new procedure for the sequential choice of observations that offers five important advantages: (1) It can be applied to multifactor experiments and is not limited to the one-factor setting; (2) it can be used with any GLM, not just binary responses; (3) both fully sequential and group sequential settings are treated; (4) it enables efficient design from the outset of the experiment; and (5) the experimenter is not constrained to specify a single model and can use the prior to reflect uncertainty as to the link function and the form of the linear predictor. Our procedure is based on a D-optimality criterion and on a Bayesian analysis that exploits a discretization of the parameter space to efficiently represent the posterior distribution. In the one-factor setting, a simulation study shows that our method is superior in efficiency to commonly used procedures, such as the "Bruceton" test, Neyer's procedure, or Wu's improved Robbins-Monro method. We also present a comparison of results obtained with the new algorithm versus the "Bruceton" method on an actual sensitivity test conducted recently at an industrial plant. Source code for the algorithms and examples throughout the article is available at http://www.math.tau.ac.il/similar to dms/GLM-Design.