Multivariate Optimizing Up and Down Design

Suppose we are interested in finding the optimal dose of two drugs (for example, Tylenol and Aspirin), that is, we are interested in determining the dose combination that maximizes the probability of patients’ success. We assume responses are binary, either failure or success, and that the treatments to be used in the study are selected from a lattice of combination drugs. We extend the univariate Optimizing Up-and-Down Design of Kpamegan (2001), using ideas from stochastic approximation, in a way that the number of subjects at each stage is independent of the number of predictor variables (e.g. drugs).