*Multivariate optimizing up -and -down design

A Bivariate Optimizing Up-and-Down design for selecting the drug combination with maximum success probability is presented. We assume success is a unimodal function of dose, i.e., too little dose or too much dose both lead to failure. This design is motivated by a stochastic approximation procedure that was developed to work with continuous response and dependent variables. The stochastic approximation procedure is modified to work more efficiently with binary random variables and a finite number of treatment combinations. The procedure is shown to cluster treatments around the treatment that has maximum success probability. We use the mode as an estimator of the best dose and we show the marginal performance of the empirical modes. We show methods of identifying the best dose combination.