Penalized and response-adaptive optimal designs. Application to dose finding

Optimal design under a cost constraint is considered, with a scalar coefficient setting the compromise between information (i.e., precision of the estimation of the model parameters) and cost. For suitable cost functions, by increasing the value of the coefficient one can force the support points of an optimal design measure to concentrate around points of minimum cost. When the experiment is constructed sequentially, the choice of each new design point being based on the current estimated value of the model parameters (response-adaptive design), the strong consistency and asymptotic normality of the estimator of the model parameters is obtained under the assumption that the design variables belong to a finite set. An example of adaptive design in a dose-finding problem with a bivariate binary model is presented, showing the effectiveness of the approach.