Optimal Exact Designs of Multiresponse Experiments under Linear and Sparsity Constraints

We propose a computational approach to constructing exact designs on finite design spaces that are optimal for multiresponse regression experiments under a combination of the standard linear and specific 'sparsity' constraints. The linear constraints address, for example, limits on multiple resource consumption and the problem of optimal design augmentation, while the sparsity constraints control the set of distinct trial conditions utilized by the design. The key idea is to construct an artificial optimal design problem that can be solved using any existing mathematical programming technique for univariate-response optimal designs under pure linear constraints. The solution to this artificial problem can then be directly converted into an optimal design for the primary multivariate-response setting with combined linear and sparsity constraints. We demonstrate the utility and flexibility of the approach through dose-response experiments with constraints on safety, efficacy, and cost, where cost also depends on the number of distinct doses used.