Optimal designs for testing the efficacy of heterogeneous experimental groups

This paper develops a unified framework for deriving optimal designs for hypothesis testing in the presence of several heteroscedastic groups. In particular, the obtained optimal designs are generalized Neyman allocations involving only two experimental groups. In order to account for the ordering among the treatments, particularly relevant in the clinical context for ethical reasons, we provide the optimal design for testing under constraints reflecting their effectiveness. The advantages of the suggested allocations are illustrated both theoretically and through several numerical examples, also compared with other designs proposed in the literature, showing a substantial gain in terms of both power and ethics.