Optimal Designs for Order-of-Addition Two-Level Factorial Experiments

A new type of experiment, called the order-of-addition factorial experiment, has recently received considerable attention in medical science and bioengineering. These experiments aim to simultaneously optimize the order of addition and dose levels of drug components. In the experimental design literature, the concept of dual-orthogonal arrays (DOAs), a class of optimal order-of-addition two-level factorial designs under the compound model, has recently been introduced for such experiments. However, constructing flexible DOAs remains a challenging task. In this article, we propose a novel theory-guided search method to efficiently identify DOAs of any feasible size. We also provide an algebraic construction method that immediately leads to certain DOAs. Moreover, to address the potential issue that DOA ignores interaction effects, we propose to construct a new type of optimal designs under the expanded compound model, named the strong DOA (SDOA). We provide two algebraic construction methods for the SDOA. We establish theoretical results on the optimality of both DOAs and SDOAs. Numerical studies illustrate the superiority of our proposed designs.