UCLA

The ordering effect of sequential treatment addition is present in many problem areas ranging from online search ranking and job scheduling to election standardization and the design of clinical trials. The straightforward approach to studying this ordering effect on a response is to test each permutation of the treatment components. When the run size becomes too costly, a random sample of permutations can instead be used for estimation and inference. Noting the inefficiencies present in both of these approaches, well-designed order-of-addition experiments have been proposed to reduce the computational complexity of studying the ordering effect without sacrificing statistical power; however, this problem is under-studied in the statistical literature.

In this work we make several state-of-the-art advancements to the order-of-addition literature. By leveraging the structure of order-of-addition data, we pose flexible, position-based models that work well in practice. These new models inspire and necessitate the creation of parsimonious designs that guarantee stable parameter estimates. We further adapt these designs for a component screening problem in which the pool of treatment components is larger than the number of available positions in the sequence.

We test our methods against several prominent order-of-addition problems, including drug chemotherapy and job scheduling. Our models and model-based optimal designs outperform the accepted alternatives in most cases, and in other situations our methods act as valuable tools for encouraging robust experimentation. To encourage the use of quality order-of-addition designs in wider practice, we implement and compare popular, nature-inspired metaheuristic algorithms for solving difficult design problems without closed-form solutions. We find that certain variants and hybridized algorithms can produce quality designs for obtaining stable parameter estimates in order-of-addition models or for studying black-box deterministic functions on the space of permutations.