Design and modeling of order of addition experiment with component effects

An order of addition experiment is an experiment to study how the order of addition of components affect the results, with the objective of predicting and determining the optimal order of addition of components. Order of addition experiment are also commonly used in the drug combination therapy, where experimenting with all drugs combinations is unaffordable. To solve this problem, we constructed a new design table, two-level component factorial design table (TLCF), which combine the component orthogonal array design table and the two-level partial factorial design table by matrix product. TLCF can explore the order and dosage effect of components on the results and can greatly reduce the number of experiments. We also prove that the relative D-efficiency of the TLCF can reach 100% and solve an explicit expression for the D-efficiency of the full design. In the simulation experiment, we compare the D-efficiency of the TLCF with the random design table to prove the superiority of TLCF. Finally, we give a treatment plan for the combination of three drugs for glioblastoma based on the TLCF, which provides a new perspective for the precision treatment of patients.