Applying the partial order continual reassessment method to high-dimensional treatment combinations

Recent years have seen increasing popularities in therapies that combines several drugs and/or schedules, which imposes great difficulties on the design of appropriate Phase I clinical trials. The Partial Ordering Continual Reassessment Method (POCRM), among others, is a popular design that can be easily adapted to those complex settings. However, the design is introduced and evaluated in the setting of the combination of two drugs, and the combination of more than two drugs has rarely been investigated. In particular, the specification of toxicity orderings has always been an essential part of the POCRM, which becomes more difficult in high-dimensional settings due to the combinatorially increasing nature of the number of possible orderings of combination/schedules. This paper proposes a systematic approach to specify orderings based on asymptotic properties in the setting of the combination of more than two drugs. Large simulation studies show that this novel ordering specification method leads to better design performance both asymptotically and with finite sample sizes.