CUSUMIN: A cumulative sum interval design for cancer phase I dose finding studies

Recently, model-assisted designs, including the Bayesian optimal interval (BOIN) design with optimal thresholds to determine the dose for the next cohort, have been proposed for cancer phase I studies. Model-assisted designs are useful because of their good performance as model-based designs in addition to their algorithm-based simplicity. In BOIN, escalation and de-escalation based on boundaries can be understood as a type of change point detection based on a sequential test procedure. Notably, the sequential test procedure is used in a wide range of fields and is known for its application to control charts, statistical monitoring methods used for detecting abnormalities in manufacturing processes. In control charts, abnormalities are detected if the control chart statistics are observed to be outside of the optimal boundaries. The cumulative sum (CUSUM) statistic, which is developed for control chart applications, derives higher power under the same erroneous judgment rate. Hence, it is expected that a more efficient model-assisted design can be achieved by the application of CUSUM statistics. In this study, a model-assisted design based on the CUSUM statistic is proposed. In the proposed design, the dose for the next cohort is decided by CUSUM statistics calculated from the counts of the dose-limiting toxicity and pre-defined boundaries, based on the CUSUM control chart scheme. Intensive simulation shows that our proposed method performs better than BOIN, and other representative model-assisted designs, including modified toxicity probability interval (mTPI) and Keyboard, in terms of controlling over-dosing rates while maintaining similar performance in the determination of maximum tolerated dose.