A two-dimensional search algorithm for dose-finding trials of two agents

Existing algorithms for identifying the maximum tolerated combination in dose-finding trials of two agents are mostly one-dimensional. Moreover, these algorithms use only the frequency of observed dose-limiting toxicities as the basis for dose escalations and deescalations. In this article, we propose a two-dimensional algorithm that uses not only the frequency but also the source of dose-limiting toxicities to direct dose escalations and deescalations. In addition, when the doses of both agents are escalated simultaneously, a more conservative design replaces a default aggressive design to evaluate the resulting dose combination. Our method aims to increase in-trial patient safety without unnecessary increase in sample size.