Sequential continual reassessment method for two-dimensional dose finding

It is common to encounter two-dimensional dose finding in phase I trials, for example, in trials combining multiple drugs, or in single-agent trials that simultaneously search for the maximum tolerated dose (MTD) and the optimal treatment schedule. In these cases, the traditional single-agent dose-finding methods are not directly applicable. We propose a simple and adaptive two-dimensional dose-finding design that can accommodate any type of single-agent dose-finding method. In particular, we convert the two-dimensional dose-finding trial to a series of one-dimensional dose-finding subtrials along shortened line search segments by fixing the dose level of one drug. We then conduct the subtrials sequentially. Based on the MTD obtained from the completed one-dimensional trial, we eliminate the doses that lie outside of the search range based on the partial order, and thereby efficiently shrink the two-dimensional dose-finding space. The proposed design dramatically reduces the sample size and still maintains good performance. We illustrate the design through extensive simulation studies motivated by clinical trials evaluating multiple drugs or dose and schedule combinations.