• combined drugs;
  • dose escalation;
  • dose-finding study;
  • maximum tolerated dose;
  • phase I clinical trial;
  • toxicity

Dose finding for combined drugs has grown rapidly in oncology drug development. The escalation with overdose control (EWOC) method is a popular model-based dose-finding approach to single-agent phase I clinical trials. When two drugs are combined as a treatment, we propose a two-dimensional EWOC design for dose finding on the basis of a four-parameter logistic regression model. During trial conduct, we continuously update the posterior distribution of the maximum tolerated dose (MTD) combination to find the most appropriate dose combination for each cohort of patients. The probability that the next assigned dose combination exceeds the MTD combination can be controlled by a feasibility bound, which is based on a prespecified quantile level of the MTD distribution such as to reduce the possibility of overdosing. We determine dose escalation, de-escalation, or staying at the same doses by searching the MTD combination along the rows and columns in a two-drug combination matrix, respectively. We conduct simulation studies to examine the performance of the two-dimensional EWOC design under various practical scenarios, and illustrate it with a trial example. Copyright © 2013 John Wiley & Sons, Ltd.