Optimal multi-stage designs for a phase II trial that permits one dose escalation

Simon's optimal two-stage design is widely used to conduct single-dose phase II clinical trials. We extend this basic methodology to the situation where the researcher desires to test an experimental drug for activity at a low dose level, but is willing to increase the dose part-way through the trial if the early results suggest that the low dose is ineffective. Interest is confined to at most one dose escalation, and no consideration is given to escalating the dose within a patient. Optimal multi-stage designs are presented that are more efficient than the naive approach of merely conducting two consecutive Simon optimal trials, one at the low dose and the second (if deemed necessary) at the high dose. As in Simon's original design, toxicity is not considered here as a primary endpoint. Hence, the designs presented in this paper are appropriate only when the toxicity of the drug is well understood at both dose levels.