A note on the robustness of the continual reassessment method

The continual reassessment method (CRM) is a model-based design that aims at finding the maximum tolerated dose (MTD) of a given drug. As the CRM is a model-based technique, its use may be restricted to cases where the true dose-response curve satisfies its underlying working model. Shen and O'Quigley (1996) prove that the CRM is consistent (converges to the MTD) for a family of dose-response curves that satisfies several quite restrictive criteria. Cheung and Chappell (2002) conjecture that the CRM is consistent under a much weaker set of conditions and test their conjecture by a simulation study, but do not provide a formal proof for their claim. The current note fills this gap and provides a formal proof for the conjecture of Cheung and Chappell, thus giving a solid justification for the robustness of the CRM for misspecified model.