Consistency of the CRM when the dose‐toxicity curve is not monotone and its application to the POCRM

The continual reassessment method (CRM) is a well-known design for dose-finding trials with the goal of estimating the maximum tolerated dose (MTD), the dose with a given probability of toxicity. The standard assumption is that the probability of toxicity monotonically increases with dose. We show that the CRM can still be consistent and correctly identify the MTD even when the dose-toxicity curve is not monotone as long as there is monotonicity of the true toxicity probabilities right below and right above the true MTD. In the case of multiple therapies, where it is unclear how to order combinations of dose levels of multiple therapies, our findings provide insight into the performance of the partial order CRM (POCRM). To select the correct dose combination at the end of a trial, the POCRM does not have to select a monotone ordering of drug combinations. We illustrate the connection between our results for the CRM with a nonmonotone dose-toxicity curve and the POCRM via simulations.