Two-sample continual reassessment method

We discuss an extension of the continual reassessment method (CRM) for use in phase I dose-finding studies. The extension enables the method to be applied to two groups of patients to determine the appropriate dose levels for each group. The method takes the specification of a simple relationship between the dose-toxicity curves for the two groups and runs the CRM on the bivariate model using maximum likelihood. We prove consistency of the method under fairly weak conditions and provide several simulations to give an idea how the method works in practice. We also undertake an evaluation of its performance by considering three possible situations: The first is the two-sample CRM, which directly uses a working model for the relationship between the two groups, carrying out a single trial using this method; the second situation carries out single trials for each of the two groups separately using the original (one-sample) CRM. The third situation is the case where such heterogeneity is ignored and the two groups are pooled into a single group, again using the original (one-sample) CRM. Simulations are carried out under a large class of model misspecifications, both of the dose-toxicity relationships and of the functional form linking the groups, and are backed up by asymptotic results. Our conclusions match intuition: The first scheme gives the most favorable results when the two groups are different but share some features. When the groups are very different, the second scheme performs similarly to the first for finite sample sizes while having some advantages in terms of asymptotic efficiency. The third, as expected, gives the best results in the absence of patient heterogeneity. The two-sample method appears particularly advantageous when there may not be enough subjects in one of the subgroups for it to be feasible to carry out two trials.