Continual reassessment method for ordered groups

We investigate the two-group continual reassessment method for a dose-finding study in which we anticipate some ordering between the groups. This is a situation in which, for either group, we have little or almost no knowledge about which of the available dose levels will correspond to the maximum tolerated dose (MTD), but we may have quite strong knowledge concerning which of the two groups will have the higher level of MTD, if indeed they do not have the same MTD. The motivation for studying this problem came from an investigation into a new therapy for acute leukemia in children. The background to this study is discussed. There were two groups of patients: one group already received heavy prior therapy while the second group had received relatively much lighter prior therapy. It was therefore anticipated that the second group would have an MTD higher or at least as high as the first. Generally, likelihood methods or, equivalently, the use of noninformative Bayes priors, can be used to model the main aspects of the study, i.e., the MTD for one of the groups, reserving more informative Bayes modeling to be applied to the secondary features of the study. These secondary features may simply be the direction of the difference between the MTD levels for the two groups or, possibly, information on the potential gap between the two MTDs.