Continual reassessment designs with early termination.

The continual reassessment method (CRM) is an increasingly popular approach for estimating the maximum tolerated dose (MTD) in phase I dose finding studies. In its original formulation, the scheme is based on a fixed sample size. Many experimenters feel that, whenever possible, it may be advantageous to bring these trials to an early halt and thus reduce average sample size required to complete the study. To address this issue a stopping rule has been proposed (O'Quigley and Reiner, 1998) based on the idea that continuing the study would not lead to a change in recommendation with high probability. The rule, based on precise probabilistic calculation, is quite involved and not straightforward to implement. A much simpler rule can be constructed based on the idea of having settled at some level. In this work we investigate more deeply the essential ingredients behind these rules and consider more closely their operating characteristics.