Phase I design for completely or partially ordered treatment schedules.

The majority of methods for the design of phase I trials in oncology are based upon a single course of therapy, yet in actual practice, it may be the case that there is more than one treatment schedule for any given dose. Therefore, the probability of observing a dose-limiting toxicity may depend upon both the total amount of the dose given, as well as the frequency with which it is administered. The objective of the study then becomes to find an acceptable combination of both dose and schedule. Past literature on designing these trials has entailed the assumption that toxicity increases monotonically with both dose and schedule. In this article, we relax this assumption for schedules and present a dose-schedule finding design that can be generalized to situations in which we know the ordering between all schedules and those in which we do not. We present simulation results that compare our method with other suggested dose-schedule finding methodology.