The expected toxicity rate at the maximum tolerated dose in the standard phase I cancer clinical trial design

A main purpose of Phase I cancer clinical trials is to identify the maximum tolerated dose (MTD) of a new agent for experimentation in Phase II and III studies. The continual reassessment method has been shown to be superior to the standard design. However, in practice, the standard design has still been widely used. Therefore, it is important to investigate the performance of the standard design accurately. In this paper, we develop an algorithm to compute the exact distribution of the recommended dose level in the standard design. The algorithm is a better tool than simulation in the investigation of the operating characteristics of the standard design, because it does not involve any sampling error and computing time is much shorter than simulation. With the algorithm, the expected toxicity rate at the MTD in the standard design is investigated extensively for some dose-toxicity curves in a certain range.