An investigation of the traditional algorithm-based designs for phase 1 cancer clinical trials

The primary aim of a phase 1 cancer clinical trial is to determine the maximum tolerated dose of a new drug. Although the continual reassessment method is shown to have better operating characteristics than traditional designs, traditional designs are still widely used in practice. Kang and Ahn (1) developed an algorithm to compute the exact distribution of the maximum tolerated dose (MTD) in traditional designs with dose deescalation and investigated the expected toxicity rate at the MTD with the algorithm. In this paper, using the exact formulae derived by Lin and Shih (2), we study the expected toxicity rate at the MTD and the expected number of patients with toxicity and patients required when the hyperbolic tangent and the logistic functions are used as the unknown dose-toxicity curves. We consider the expected toxicity rate both without and with dose deescalation. No further study was done before in cases where dose level zero is chosen as the MTD. Since, in real practice, dose levels are lowered for adjustment and a new trial is conducted when dose level zero is decided as the MTD, we also incorporate this dose adjustment.