The adaptive accelerated biased coin design for phase I clinical trials

Phase I clinical trials are designed to study several doses of the same drug in a small group of patients to determine the maximum tolerated dose (MTD), which is defined as the dose that is associated with dose-limiting toxicity (DLT) in a desired fraction Γ of patients. Durham and Flournoy [5 Durham, S. and Flournoy, N. 1995. Up-and-down designs I: Stationary treatment distributions. IMS Lecture Notes – Monogr. Ser., 25: 139–157.  [Google Scholar]] proposed the biased coin design (BCD), which is an up-and-down design that assigns a new patient to a dose depending upon whether or not the current patient experienced a DLT. However, the BCD in its standard form requires the complete follow-up of the current patient before the new patient can be assigned a dose. In situations where patients’ follow-up times are relatively long compared to patient inter-arrival times, the BCD will result in an impractically long trial and cause patients to either have delayed entry into the trial or refusal of entry altogether. We propose an adaptive accelerated BCD (aaBCD) that generalizes the traditional BCD design algorithm by incorporating an adaptive weight function based upon the amount of follow-up of each enrolled patient. By doing so, the dose assignment for each eligible patient can be determined immediately with no delay, leading to a shorter trial overall. We show, via simulation, that the frequency of correctly identifying the MTD at the end of the study with the aaBCD, as well as the number of patients assigned to the MTD, are comparable to that of the traditional BCD design. We also compare the performance of the aaBCD with the accelerated BCD (ABCD) of Stylianou and Follman [19 Stylianou, M. and Follmann, D. A. 2004. The accelerated biased coin up-and-down design in phase I trials. J. Biopharmaceutical Statist., 14: 249–260. [Taylor & Francis Online] [Google Scholar]], as well as the time-to-event continual reassessment method (TITE-CRM) of Cheung and Chappell [4 Cheung, Y. K. and Chappell, R. 2000. Sequential designs for phase I clinical trials with late-onset toxicities. Biometrics, 56: 1177–1182. [Crossref], [PubMed], [Web of Science ®] [Google Scholar]].