Keywords: phase I clinical trials, standard algorithm, likelihood method, evidential paradigm. Abstract: In phase I clinical trials, the standard ‘3+3’ design has passed the test of time and survived various sample size adjustments, or other dose-escalation dynamics. The objective of this study is to provide a probabilistic support for analyzing the heuristic performance of the ‘3+3’ design. Our likelihood method is based on the evidential paradigm that uses the likelihood ratio to measure the strength of statistical evidence for one simple hypothesis over the other. We compute the operating characteristics and compare the behavior of the standard algorithm under different hypotheses, levels of evidence, and true (or best guessed) toxicity rates. Given observed toxicities per dose level, the likelihood-ratio is evaluated according to a certain k threshold (level of evidence). Under an assumed true toxicity scenario the following statistical characteristics are computed and compared: i) probability of weak evidence, ii) probability of favoring under (analogous to 1-α), iii) probability of favoring under (analogous to 1-β). This likelihood method allows consistent inferences to be made and evidence to be quantified regardless of cohort size. Moreover, this approach can be extended and used in phase I designs for identifying the highest acceptably safe dose and is akin to the sequential probability ratio test.
Phase II studies in oncology have evolved over the previous several decades. Currently, the number of drugs in phase II development has increased, and patient eligibility has narrowed due to targeted agents, competing trials and curative therapies in the first-line setting. As a result of these changes, more attention needs to be focused toward conducting more efficient phase II trials. Given the increased difficulty in accruing patients to phase II studies and the ethical concern of treating patients with agents that are ineffective, there is significant motivation to stop a single arm trial early when the investigational agent shows evidence of a low response rate.