A confidence function‐based posterior probability design for phase II cancer trials

Single‐arm one‐ or multi‐stage study designs are commonly used in phase II oncology development when the primary outcome of interest is tumor response, a binary variable. Both two‐ and three‐outcome designs are available. Simon two‐stage design is a well‐known example of two‐outcome designs. The objective of a two‐outcome trial is to reject either the null hypothesis that the objective response rate (ORR) is less than or equal to a pre‐specified low uninteresting rate or to reject the alternative hypothesis that the ORR is greater than or equal to some target rate. Three‐outcome designs proposed by Sargent et al. allow a middle gray decision zone which rejects neither hypothesis in order to reduce the required study size. We propose new two‐ and three‐outcome designs with continual monitoring based on Bayesian posterior probability that meet frequentist specifications such as type I and II error rates. Futility and/or efficacy boundaries are based on confidence functions, which can require higher levels of evidence for early versus late stopping and have clear and intuitive interpretations. We search in a class of such procedures for optimal designs that minimize a given loss function such as average sample size under the null hypothesis. We present several examples and compare our design with other procedures in the literature and show that our design has good operating characteristics.