title: Bayesian designs with frequentist and Bayesian error rate considerations.
abstract: So far, most Phase II trials have been designed and analysed under a frequentist framework. Under this framework, a trial is designed so that the overall Type I and Type II errors of the trial are controlled at some desired levels. Recently, a number of articles have advocated the use of Bayesian designs in practice. Under a Bayesian framework, a trial is designed so that the trial stops when the posterior probability of treatment is within certain prespecified thresholds. In this article, we argue that trials under a Bayesian framework can also be designed to control frequentist error rates. We introduce a Bayesian version of Simon's well-known two-stage design to achieve this goal. We also consider two other errors, which are called Bayesian errors in this article because of their similarities to posterior probabilities. We show that our method can also control these Bayesian-type errors. We compare our method with other recent Bayesian designs in a numerical study and discuss implications of different designs on error rates. An example of a clinical trial for patients with nasopharyngeal carcinoma is used to illustrate differences of the different designs.
authors.affiliation: Department of Statistics and Applied Probability, National University of Singapore, Singapore. you-gan.wang@csiro.au
authors.forename: You-Gan
authors.initials: YG
authors.lastname: Wang
authors.forename: Denis Heng-Yan
authors.initials: DH
authors.lastname: Leung
authors.forename: Ming
authors.initials: M
authors.lastname: Li
authors.forename: Say-Beng
authors.initials: SB
authors.lastname: Tan
mesh_terms: D001499:Bayes Theorem; D015982:Bias; D017322:Clinical Trials, Phase II as Topic / Q000706:statistics & numerical data; D006801:Humans; D015233:Models, Statistical; D012107:Research Design; D012846:Singapore