Special Issue Paper Received 9 September 2011, Accepted 4 June 2012 Published online 16 July 2012 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/sim.5505 A Bayesian predictive sample size selection design for single-arm exploratory clinical trials Satoshi Teramukai, a * † Takashi Daimon b and Sarah Zohar c The aim of an exploratory clinical trial is to determine whether a new intervention is promising for further test- ing in confirmatory clinical trials. Most exploratory clinical trials are designed as single-arm trials using a binary outcome with or without interim monitoring for early stopping. In this context, we propose a Bayesian adaptive design denoted as predictive sample size selection design (PSSD). The design allows for sample size selection following any planned interim analyses for early stopping of a trial, together with sample size determination before starting the trial. In the PSSD, we determine the sample size using the method proposed by Sambucini (Statistics in Medicine 2008; 27:1199–1224), which adopts a predictive probability criterion with two kinds of prior distributions, that is, an ‘analysis prior’ used to compute posterior probabilities and a ‘design prior’ used to obtain prior predictive distributions. In the sample size determination of the PSSD, we provide two sample sizes, that is, N and N max , using two types of design priors. At each interim analysis, we calculate the predictive probabilities of achieving a successful result at the end of the trial using the analysis prior in order to stop the trial in case of low or high efficacy (Lee et al., Clinical Trials 2008; 5:93–106), and we select an optimal sample size, that is, either N or N max as needed, on the basis of the predictive probabilities. We investigate the operating characteristics through simulation studies, and the PSSD retrospectively applies to a lung cancer clinical trial. (243) Copyright © 2012 John Wiley & Sons, Ltd. Keywords: Bayesian approach; adaptive design; analysis and design priors; prior predictive distributions; interim monitoring 1. Introduction The aim of exploratory clinical trials, such as phase II trials and proof-of-concept studies, is to determine whether a new intervention is promising for further testing in confirmatory clinical trials, such as phase III randomised controlled trials. Most exploratory clinical trials are designed as single-arm trials with or without interim monitoring for early stopping. In this setting, the efficacy of treatment is commonly evaluated using a binary outcome such as tumour shrinkage or response to treatment. Zohar et al. [1] emphasised that Bayesian approaches are ideal for such exploratory clinical trials as they take into account previous information about the quantity of interest as well as accumulated data during a trial. In this context, various Bayesian approaches or designs have been proposed for single-arm clinical trials. For instance, Tan and Machin [2] developed a Bayesian two-stage design called single threshold design (STD), and Mayo and Gajewski [3, 4] extended this proposition into a design incorporating informative prior distributions. Whitehead et al. [5] formulated a simple approach to sample size determination (SSD) in which they incorporate historical data in the Bayesian inference. Furthermore, Sambucini [6] proposed a predictive version of the STD (PSTD) using two kinds of prior distributions a Department of Clinical Trial Design and Management, Translational Research Center, Kyoto University Hospital, Kyoto, Japan b Department of Biostatistics, Hyogo College of Medicine, Hyogo, Japan c Inserm, U717 Biostatistics Department, F75010 Paris, France *Correspondence to: Satoshi Teramukai, Department of Clinical Trial Design and Management, Translational Research Center, Kyoto University Hospital, 54 Shogoin-kawaharacho, Sakyo-ku, Kyoto 606-8507, Japan. † E-mail: steramu@kuhp.kyoto-u.ac.jp Copyright © 2012 John Wiley & Sons, Ltd. Statist. Med. 2012, 31 4243–4254 4243