title: On Simon's two-stage design for single-arm phase IIA cancer clinical trials under beta-binomial distribution.
abstract: Simon (Control. Clin. Trials 1989; 10:1-10)'s two-stage design has been broadly applied to single-arm phase IIA cancer clinical trials in order to minimize either the expected or the maximum sample size under the null hypothesis of drug inefficacy, i.e. when the pre-specified amount of improvement in response rate (RR) is not expected to be observed. This paper studies a realistic scenario where the standard and experimental treatment RRs follow two continuous distributions (e.g. beta distribution) rather than two single values. The binomial probabilities in Simon's (Control. Clin. Trials 1989; 10:1-10) design are replaced by prior predictive Beta-binomial probabilities that are the ratios of two beta functions and domain-restricted RRs involve incomplete beta functions to induce the null hypothesis acceptance probability. We illustrate that Beta-binomial mixture model based two-stage design retains certain desirable properties for hypothesis testing purpose. However, numerical results show that such designs may not exist under certain hypothesis and error rate (type I and II) setups within maximal sample size approximately 130. Furthermore, we give theoretical conditions for asymptotic two-stage design non-existence (sample size goes to infinity) in order to improve the efficiency of design search and to avoid needless searching.
authors.affiliation: Biometrics Division at The Cancer Institute of New Jersey, 195 Little Albany Street, New Brunswick, NJ 08901, USA. liu16@umdnj.edu
authors.forename: Junfeng
authors.initials: J
authors.lastname: Liu
authors.forename: Yong
authors.initials: Y
authors.lastname: Lin
authors.forename: Weichung Joe
authors.initials: WJ
authors.lastname: Shih
mesh_terms: D000970:Antineoplastic Agents / Q000008:administration & dosage* / Q000493:pharmacokinetics; D016010:Binomial Distribution; D017322:Clinical Trials, Phase II as Topic / Q000379:methods*; D006801:Humans; D009369:Neoplasms / Q000188:drug therapy*; D018401:Sample Size
chemical_list: D000970:Antineoplastic Agents