## 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 ∼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.

Original language | English (US) |
---|---|

Pages (from-to) | 1084-1095 |

Number of pages | 12 |

Journal | Statistics in Medicine |

Volume | 29 |

Issue number | 10 |

DOIs | |

State | Published - May 10 2010 |

## All Science Journal Classification (ASJC) codes

- Epidemiology
- Statistics and Probability

## Keywords

- (incomplete) beta distribution
- (incomplete) beta function
- Design existence
- Hypothesis test
- Prior predictive probability
- Simon's two-stage design