**Notation** |
**Parameter** |

p |
(Unknown) true response probability of the treatment |

p_{0}, p_{1} |
Probabilities that are deemed unpromising (p_{0}) and promising (p_{1}) |

δ |
Effect size (δ=p_{1}-p_{0} ) |

α, β |
Type I and II error probability |

n, n_{1} |
Total sample size and sample size after the first stage of a two-stage design |

r, r_{1} |
Rejection number at the end of a trial and after the first stage of a two-stage design |

B( · ; n, p) |
Binomial distribution function with parameters n and p |

p_{0;min}, p_{0;max} |
Lower and upper bound of the acceptable range of p_{0} |

α_{max}, β_{max} |
Upper bounds for acceptable values of α and β |

τ |
Step size for the discretized ranges of acceptable values of p_{0} , α and β |

EN |
Expected sample size of a two-stage design |

ε |
Small value of misspecification of the true p_{0} |

n_{ε}, r_{ε} |
Sample size and rejection number of a design where p_{0} is misspecified by ε |

α_{ε}(p_{0}) |
Probability of rejecting H0: p ≤ p_{0} + ε, given p=p_{0} |

β_{ε}(p_{0}) |
Probability of not rejecting H0: p ≤ p_{0} + ε, given p=p_{1} |