Lee and Liu's criterion function for determining the trial decision cutoffs based on the predictive probability.

1 | ```
PredP(x, n, nmax, a, b, p0, theta_t)
``` |

`x` |
the number of responses among |

`n` |
the number of patients treated by the experimental drug at a certain stage of the trial. |

`nmax` |
the maximum number of patients treated by the experimental drug. |

`a` |
the hyperparameter (shape1) of the Beta prior for the experimental drug. |

`b` |
the hyperparameter (shape2) of the Beta prior for the experimental drug. |

`p0` |
the the response rate for the standard drug. |

`theta_t` |
the cutoff probability for efficacy including future patients; typically, |

`prob` |
the predictive probability: |

Lee, J. J., Liu, D. D. (2008).
A predictive probability design for phase II cancer clinical trials.
*Clinical Trials* **5**: 93-106.

Yin, G. (2012).
*Clinical Trial Design: Bayesian and Frequentist Adaptive Methods.*
New York: Wiley.

1 2 | ```
# Using vague prior Uniform(0,1), i.e. Beta(1,1)
PredP(16, 23, 40, 1, 1, 0.5, 0.9)
``` |

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