# The stopping boundaries based on the posterior probability criterion

### Description

The design function to sequentially monitor sample size and boundary based on Thall and Simon's criterion.

### Usage

1 | ```
PostP.design(type, nmax, a, b, p0, theta, optimize)
``` |

### Arguments

`type` |
type of boundaries: "efficacy" or "futility". |

`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 pre-specified reseponse rate. |

`theta` |
the cutoff probability: typically, |

`optimize` |
logical value, if optimize=TRUE, then only output the minimal sample size for the same number of futility and efficacy boundaries. |

### Value

`boundset` |
the boundaries set: |

### References

Thall, P. F., Simon, R. (1994).
Practical Bayesian guidelines for phase IIB clinical trials.
*Biometrics* **50**: 337-349.

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

### Examples

1 2 3 4 5 6 | ```
## Using vague prior Unif(0,1)
PostP.design(type = "futility", nmax=100, a=1, b=1, p0=0.3, theta=0.05)
PostP.design(type = "efficacy", nmax=100, a=1, b=1, p0=0.3, theta=0.9)
## Or using Jeffery prior with Beta(0.5,0.5)
PostP.design(type = "futility", nmax=100, a=0.5, b=0.5, p0=0.3, theta=0.05)
PostP.design(type = "efficacy", nmax=100, a=0.5, b=0.5, p0=0.3, theta=0.9)
``` |

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