# Finding extended power-family group-sequential designs

### Description

powerfamily is used to find a one-sided extended power-family group-sequential design

### Usage

1 2 | ```
powerfamily(futility = 0, efficacy = 0, delta0 = 0, delta1 = 1/3,
J = 2, sigma = 1, sd.known = TRUE, alpha = 0.05, power = 0.9)
``` |

### Arguments

`futility` |
shape parameter for futility boundaries (default: 0) |

`efficacy` |
shape parameter for efficacy boundaries (default: 0) |

`delta0` |
mean difference in treatment effect under the null hypothesis (default: 0) |

`delta1` |
clinically relevant difference used to power the trial (default: 1/3) |

`J` |
number of stages in the trial (default: 2) |

`sigma` |
assumed standard deviation of treatment responses (default: 1) |

`sd.known` |
logical value indicating if sigma will be treated as known; if FALSE, a quantile substitution method will be used to modify the stopping boundaries (default TRUE) |

`alpha` |
one-sided type-I error rate required (default: 0.05) |

`power` |
power required (default: 0.9) |

### Details

powerfamily uses the extended power-family of group-sequential tests. A description of the extended power-family is provided in Wason (2012).

### Value

`groupsize` |
the number of patients required per arm, per stage |

`futility` |
the futility boundaries for the design |

`efficacy` |
the efficacy boundaries for the design |

`ess` |
the expected sample size at the delta0; the expected sample size at the delta1; and the maximum expected sample size |

`typeIerror` |
the actual type-I error rate of the design |

`power` |
the actual power of the design |

### References

Wason, J.M.S. OptGS: an R package for finding near-optimal group-sequential designs. Journal of Statistical Software, 66(2), 1-13. http://www.jstatsoft.org/v66/i02/

### Examples

1 2 3 | ```
##Find a three-stage design that has shape parameters -0.5 and 0.5.
threestagedesign=powerfamily(J=3,futility=-0.5,efficacy=0.5)
plot(threestagedesign)
``` |