# Finding optimal and balanced group-sequential designs

### Description

optgs is used to find a one-sided multi-stage design that balances four optimality criteria for a RCT with normally distributed outcomes

### Usage

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### Arguments

`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) |

`weights` |
vector of length 4 giving the weights put on the four optimality criteria (default: c(0.95,0,0,0.05)). See details for more information |

`initial` |
starting values for the Nelder-Mead algorithm if the user wishes to override the default (default: NULL). Initial values must be specified as a two-dimensional vector where both entries are between -0.5 and 0.5. |

### Details

optgs uses the extended power-family of group-sequential tests, and searches for the values of the futility and efficacy shape parameters that optimise the specified weighting. A description of the extended power-family and optgs is provided in Wason (2012). The ‘weights’ argument corresponds to the weight put on: 1) the expected sample size at delta=delta0; 2) the expected sample size at delta=delta1; 3) the maximum expected sample size; 4) the maximum sample size (i.e. J*groupsize).

### 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

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