# To calculate the least sample size required to achieve a certain power

### Description

For the problem of comparing means of k treatment groups to the mean of one control group, the implementation of the function needs the following three assumptions: 1. The k treatment groups have identical treatment effect size. 2. The sample allocation ratio is pre-specified, and meanwhile the samples to be assigned to each of the k treatment groups are expected to be equal at size n. 3. The alternative hypotheses are one-sided. With the violations assumption 2, the sample size could not be evaluated numerically, and with the violation of assumption 1 and 3, the evaluation of sample size needs great computational effort and thus not implemented. In the situation, simulation-based evaluation is suggested.

### Usage

1 |

### Arguments

`ratio` |
The pre-specified ratio of sample size in each of the treatment groups to the sample size in the control group |

`power` |
The power required to be achieved. |

`r` |
The least number of null hypotheses to be rejected, e.g.,when r=1, the sample size is evaluated on disjunctive power and when r=k, the sample size is evaluated on conjunctive power. |

`k` |
Number of hypotheses to be tested, |

`mu` |
Assumed population mean in each of the k treatment groups. |

`mu0` |
Assumed population mean in the control group. |

`contrast` |
If mu and mu0 are concerned of means of continous outcome, specify contrast="means"; if mu and mu0 are concerned of proportions of binary outcome, specify contrast="props". |

`sigma` |
The population error variance, which should be specified when contrast="means"; if contrast="props", set sigma=NA as default and it will be calculated based on mu and mu0 specified within the function. |

`dist` |
Whether the sample size is calculated for t-distributed test statistics (dist="tdist") or standard normally distributed test statistics (dist="zdist"). |

`alpha` |
The pre-specified overall significance level, default=0.05. |

`mcs` |
The number of monte-carlo sample points to numerically approximate the power for a given sample size, refer to Equation (4.3) and Equation (4.5) in Dunnett and Tamhane (1992). |

`testcall` |
The applied Dunnett test procedure: "SD"=step-down Dunnett test; "SU"=step-up Dunnett test. |

### Value

Return a LIST containing:

`"least sample size required in each treatment groups"` |
value of n |

`"least sample size required in the control group"` |
value of n0 |

### Author(s)

FAN XIA <phoebexia@yahoo.com>

### References

Charles W. Dunnett and Ajit C. Tamhane. A step-up multiple test procedure. Journal of the American Statistical Association, 87(417):162-170, 1992.

### See Also

`powDT`

### Examples

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