# Number of Subjects Required for a Cluster Randomized Trial with a Continuous Outcome

### Description

This function provides detailed sample size estimation information to determine the number of subjects that must be enrolled in a cluster randomized trial to compare two means.

### Usage

1 |

### Arguments

`delta` |
The minimum detectable difference between population means. |

`sigma` |
The standard deviation of the outcome. |

`m` |
The anticipated average (or actual) cluster size. |

`ICC` |
The anticipated value of the intraclass correlation coefficient, |

`AR` |
The Allocation Ratio: AR=1 implies an equal number of subjects per treatment and control group (maximum efficiency), AR > 1, implies more subjects will be enrolled in the control group (e.g. in the case of costly intervention), AR < 1 implies more subjects in the treatment group (rarely used). |

`alpha` |
The desired type I error rate. |

`power` |
The desired level of power, recall power = 1 - type II error. |

`two.tailed` |
Logical, If TRUE calculations are based on a two-tailed type I error, if FALSE, a one-sided calculation is performed. |

`digits` |
Number of digits to round calculations. |

### Details

This function provides detailed sample size information, similar to PROC POWER in SAS, but with less functionality and more concise output, and of course, adapted for the design of cluster randomized trial. It is used for sample size estimation in a cluster randomized trial where the outcome is continuous, e.g. blood pressure, or weight. Note that if the results suggest a small number of clusters is required, an iterative procedure will include the T distribution instead of the normal critical value for alpha, iterating until convergence. In some cases, such as small ICC values, the algorithm may fail to converge and may need to be stopped.

### Value

`nE` |
The minimum number of subjects required in the experimental group. |

`nC` |
The minimum number of subjects required in the control group. |

`delta` |
The minimum detectable difference between population means. |

`sigma` |
The standard deviation of the outcome. |

`alpha` |
The desired type I error rate. |

`power` |
The desired level of power, recall power = 1 - type II error. |

`AR` |
The Allocation Ratio. |

### Author(s)

Michael Rotondi, mrotondi@yorku.ca

### References

Matthews JNS. Introduction to Randomized Controlled Clinical Trials (2nd Ed.) Chapman & Hall: New York, 2006.

Donner A and Klar N. Design and Analysis of Cluster Randomization Trials in Health Research. Arnold: London, 2000.

### See Also

`n4props`

, `n4incidence`

### Examples

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