n4incidence {CRTSize} | R Documentation |

## Number of Subjects Required for a Cluster Randomized Trial Comparing Incidence Rates

### 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 test for a significant difference in incidence rates.

### Usage

`n4incidence(le, lc, m, t, CV, alpha=0.05, power = 0.80, AR=1, two.tailed=TRUE, digits=3)`

### Arguments

`le` |
The anticipated incidence rate, |

`lc` |
The anticipated incidence rate, |

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

`t` |
The planned follow-up time for the study (in weeks, months, etc.) |

`CV` |
The coefficient of variation, assumed constant over both the treatment and control groups.
Note that CV = |

`AR` |
The Allocation Ratio: AR |

`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 information, similar to PROC POWER in SAS, but with less
functionality and more concise output. It is used for sample size estimation in
a cluster randomized trial where the outcome of interest is an incidence rate. A simple example may include
whether a new treatment can successfully reduce the incidence of heart attacks over a six month period.
In epidemiological terms, `\lambda_E`

and `\lambda_C`

are the expected incidence rate of the outcome in the experimental and control group. 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 clusters required in the experimental group. |

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

`le` |
The anticipated incidence rate, |

`lc` |
The anticipated incidence rate, |

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

`t` |
The planned follow-up time for the study. |

`CV` |
The coefficient of variation. |

`AR` |
The Allocation Ratio: One implies an equal number of subjects per treatment and control groups. |

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

`power` |
The desired level of power. |

`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

### Examples

```
## Not run:
Suppose a new drug is thought to reduce the incidence of HIV from 0.01 per person-year to 0.005
per person-year. Assume the coefficient of variation is 0.25 and that 1000 subjects will be
followed for a two year period. Calculate the required number of subjects that must be enrolled
in a study to detect this difference with alpha = 0.05 and power = 0.80.
## End(Not run)
n4incidence(le=0.01, lc=0.005, m=1000, t=2, CV=0.25);
```

*CRTSize*version 1.2 Index]