# Confidence Interval Approach for the Number of Subjects Required for a Study of Interobserver Agreement with Four Outcome Categories

### Description

This function provides detailed sample size estimation information to determine
the number of subjects required using the confidence interval perspective to sample
size estimation for *κ*. This version assumes that the outcome has four categories.

### Usage

1 |

### Arguments

`kappa0` |
The preliminary (anticipated) value of |

`kappaL` |
The desired expected lower bound for a two-sided 100(1 - |

`kappaU` |
The desired expected upper confidence limit for |

`props` |
The anticipated prevalence of the desired trait. Note that the elements of the four element vector must be non-negative and sum to one. |

`raters` |
The number of raters that are available. This function allows between 2 and 6 raters. |

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

### Details

This function provides detailed sample size estimation computation for studies of interobserver agreement with four outcomes. This function employs the confidence interval perspective, determining the correct sample size that provides the specified expected confidence limits. Sample size estimation is based on the precision of the estimate, instead of a simple hypothesis testing perspective. Note that a warning message is provided if any of the expected cell counts are less than 5.

### Value

`N` |
The calculated sample size. |

`kappa0` |
The specified anticipated value of |

`kappaL` |
The specified expected lower limit. |

`kappaU` |
The specified expected upper limit. |

`props` |
The anticipated proportions of individuals with the outcomes of interest. |

`raters` |
The number of raters. |

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

`ChiCrit` |
The critical value that is required for sample size estimation. It is typically not required and is not displayed in the summary output. |

### Author(s)

Michael Rotondi, mrotondi@uwo.ca

### References

Donner A, Rotondi MA. (2010). Sample Size Requirements for Interval Estimation of the Kappa Statistic for Interobserver Agreement Studies with a Binary Outcome and Multiple Raters. International Journal of Biostatistics 6:31.

Altaye M, Donner A, Klar N. (2001). Procedures for Assessing Interobserver Agreement among Multiple Raters. Biometrics 57:584-588.

Donner A. (1999). Sample Size Requirements for Interval Estimation of the Intraclass Kappa Statistic. Communication in Statistics 28:415-429.

Bartfay E, Donner A. (2001). Statistical Inferences for Interobserver Agreement Studies with Nominal Outcome Data. The Statistician 50:135-146.

Donner A, Eliasziw M. (1987) Sample size requirements for reliability studies. Statistics in Medicine 6:441-448.

### See Also

`Power4Cats`

### Examples

1 2 3 4 5 6 | ```
## Not run: Suppose an investigator would like to determine the required sample size to test
kappa0=0.4 with precision of 0.1 on each side, in a study of interobserver agreement.
Further suppose that the prevalence of the traits are 0.30, 0.2, 0.2, 0.3.
## End(Not run)
CI4Cats(kappa0=0.4, kappaL=0.3, kappaU=0.5, props=c(0.30, 0.2, 0.2, 0.3), alpha=0.05);
``` |

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