# Power-Based 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 that are required to test the hypothesis *H_0: κ = κ_0* vs. *H_1: κ = κ_1*, at two-sided
significance level *α*, with power, *1 - β*. This version assumes that the outcome is multinomial with four levels.

### Usage

1 | ```
Power4Cats(kappa0, kappa1, props, raters=2, alpha=0.05, power=0.80)
``` |

### Arguments

`kappa0` |
The null hypothesis for the |

`kappa1` |
The alternate hypothesis for the |

`props` |
The anticipated prevalence of the desired traits. Note that this four element vector must 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. |

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

### Details

This function provides detailed sample size estimation tools for studies
of interobserver agreement with four levels. This function employs the
power approach, rejecting *κ_0* in favour of *κ_1* for a pre-specified significance
level and power. 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 null hypothesis. |

`kappa1` |
The specified alternative hypothesis. |

`props` |
The anticipated proportion of individuals with the outcome. |

`raters` |
The number of raters. |

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

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

### 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

`CI4Cats`

### 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 vs. kappa1=0.6 with alpha=0.05 and power=0.80 in a study of
interobserver agreement. Further suppose that the prevalence of the categories is
0.30, 0.30, 0.30 and 0.10.
## End(Not run)
Power4Cats(kappa0=0.4, kappa1=0.6, props=c(0.30, 0.30, 0.30, 0.10), alpha=0.05, power=0.80);
``` |