Description Usage Arguments Details Value Author(s) References See Also Examples

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.

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

`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. |

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.

`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. |

Michael Rotondi, mrotondi@yorku.ca

Rotondi MA, Donner A. (2012). A Confidence Interval Approach to Sample Size Estimation for Interobserver Agreement Studies with Multiple Raters and Outcomes. Journal of Clinical Epidemiology, 65:778-784.

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.

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);
``` |

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