kappaSize (version 1.1)

FixedN4Cats: Calculation of the Lowest Expected Value, kappaL, for a fixed sample size in a Study of Interobserver Agreement with a Multinomial Outcome (4 Levels)

Description

This function provides the potential lower bound for a 100(1 - \(\alpha\)) % confidence interval that can be calculated for a fixed sample size, n, and an anticipated value of \(\kappa\), kappa0. This version assumes that the outcome of interest has four levels.

Usage

FixedN4Cats(kappa0, n, props, raters=2, alpha=0.05)

Arguments

kappa0

The anticipated value of \(\kappa\).

n

The total number of available subjects.

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.

Value

n

The specified sample size.

kappa0

The specified anticipated value of \(\kappa\).

kappaL

The calculated expected lower limit.

props

The anticipated proportion of individuals with the outcome.

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.

Details

This function calculates the expected lower bound of a one-sided confidence interval for a fixed sample size, n, and an anticipated value of \(\kappa\), kappa0. This function can illustrate the amount of precision available in the estimation of \(\kappa\) for a fixed sample size. Note that a warning message is provided if any of the expected cell counts are less than 5.

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.

Examples

# NOT RUN {
Suppose an investigator would like to determine the expected lower bound for 
kappa0=0.7 assuming he has access to 80 subjects and 5 raters.  Further suppose that 
the prevalence of the traits of interest are 0.4, 0.4, 0.1, 0.1.
# }
# NOT RUN {
FixedN4Cats(kappa0=0.7, n=80, props=c(0.4, 0.4, 0.1, 0.1), alpha=0.05, raters=5);
# }