Power Calculation for Exact Agreement/Tolerance Test

Computes sample size, power, or other parameters for the exact method of assessing agreement between two measurement methods, as described in Shieh (2019). This method tests whether the central portion of paired differences falls within specified bounds. This roughly equates to the power for tolerance limits.

Usage

power_agreement_exact(
  n = NULL,
  delta = NULL,
  mu = 0,
  sigma = NULL,
  p0_star = 0.95,
  power = NULL,
  alpha = 0.05,
  max_iter = 1000
)

Arguments

n

Number of subject pairs (sample size)

delta

Maximum allowable difference bound (half-width of tolerance interval)

mu

Mean of paired differences

sigma

Standard deviation of paired differences

p0_star

The coverage proportion (content) of the tolerance interval. Central proportion under null hypothesis (default = 0.95)

power

Target power (probability of rejecting false null)

alpha

Significance level (Type I error rate, default = 0.05, Confidence level = 1-alpha)

max_iter

Maximum iterations for gamma computation (default = 1000)

Value

An object of class "power.htest", a list with components:

n

Sample size

delta

c

mu

Mean of differences

sigma

Standard deviation of differences

p0_star

Central proportion (null hypothesis)

p1_star

Central proportion (alternative hypothesis)

alpha

Significance level

power

Power of the test

critical_value

Critical value for test statistic

method

Description of the method

note

Additional notes

Details

This function implements the exact agreement test procedure of Shieh (2019) for method comparison studies. The test evaluates whether the central proportion of the distribution of paired differences lies within the interval [-delta, delta].

The null hypothesis is: H0: theta_(1-p) <= -delta or delta <= theta_p The alternative is: H1: -delta < theta_(1-p) and theta_p < delta

where p = (1 + p0_star)/2, and theta_p represents the 100p-th percentile of the paired differences.

Specify three of: n, delta, power, and sigma. The fourth will be calculated. If mu is not specified, it defaults to 0.

Tolerance Interval Interpretation:

The parameter p0_star represents the tolerance coverage proportion, i.e., the proportion of the population that must fall within the specified bounds [-delta, delta] under the null hypothesis. This is conceptually related to tolerance intervals, but formulated as a hypothesis test rather than an estimation problem.

Note: This differs from Bland-Altman's "95% limits of agreement," which are confidence intervals for the 2.5th and 97.5th percentiles, not tolerance intervals.

References

Shieh, G. (2019). Assessing Agreement Between Two Methods of Quantitative Measurements: Exact Test Procedure and Sample Size Calculation. Statistics in Biopharmaceutical Research, 12(3), 352-359. https://doi.org/10.1080/19466315.2019.1677495

Examples

# Example 1: Find required sample size
power_agreement_exact(delta = 7, mu = 0.5, sigma = 2.5,
                      p0_star = 0.95, power = 0.80, alpha = 0.05)
#> Maximum iterations reached in gamma computation
#> 
#>      Power for Exact Method for Assessing Agreement Between Two Methods 
#> 
#>               n = 34
#>           delta = 7
#>              mu = 0.5
#>           sigma = 2.5
#>         p0_star = 0.95
#>         p1_star = 0.9939889
#>           alpha = 0.05
#>           power = 0.8018321
#>  critical_value = 13.57044
#> 
#> NOTE: H0: Central 95% of differences not within [-delta, delta]
#>      H1: Central 99.4% of differences within [-delta, delta] 
#> n is number pairs. Two measurements per unit; one for each method.
#> 

# Example 2: Calculate power for given sample size
power_agreement_exact(n = 15, delta = 0.1, mu = 0.011,
                      sigma = 0.044, p0_star = 0.80, alpha = 0.05)
#> 
#>      Power for Exact Method for Assessing Agreement Between Two Methods 
#> 
#>               n = 15
#>           delta = 0.1
#>              mu = 0.011
#>           sigma = 0.044
#>         p0_star = 0.8
#>         p1_star = 0.9726269
#>           alpha = 0.05
#>           power = 0.8315332
#>  critical_value = 6.391135
#> 
#> NOTE: H0: Central 80% of differences not within [-delta, delta]
#>      H1: Central 97.3% of differences within [-delta, delta] 
#> n is number pairs. Two measurements per unit; one for each method.
#> 

# Example 3: Find required delta for given power and sample size
power_agreement_exact(n = 50, mu = 0, sigma = 2.5,
                      p0_star = 0.95, power = 0.90, alpha = 0.05)
#> 
#>      Power for Exact Method for Assessing Agreement Between Two Methods 
#> 
#>               n = 50
#>           delta = 6.65619
#>              mu = 0
#>           sigma = 2.5
#>         p0_star = 0.95
#>         p1_star = 0.9922432
#>           alpha = 0.05
#>           power = 0.9000104
#>  critical_value = 15.89319
#> 
#> NOTE: H0: Central 95% of differences not within [-delta, delta]
#>      H1: Central 99.2% of differences within [-delta, delta] 
#> n is number pairs. Two measurements per unit; one for each method.
#>