power_agreement_exact: Power Calculation for Exact Agreement/Tolerance Test

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Power Calculation for Exact Agreement/Tolerance Test

Description

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)

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.

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

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)

# 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)

# 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)

SimplyAgree documentation built on Jan. 22, 2026, 1:08 a.m.