Simulate Deming Regression Power — deming

Functions for conducting power analysis and sample size determination for Deming regression in method comparison studies. These functions help determine the sample size needed to detect specified biases (proportional and/or constant) between two measurement methods.

Estimates statistical power to detect deviations from the line of identity using simulated data with known properties.

Usage

deming_power_sim(
  n_sims = 1000,
  sample_size = 50,
  x_range = c(10, 100),
  x_dist = "uniform",
  actual_slope = 1.05,
  actual_intercept = 0,
  ideal_slope = 1,
  ideal_intercept = 0,
  y_var_params = list(beta1 = 1, beta2 = 0, J = 1, type = "constant"),
  x_var_params = list(beta1 = 1, beta2 = 0, J = 1, type = "constant"),
  weighted = FALSE,
  conf.level = 0.95
)

Arguments

n_sims: Number of simulation iterations. Default is 1000.
sample_size: Sample size (number of paired observations) per simulation.
x_range: Numeric vector of length 2 specifying min and max of X values (e.g., c(10, 100)).
x_dist: Character specifying distribution of X values: "uniform", "central", or "right_skewed".
actual_slope: Actual slope used to generate data (e.g., 1.05 for 5% proportional bias).
actual_intercept: Actual intercept used to generate data.
ideal_slope: Hypothesized slope to test against (typically 1 for identity line).
ideal_intercept: Hypothesized intercept to test against (typically 0 for identity line).
y_var_params: List with Y variance parameters: beta1, beta2, J, type. Type can be "constant", "proportional", or "power". For power function: sigma^2 = (beta1 + beta2*U)^J
x_var_params: List with X variance parameters (same structure as y_var_params).
weighted: Logical. Use weighted Deming regression? Default is FALSE.
conf.level: Confidence level for tests. Default is 0.95.

Value

A list of class "deming_power" containing:

power_ci_slope: Power based on slope confidence interval
power_ci_intercept: Power based on intercept confidence interval
power_either_ci: Power when either CI detects difference
power_joint: Power based on joint confidence region
settings: List of simulation settings
advantage: Difference in power between joint region and CIs

Details

Power Analysis for Deming Regression

This function generates simulated datasets with specified error characteristics and tests whether confidence intervals and joint confidence regions detect deviations from hypothesized values. The joint confidence region typically provides higher statistical power, especially when the X-range is narrow (high slope-intercept correlation).

The variance functions allow flexible modeling of heteroscedastic errors:

constant: sigma^2 = beta1
proportional: sigma^2 = beta1 * U^2 (constant CV%)
power: sigma^2 = (beta1 + beta2*U)^J

References

Sadler, W.A. (2010). Joint parameter confidence regions improve the power of parametric regression in method-comparison studies. Accreditation and Quality Assurance, 15, 547-554.

Examples

if (FALSE) { # \dontrun{
# Simple example: detect 5% proportional bias with constant variance
power_result <- deming_power_sim(
  n_sims = 500,
  sample_size = 50,
  x_range = c(10, 100),
  actual_slope = 1.05,
  ideal_slope = 1.0,
  y_var_params = list(beta1 = 25, beta2 = 0, J = 1, type = "constant"),
  x_var_params = list(beta1 = 20, beta2 = 0, J = 1, type = "constant")
)
print(power_result)

# More complex: heteroscedastic errors
power_result2 <- deming_power_sim(
  n_sims = 500,
  sample_size = 75,
  x_range = c(1, 100),
  actual_slope = 1.03,
  y_var_params = list(beta1 = 0.5, beta2 = 0.05, J = 2, type = "power"),
  x_var_params = list(beta1 = 0.4, beta2 = 0.04, J = 2, type = "power"),
  weighted = TRUE
)
} # }