valytics (version 0.3.0)

deming_regression: Deming Regression for Method Comparison

Description

Performs Deming regression to assess agreement between two measurement methods. Unlike ordinary least squares, Deming regression accounts for measurement error in both variables, making it appropriate for method comparison studies where neither method is a perfect reference.

Usage

deming_regression(
  x,
  y = NULL,
  data = NULL,
  error_ratio = 1,
  conf_level = 0.95,
  ci_method = c("jackknife", "bootstrap"),
  boot_n = 1999,
  weighted = FALSE,
  na_action = c("omit", "fail")
)

Value

An object of class c("deming_regression", "valytics_comparison", "valytics_result"), which is a list containing:

input

List with original data and metadata:

• x, y: Numeric vectors (after NA handling)

• n: Number of paired observations

• n_excluded: Number of pairs excluded due to NAs

• var_names: Named character vector with variable names

results

List with statistical results:

• intercept: Intercept point estimate

• slope: Slope point estimate

• intercept_ci: Named numeric vector with lower and upper CI

• slope_ci: Named numeric vector with lower and upper CI

• intercept_se: Standard error of intercept

• slope_se: Standard error of slope

• residuals: Perpendicular residuals

• fitted_x: Fitted x values

• fitted_y: Fitted y values

settings

List with analysis settings:

• error_ratio: Error variance ratio used

• conf_level: Confidence level used

• ci_method: CI method used

• boot_n: Number of bootstrap samples (if applicable)

• weighted: Whether weighted regression was used

call

The matched function call.

Arguments

x

Numeric vector of measurements from method 1 (reference method), or a formula of the form method1 ~ method2.

y

Numeric vector of measurements from method 2 (test method). Ignored if x is a formula.

data

Optional data frame containing the variables specified in x and y (or in the formula).

error_ratio

Ratio of error variances (Var(error_y) / Var(error_x)). Default is 1 (orthogonal regression, assuming equal error variances). Can be estimated from replicate measurements or set based on prior knowledge of method precision.

conf_level

Confidence level for intervals (default: 0.95).

ci_method

Method for calculating confidence intervals: "jackknife" (default) uses delete-one jackknife resampling, "bootstrap" uses BCa bootstrap resampling.

boot_n

Number of bootstrap resamples when ci_method = "bootstrap" (default: 1999).

weighted

Logical; if TRUE, performs weighted Deming regression where weights are inversely proportional to the variance at each point. Requires replicate measurements to estimate weights. Default is FALSE.

na_action

How to handle missing values: "omit" (default) removes pairs with any NA, "fail" stops with an error.

Interpretation

• Slope = 1: No proportional difference between methods

• Slope != 1: Proportional (multiplicative) difference exists

• Intercept = 0: No constant difference between methods

• Intercept != 0: Constant (additive) difference exists

Use the confidence intervals to test these hypotheses: if 1 is within the slope CI and 0 is within the intercept CI, the methods are considered equivalent.

Comparison with Other Methods

• Ordinary Least Squares (OLS): Assumes X is measured without error. Biases slope toward zero when both variables have error.

• Passing-Bablok: Non-parametric, robust to outliers, but assumes linear relationship and no ties.

• Deming: Parametric, accounts for error in both variables, allows specification of error ratio.

Assumptions

• Linear relationship between X and Y

• Measurement errors are normally distributed

• Error variances are constant (homoscedastic) or known ratio

• Errors in X and Y are independent

Details

Deming regression (also known as errors-in-variables regression or Model II regression) is designed for situations where both X and Y are measured with error. This is the typical case in method comparison studies where both the reference and test methods have measurement uncertainty.

The error ratio (lambda, \(\lambda\)) represents the ratio of error variances: $$\lambda = \frac{Var(\epsilon_y)}{Var(\epsilon_x)}$$

When \(\lambda\) = 1 (default), this is equivalent to orthogonal regression, which minimizes perpendicular distances to the regression line. When \(\lambda\) != 1, the regression minimizes a weighted combination of horizontal and vertical distances.

Choosing the error ratio:

• If both methods have similar precision: use \(\lambda\) = 1

• If precision differs: estimate from replicate measurements as \(\lambda\) = CV_y² / CV_x² (squared coefficient of variation ratio)

• If one method is much more precise: consider ordinary least squares

References

Deming WE (1943). Statistical Adjustment of Data. Wiley.

Linnet K (1990). Estimation of the linear relationship between the measurements of two methods with proportional errors. Statistics in Medicine, 9(12):1463-1473. tools:::Rd_expr_doi("10.1002/sim.4780091210")

Linnet K (1993). Evaluation of regression procedures for methods comparison studies. Clinical Chemistry, 39(3):424-432. tools:::Rd_expr_doi("10.1093/clinchem/39.3.424")

Cornbleet PJ, Gochman N (1979). Incorrect least-squares regression coefficients in method-comparison analysis. Clinical Chemistry, 25(3):432-438.

See Also

plot.deming_regression() for visualization, summary.deming_regression() for detailed summary, pb_regression() for non-parametric alternative, ba_analysis() for Bland-Altman analysis

Examples

# Simulated method comparison data
set.seed(42)
true_values <- rnorm(50, mean = 100, sd = 20)
method_a <- true_values + rnorm(50, sd = 5)
method_b <- 1.05 * true_values + 3 + rnorm(50, sd = 5)

# Basic analysis (orthogonal regression, lambda = 1)
dm <- deming_regression(method_a, method_b)
dm

# Using formula interface with data frame
df <- data.frame(reference = method_a, test = method_b)
dm <- deming_regression(reference ~ test, data = df)

# With known error ratio (e.g., test method has 2x variance)
dm <- deming_regression(method_a, method_b, error_ratio = 2)

# With bootstrap confidence intervals
dm_boot <- deming_regression(method_a, method_b, ci_method = "bootstrap")

# Using package example data
data(glucose_methods)
dm <- deming_regression(reference ~ poc_meter, data = glucose_methods)
summary(dm)
plot(dm)