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Deming Regression for Method Comparison

Source: R/method-comparison.R
measure_deming_regression.Rd

Performs Deming regression to compare two measurement methods when both have measurement error. This is preferred over ordinary least squares when both methods have non-negligible error.

Usage

measure_deming_regression(
  data,
  method1_col,
  method2_col,
  error_ratio = NULL,
  method1_sd = NULL,
  method2_sd = NULL,
  bootstrap = FALSE,
  bootstrap_n = 1000,
  conf_level = 0.95
)

Arguments

data

A data frame containing paired measurements.

method1_col

Name of column for method 1 (typically reference/comparator).

method2_col

Name of column for method 2 (typically test method).

error_ratio

Ratio of error variances (var_method2 / var_method1). Default is 1 (equal variances). Can be estimated from replicate data.

method1_sd

Optional known SD of method 1. Used to calculate error_ratio.

method2_sd

Optional known SD of method 2. Used to calculate error_ratio.

bootstrap

Use bootstrap for confidence intervals? Default is FALSE.

bootstrap_n

Number of bootstrap samples. Default is 1000.

conf_level

Confidence level for intervals. Default is 0.95.

Value

A measure_deming_regression object containing:

  • coefficients: Tibble with intercept and slope estimates and CIs

  • statistics: List of diagnostic statistics (RMSE, R-squared)

  • data_summary: Summary of input data

  • bootstrap: Bootstrap results if requested

Details

Error Ratio

The error ratio (lambda) represents the ratio of error variances: lambda = var(method2) / var(method1)

Common approaches:

  • lambda = 1: Assume equal error variances

  • Estimate from replicates: Use SDs from replicate measurements

  • Estimate from calibration: Use known method precision data

Interpretation

For equivalent methods:

  • Slope should be close to 1 (proportional agreement)

  • Intercept should be close to 0 (no constant bias)

If 95% CI for slope includes 1 and CI for intercept includes 0, methods are considered equivalent.

Implementation

If the mcr package is available, it is used for fitting. Otherwise, a manual implementation is used with optional bootstrap CIs.

See also

measure_bland_altman(), measure_passing_bablok()

Other method-comparison: measure_bland_altman(), measure_passing_bablok(), measure_proficiency_score()

Examples

# Method comparison data
data <- data.frame(
  reference = c(5.2, 10.5, 15.8, 25.3, 50.1, 75.4, 100.2),
  new_method = c(5.1, 10.8, 16.2, 25.9, 49.8, 76.1, 101.3)
)

# Deming regression with bootstrap CIs
result <- measure_deming_regression(
  data,
  method1_col = "reference",
  method2_col = "new_method",
  bootstrap = TRUE,
  bootstrap_n = 500
)
#> Using default error ratio of 1. Provide `error_ratio` or SDs for more accurate
#> results.

print(result)
#> measure_deming_regression
#> ──────────────────────────────────────────────────────────────────────────────── 
#> 
#> Coefficients:
#> # A tibble: 2 × 4
#>   term      estimate ci_lower ci_upper
#>   <chr>        <dbl>    <dbl>    <dbl>
#> 1 intercept   0.0594   -0.359    0.447
#> 2 slope       1.01      0.988    1.03 
#> 
#> Statistics:
#>   n = 7 
#>   Error ratio = 1 
#>   RMSE = 0.3508 
#>   R² = 0.9999 
#> 
#> (Fitted using mcr package)
tidy(result)
#> # A tibble: 2 × 4
#>   term      estimate ci_lower ci_upper
#>   <chr>        <dbl>    <dbl>    <dbl>
#> 1 intercept   0.0594   -0.359    0.447
#> 2 slope       1.01      0.988    1.03