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Passing-Bablok Regression for Method Comparison

Source: R/pb_reg.R
pb_reg.Rd

[Experimental]

A robust, nonparametric method for fitting a straight line to two-dimensional data where both variables (X and Y) are measured with error. Particularly useful for method comparison studies.

Usage

pb_reg(
  formula,
  data,
  id = NULL,
  method = c("scissors", "symmetric", "invariant"),
  conf.level = 0.95,
  weights = NULL,
  error.ratio = 1,
  replicates = 0,
  model = TRUE,
  keep_data = TRUE,
  ...
)

Arguments

formula

A formula of the form y ~ x specifying the model.

data

Data frame with all data.

id

Column with subject identifier (optional). If provided, measurement error ratio is calculated from replicate measurements.

method

Method for Passing-Bablok estimation. Options are:

  • "scissors": Scissors estimator (1988) - most robust, scale invariant (default)

  • "symmetric": Original Passing-Bablok (1983) - symmetric around 45-degree line

  • "invariant": Scale-invariant method (1984) - adaptive reference line

conf.level

The confidence level required. Default is 95%.

weights

An optional vector of case weights to be used in the fitting process. Should be NULL or a numeric vector.

error.ratio

Ratio of measurement error variances (var(x)/var(y)). Default is 1. This argument is ignored if subject identifiers are provided via id.

replicates

Number of bootstrap iterations for confidence intervals. If 0 (default), analytical confidence intervals are used. Bootstrap is recommended for weighted data and 'invariant' or 'scissors' methods.

model

Logical. If TRUE (default), the model frame is stored in the returned object. This is needed for methods like plot(), fitted(), residuals(), and predict() to work without supplying data. If FALSE, the model frame is not stored (saves memory for large datasets), but these methods will require a data argument.

keep_data

Logical indicator (TRUE/FALSE). If TRUE, intermediate calculations are returned; default is FALSE.

...

Additional arguments (currently unused).

Value

The function returns a simple_eiv object with the following components:

  • coefficients: Named vector of coefficients (intercept and slope).

  • residuals: Residuals from the fitted model.

  • fitted.values: Predicted Y values.

  • model_table: Data frame presenting the full results from the Passing-Bablok regression.

  • vcov: Variance-covariance matrix for slope and intercept (if bootstrap used).

  • df.residual: Residual degrees of freedom.

  • call: The matched call.

  • terms: The terms object used.

  • model: The model frame.

  • x_vals: Original x values used in fitting.

  • y_vals: Original y values used in fitting.

  • weights: Case weights (if provided).

  • error.ratio: Error ratio used in fitting.

  • conf.level: Confidence level used.

  • method: Character string describing the method.

  • method_num: Numeric method identifier (1, 2, or 3).

  • kendall_test: Results of Kendall's tau correlation test.

  • cusum_test: Results of CUSUM linearity test.

  • n_slopes: Number of slopes used in estimation.

  • boot: Bootstrap results (if replicates > 0).

Details

Passing-Bablok regression is a robust nonparametric method that estimates the slope as the shifted median of all possible slopes between pairs of points. The intercept is then calculated as the median of y - slope*x. This method is particularly useful when:

  • Both X and Y are measured with error

  • You want a robust method not sensitive to outliers

  • The relationship is assumed to be linear

  • X and Y are highly positively correlated

Methods

Three Passing-Bablok methods are available:

"scissors" (default): The scissors estimator (1988), most robust and scale-invariant. Uses the median of absolute values of angles.

"symmetric": The original method (1983), symmetric about the y = x line. Uses the line y = -x as the reference for partitioning points.

"invariant": Scale-invariant method (1984). First finds the median angle of slopes below the horizontal, then uses this as the reference line.

Measurement Error Handling

If the data are measured in replicates, then the measurement error ratio can be directly derived from the data. This can be accomplished by indicating the subject identifier with the id argument. When replicates are not available in the data, then the ratio of error variances (var(x)/var(y)) can be provided with the error.ratio argument (default = 1, indicating equal measurement errors).

The error ratio affects how pairwise slopes are weighted in the robust median calculation. When error.ratio = 1, all pairs receive equal weight. When error.ratio != 1, pairs are weighted to account for heterogeneous measurement precision.

Weighting

Case weights can be provided via the weights argument. These are distinct from measurement error weighting (controlled by error.ratio). Case weights allow you to down-weight or up-weight specific observations in the analysis.

Bootstrap

Wild bootstrap resampling is used when replicates > 0. This is particularly useful for:

  • Weighted regression (case weights or error.ratio != 1)

  • Methods 'invariant' and 'scissors' (where analytical CI validity is uncertain)

  • Small sample sizes

The method automatically:

  • Tests for high positive correlation using Kendall's tau

  • Tests for linearity using a CUSUM test

  • Computes confidence intervals (analytical or bootstrap)

References

Passing, H., & Bablok, W. (1983). A New Biometrical Procedure for Testing the Equality of Measurements from Two Different Analytical Methods. Application of linear regression procedures for method comparison studies in Clinical Chemistry, Part I. Cclm, 21(11), 709-720. doi: 10.1515/cclm.1983.21.11.709

Passing, H., & Bablok, W. (1984). Comparison of Several Regression Procedures for Method Comparison Studies and Determination of Sample Sizes Application of linear regression procedures for method comparison studies in Clinical Chemistry, Part II. Clinical Chemistry and Laboratory Medicine, 22(6). doi: 10.1515/cclm.1984.22.6.431

Bablok, W., Passing, H., Bender, R., & Schneider, B. (1988). A General Regression Procedure for Method Transformation. Application of Linear Regression Procedures for Method Comparison Studies in Clinical Chemistry, Part III. Clinical Chemistry and Laboratory Medicine, 26(11). doi: 10.1515/cclm.1988.26.11.783

Examples

if (FALSE) { # \dontrun{
# Basic Passing-Bablok regression (scissors method, default)
model <- pb_reg(method2 ~ method1, data = mydata)

# With known error ratio
model_er <- pb_reg(method2 ~ method1, data = mydata, error.ratio = 2)

# With replicate measurements
model_rep <- pb_reg(method2 ~ method1, data = mydata, id = "subject_id")

# With bootstrap confidence intervals
model_boot <- pb_reg(method2 ~ method1, data = mydata,
                     error.ratio = 1.5, replicates = 1000)

# Symmetric method
model_sym <- pb_reg(method2 ~ method1, data = mydata, method = "symmetric")

# Scale-invariant method
model_inv <- pb_reg(method2 ~ method1, data = mydata, method = "invariant")

# With case weights
model_wt <- pb_reg(method2 ~ method1, data = mydata,
                   weights = mydata$case_weights)

# View results
print(model)
summary(model)
plot(model)
} # }