Passing-Bablok regression

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Description

Passing & Bablok (1983) have described a linear regression procedure with no special assumptions regarding the distribution of the samples and the measurement errors. The result does not depend on the assignment of the methods (or instruments) to X and Y. The slope B and intercept A are calculated with their 95% confidence interval. These confidence intervals are used to determine whether there is only a chance difference between B and 1 and between A and 0.

Required input

  • Variable Y and Variable X: select the variables for the two techniques you want to compare.
  • Filter: an optional filter.
  • Options
    • Calculate perpendicular residuals: select this option to calculate the residuals perpendicular to the regression line (see Passing & Bablok, 1983). This is different from the traditional (least squares) method which measures residuals parallel to the y-axis.

    • Scatter diagram & regression line: a graph window with scatter diagram and regression line, including confidence interval for the regression line and identity line (x=y).
    • Residuals: a graph window with a residuals plot. As an option, the Residuals can be plotted by rank number (see Passing & Bablok, 1983).
    • Subgroups: click the Subgroups button if you want to identify subgroups in the scatter diagram and residuals plot. A new dialog box is displayed in which you can select a categorical variable. The graph will display different markers for the different categories in this variable.

Results

When you have completed the dialog box, click the OK button to proceed. The following results will be displayed in a text window.

  • Sample size: the number of (selected) data pairs
  • Summary statistics for both variables: lowest and highest value, mean, median, standard deviation and standard error of the mean
  • The regression equation: the regression equation with the calculated values for A and B according to Passing & Bablok (1983).
  • Systematic differences. The intercept A is a measure of the systematic differences between the two methods. The 95% confidence interval for the intercept A can be used to test the hypothesis that A=0. This hypothesis is accepted if the confidence interval for A contains the value 0. If the hypothesis is rejected, then it is concluded that A is significantly different from 0 and both methods differ at least by a constant amount.
  • Proportional differences. The slope B is a measure of the proportional differences between the two methods. The 95% confidence interval for the slope B can be used to test the hypothesis that B=1. This hypothesis is accepted if the confidence interval for B contains the value 1. If the hypothesis is rejected, then it is concluded that B is significantly different from 1 and there is at least a proportional difference between the two methods.
  • Random differences. The residual standard deviation (RSD) is a measure of the random differences between the two methods. 95% of random differences are expected to lie in the interval -1.96 RSD to +1.96 RSD. If this interval is large, the two methods may not be comparable.
  • Linear model validity: the Cusum test for linearity is used to evaluate how well a linear model fits the data.

Graphs

This is the scatter diagram with the regression line (solid line), the confidence interval for the regression line (dashed lines) and identity line (x=y, dotted line):

A second graph window shows the residuals:

Notes

  • The Passing-Bablok procedure should only be used on variables that have a linear relationship and are highly correlated.

  • Since it is a non-parametric procedure, Passing-Bablok regression is not influenced by the presence of one or relative few outliers.

  • We advise to supplement the results of the Passing-Bablok procedure with a Bland-Altman plot.

Literature

  • 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. J. Clin. Chem. Clin. Biochem. 21:709-720. [Abstract]

See also

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