 SciStat

# Passing-Bablok regression

## Description

Allows to performs method comparison using the Passing & Bablok (1983) method. Passing & Bablok 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

• Select the variables for the two methods to compare.

• Optionally select a filter to include a subset of cases.

## 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 plot: a graph window with a residuals plot. As an option, the Residuals can be plotted by rank number (see Passing & Bablok, 1983).

## Results

The results window for Passing & Bablok regression displays:

• 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 in agreement.
• Linear model validity: the Cusum test for linearity is used to evaluate how well a linear model fits the data. The Cusum test for linearity only tests the applicability of the Passing-Bablok method; it has no further interpretation with regards to comparability of the two laboratory methods. A small P value (P<0.05) indicates that there is no linear relationship between the two measurements and therefore the Passing-Bablok method is not applicable.

Optionally, the program reports Spearman's rank correlation coefficient (rho) with P-value and 95% Confidence Interval. Note that Passing & Bablok (1983) discourage reporting the correlation coefficient in method comparison studies. We have found that Passing & Bablok regression does not work when correlation is low; we report it not as a method-comparison statistic, but as a factor in the evaluation of the validity of the Passing-Bablok regression procedure itself.

## Graphs

### Scatter diagram and regression line

This graph displays a scatter diagram and the regression line according to Passing & Bablok (1983).

In addition to the regression line (solid line), the confidence interval for the regression line (dashed lines) and identity line (x=y, dotted line) are displayed.

### Residuals plot

Residuals are the differences between the predicted values and the observed values for the dependent variable.

The residual plot allows for the visual evaluation of the goodness of fit of the linear model. If the residuals display a certain pattern, you can expect the two variables not to have a linear relationship.

Since it is a non-parametric procedure, Passing-Bablok regression is not influenced by the presence of one or relative few outliers. Nevertheless, outliers - defined here as residuals outside the 4 SD limit - are plotted in a different color. Linnet & Boyd (2012) recommend that these measurements should not just be rejected automatically, but the reason for their presence should be scrutinized.

## 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

• CLSI (2018) Measurement procedure comparison and bias estimation using patient samples. 3rd ed. CLSI guideline EP09c. Wayne, PA: Clinical and Laboratory Standards Institute.
• Linnet K, Boyd JC (2012) Selection and analytical evaluation of methods - with statistical techniques. In Burtis CA, Ashwood ER, Bruns DE (eds). Tietz Textbook of Clinical Chemistry and Molecular Diagnostics (5th edn). Elsevier Saunders, St Louis, MO, pp. 201-228.
• 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.