# Passing-Bablok regression

Command: | Statistics Method comparison & evaluation Passing-Bablok regression |

## Description

**Passing-Bablok regression** is a linear regression procedure with no special assumptions regarding the distribution of the samples and the measurement errors (Passing & Bablok, 1983). 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.**Spearman rank correlation coefficient**: select this option to include Spearman's rank correlation coefficient in the report.**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.**Advanced**: click the Advanced button so select Advanced options for the Passing-Bablok procedure. These include the calculation of bootstrap parameters of the regression coefficients, or the calculation of expected bias at selected threshold values according to CLSI guideline EP09c (3^{rd}ed, 2018). See also Bootstrapping options.

## Results

When you have completed the dialog box, click OK 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 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.

## Scatter diagram and regression line

This graph shows the observations with the regression line (solid line), the confidence interval for the regression line (dashed lines) and identity line (x=y, dotted line):

### Extrapolation

MedCalc only shows the regression line in the range of observed values. As a rule, it is not recommended to extrapolate the regression line beyond the observed range. To allow extrapolation anyway, right-click in the graph and click **Allow extrapolation** on the context menu.

## Residuals plot

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.

## Outliers

Since it is in essence 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 in the residuals plot. Linnet & Boyd (2012) recommend that these measurements should not just be rejected automatically, but the reason for their presence should be scrutinized.

Bablok & Passing (1985) recommend that "Samples which produced deviant values should be analysed again by both methods. Any measurement value should only be termed as an outlier and be excluded from the data, if an analytical error was identified or the analyser declared the result as questionable. If the distribution of the data is known, a statistical test for detecting outliers can be used."

## Importance of sample size

When sample size is small, the width of the 95% Confidence Intervals for intercept and slope will be large, and will more likely contain the values 0, resp. 1 (see also Mayer et al, 2016). The result is that method comparison studies based on small sample sizes are biased to the conclusion that the laboratory methods are in agreement.

Therefore **a correct and large enough sample size must be used.**

Passing & Bablok W (1984) and Bablok & Passing (1985) give tables with suggested adequate sample sizes (ranging from 30 to 90). Bablok & Passing (1985) advise to have at least 30 samples. Ludbrook (2010) cites a sample size of at least 50.

## Notes

- The Passing-Bablok procedure should only be used on variables that have a linear relationship and are highly correlated.
- We advise to supplement the results of the Passing-Bablok procedure with a Bland-Altman plot.

## Literature

- Bablok W, Passing H (1985) Application of statistical procedures in analytical instrument testing. Journal of Automatic Chemistry 7:74-79.
- CLSI (2018) Measurement procedure comparison and bias estimation using patient samples. 3
^{rd}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 (5
^{th}ed). Elsevier Saunders, St Louis, MO, pp. 201-228. - Ludbrook J (2010) Linear regression analysis for comparing two measures or methods of measurement: but which regression? Clinical and Experimental Pharmacology & Physiology 37:692-699.
- Mayer B, Gaus W, Braisch U (2016) The fallacy of the Passing-Bablok-regression. Jökull Journal 66:95-106.
- 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.
- 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. J. Clin. Chem. Clin. Biochem. 22:431-445.